Various Authors-materials And Structure Of Music

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MATERIALS

AND STRUCTURE

I

OF MUSIC

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MATERIALS

AND STRUCTURE OF MUSIC

William Christ Richard DeLone

Vernon Kliewer Lewis Rowell

William Thomson Indiana University

Prentice-Hall, Inc.,

Englewood

Cliffs,

New

Jersey

©

PRENTICE-HALL, INC. Englewood Cliffs, New Jersey 1966 by

No

part of this book may be reproduced in any form, by mimeograph or any

All rights reserved.

other means, without permission in writing from the publishers.

Current printing 10

9

8

(last

7

number): 6

5

4

Library of Congress Catalog Card Number: 66-14354 Printed in the United States of America. C-56030

PRENTICE-HALL INTERNATIONAL, INC., London PRENTICE-HALL OF AUSTRALIA, PTY. LTD., Sydney PRENTICE-HALL OF CANADA, LTD., TorontO PRENTICE-HALL OF INDIA (PRIVATE) LTD., NeW Delhi PRENTICE-HALL OF JAPAN, INC., TokyO

To Nelda, Joanne, Diane, Annette, and Betty, who were so patient

^.

.•'^."

Prehace

There can be only one valid reason for writing still another book tiiat deals with the materials of music: the desire to contribute insights and techniques of learning that are fresh and that are superior to those already presented for our understanding of music. The two volumes of Materials and Structure of Music are unique in several ways: they represent the synthesis of the

know music

broad experience of

five

as composers, performers, listeners,

people

and

who

teachers;

they are an accounting of the time and pitch bases of the

music of Western Civilization, not a rechewing of the dubious "rules" of a limited body of music. Perhaps most significant is the fact that they stand as an attempt to strip away the surface peculiarities of the music of any one composer or "style"

and delve into more basic matters. In these two volumes we have attempted to accomplish two main tasks: (1) To set out in effective pedagogical order a framework of understanding for the materials and structure of music; and (2) to transmit this understanding by means of the actual music produced in the Western world.

To

achieve the

melody.

The

first

goal,

Volume

I

begins with a study of

complexities of the traditional four-part "har-

mony" work have been

deferred until step-by-step knowledge

and three-voice combinations has been introduced. In this way the learning sequence is realistically geared to student comprehension, and a true ordering from simple to complex is realized. of basic pitch organization in two-

The

format of introducing pitch association through rudi-

ments of counterpoint

in these early chapters (9-12)

is

more

akin to the traditions of sixteenth century contrapuntal teaching than to any other, for the internal

determination. Ours

is

is

the basis of pitch

not, however, a "species"

the study of tonal association;

we

feel

approach

to

that at this stage of v;;

PREFACE

VIII

learning this technique of rhythmic structuring tifying than

it

is

illuminating.

We

is

more

stul-

believe that the teaching

of counterpoint as a compositional discipline

within the domain of the composition

is

more properly

than the theory class; in the theory class the work aims more toward comprehension of music than toward demonstrable skill in writing,

work

class

only a means to the more basic and significant goal of understanding. The object of this early for the written

is

introduction to rudimentary counterpoint

is

not to provide a

rigidly disciplined course in -contrapuntal skill, but rather to

enrich the student's understanding of music.

In these two volumes the different structural elements of music, such as tonality, melody, harmony, texture, and form, are

presented as

inter-related

phenomena without unwar-

ranted emphasis upon the formulation and application of contrived principles of chord connection. Through this approach, and through

liis

own involvement with

all

of the

materials of music, the student develops a wider perspective

and a deeper understanding of its organization. To meet the second goal, an abundance of musical examples, each selected for exacting purposes of illustration, accompanies

These volumes contain more examples from before 1700 and after 1900 than any other basic theory text that is available at this time. There is an emphasis, of course, on the music of the so-called "period of common practice" which is included with the full realization the text of

Volumes

I

and

II.

of the significance of this repertoire both to the performing

and

listening musician.

Materials and Structure of Music I and // are designed for a basic music theory curriculum. It is assumed that the materials of the

two volumes and accompanying workbooks

will

be used as the basis for the entire course of study, with the supplementation of melodies for music-reading practice and at least some of the scores for works that are discussed in the texts. Each chapter is followed by suggested Exercises designed for the application of information exposed in the text. These sections contain guides for aural training, written application,

keyboard work, and sight-singing practice, thus utilizing all approaches to the understanding of subject matter presented in the text. These Exercises are minimal and are intended only as outlines of supplementary work that should be done. Both of the accompanying workbooks, however, are planned to furnish sufficient materials for a comprehensive course of

and for maximum efficiency it is highly recommended that the workbooks be utilized. The teacher should by all means plan his use of these books

study,

PREFACE

IX

meet the needs of his own class and his own academic situation. The separate volumes are planned around the thirty week academic year of a four semester course, the "freshman and sophomore theory classes." Many of the concepts and procedures presented here have been applied successfully in music programs of such diverse institutions as a state univerto

sity of

the Northwest, a southwestern teacher's college, a large

midwestern university, and an eastern private school. Some of the chapters might well be dealt with in less than a week of class time, while others conceivably should be granted more time for discussion and assimilation. The experienced teacher should encounter no difficulty in establishing a workable time sequence that will fit the texts and workbooks to the needs of his own classes. It is intended that Book I be the basis of a beginning theory program with no prerequisites other than demonstrable performance skill on an instrument and a serious interest in learning more about the nature of music. Chapter 1 of Book I is a kind of reintroduction to fundamental matters which the average music major already knows from his applied experiences.

Book

II is a logical

continuation of Book

I.

While Book

I

devoted mainly to the materials of music. Book II deals more with the organization of these materials. The subjects covered in Book II represent some departures from the conis

ventional second-year theory text. In addition to the treatment

and rhythmic concepts and materials are introduced which exceed the bounds of the "traditional." Their inclusion is essential because the student of music will not be equipped to understand the music of of musical forms, melodic, harmonic,

terminated with the materials that were typical of Bach, Mozart, Beethoven, or even \Vagner. this

century

if

his study

is

These "new" materials are introduced when possible as the extension of matters fundamental to all music. For instance, chords are built of intervals: therefore, chords can be constructed of fourths, or seconds as logically as from thirds, even

though the past four-hundred years of musical practice might lead one to assume that tertian chords are normative for

all

music.

Some

unique, and as a in

and terms used in these volumes are consequence some of the terminology is not

of the concepts

common

parlance, such as basic melody, cadcntial conso-

nance, leaning tone, tonality frame, and terminal cadence. A Glossary at the back of Book II gives definitions of important

terms that are discussed in Book

who

is

not familiar with Book

I. I,

This should aid the reader as well as the reader who,

PREFACE

though familiar with the first volume, feels the need of reviewing some of the important terms and concepts that are treated there.

approach during the final six chapters which are devoted to Impressionism and contemporary materials and procedures, a shift necessitated by the fact that the music involved represents a diversity of musical types for which no universal pattern of common practice has been developed. These final chapters are devoted to a systematic and comparative examination of significant musical resources and individual techniques both "old" and "new," with an explanation of the musical logic of each. Though no Furthermore, there

is

a shift of basic

all-embracing rationale of analysis

is

offered to elucidate all

contemporary music, techniques of analysis and points of view are explained. We wish to thank all of those who were directly helpful in the preparation of the manuscript and the compilation of musical examples. Particularly of significance was the accurate and faithful typing of Miss Alison Rivers and Mrs. Mary Cooper, and the editorial aid of our colleague. Miss Mary \Vennerstrom.

The Authors

Contents

AND NOTATION OF TONE

BASIC PROPERTIES

Basic durations and the

Characteristics of rhythm, 1 beat, 2 tion's length

Compound

Meter signatures; establishing the basic duraNotation of rhythm, 5 and grouping, 4

TONALITY

Notation of pitch, 12

Intervals, 16

19

Pitch roots, 24

Interval quality

and melodic organiza-

27

tion,

MODE, AND SCALE

KEY,

The

Subdivisions of the basic dura-

meter, 10

tion, 12

1

32

Terminology of scale deKey signatures, 40 Modulation and

diatonic scale systems, 34

39 mutation, 45

grees,

MELODIC CADENCES

50

and imperfect terminal cadences, 55 Transientterminal cadences, 56 Cadences and musical style, 58

Perfect

FORMAL CHARACTERISTICS OF MELODY: THE MOTIVE AND PHRASE 62 Motive structure, 63

6

THE EXTENDED MELODY

7

BASIC MELODY

Phrase structure, 66

76

87

Melodic terminal points, 89 Duration and metric locations, 96

8

MELODIC ELABORATION

Melodic

100 XI

contour,

92

CONTENTS

XII

9

TWO-VOICE COMBINATIONS Rhythmic

Texture, 113

113

Combimelodies; the two-voice framework, 119 of Pitch material, 124 Vertical considerations in two voices; consonance and dissonance, 127 Vocal ranges and spacing, 130 nation

70

Association, 113

basic

TWO-VO/CE COmiNATIONS: DECORATIVE 133

PITCHES

Contrapuntal motion between

Decorative pitches, 133

parts and approaches to structural intervals, 137

Con-

Sum-

trapuntal treatments of other consonances, 141

mation of principles of melodic movement and

Basic contrapuntal treatments of unOther unstable intervals, 146

succession, 143 stable intervals, 144

7 7

CONTINUATION OF TWO-VOICE COMBINATIONS Cadences, 148 154

keys,

two-voice

frame,

phrases, 162

165

148

Two-voice cadences in major and minor Other interior cadence patterns, 159

Tonal function within the phrase; root

12

intervallic

161

Organization

relations

in

the

two-voice

of

Repetitive factors in phrase organization,

Sequence, 166

CONCLUSION OF TWO-VOICE COMBINATIONS Ornamental

Suspensions, 170

170

The

resolutions, 176

change of bass resolution, 178 Other Imitation, 183 and melodic decoration: leaning tone forms of anticipation, escape tone, 186

nance, 190

7

3

Structural aspects of melodic disso-

Cross relation, 192

THREE-VOICE COMBINATIONS Rhythmic

association, 196

196

Rhythmic

association of three parts, 205

unity, 200

Pitch

Spatial distribution of

parts, 209

14

CHORD STRUCTURE Chord

Chord Chord position, 223 Melodic-harmonic synthesis, 228

succession, 219

inversion, 224

15

214

CONCLUSION OF THREE-VOICE COMBINATIONS Crossing voices, 235

Spacing, 232

and

homophonic

voices,

238

textures,

Contrapuntal

Doubling

Decorative patterns, 240

in three-voice textures, 244

suspensions, 247

235

232

in

three

Suspensions

Ornamental resolutions

of

Other forms of pitch decoration, 248

CONTENTS

XIII

16

HOMOPHONIC TEXTURES OF FOUR NON-CHORD TONES 251 Textural

considerations,

Spacing

253

Harmonic

textures, 255

VOICES.

four-voice

of

succession, 260

Contra-

Non-chord

puntal considerations (voice leading), 262 tones,

Simultaneous non-

Pedal point, 270

266

chord tones, 273

17

TONIC, DOMINANT, AND SUBDOMINANT CHORDS IN ROOT POSITION AND FIRST INVERSION: DOMINANT SEVENTH CHORD 276

The The The 281

and first inversion tonic chord, 276 root position and first inversion dominant chord, 279 root position and first inversion subdominant chord, The dominant seventh chord, 286 Harmonic position

root

cadences, 288

18

INVERSIONS OF THE DOMINANT SEVENTH:

HARMONIC RHYTHM The

The The Vt chord, 298 Harmonic rhythm—further study, 303

V* chord, 297

chord, 301

19

293

SECOND-INVERSION TRIADS The

cadential

309

it,

Passing

six-four

21

TERNARY FORM: THE SUPERTONIC CHORD

312 six-

320

chord, 326

SUBMEDIANT AND MEDIANT CHORDS:

CHORD RELATIONSHIPS

337

The submediant chord, 337 Tonal relationships

22

chords,

Other uses of

Parallel six-four chords, 317

four chords, 315

The supertonic

5

309

Embellishing six-four chords, 314

20

vii^

The mediant

chord, 343

of the diatonic triads, 351

THROUGH-COMPOSED FORM: MUTATED CHORDS, HARMONIC SEQUENCE 353 Mutated

chords:

quence, 364

and ^VI, 359 Harmonic seOther examples of harmonic parallelism, ''111

367

23

BINARY FORM

370

Baroque binary form, 373 contrasted, 379

and

trio,

381

Rounded

Binary and ternary forms binary, 379

Song form

CONTENTS

x/v

24

SECONDARY DOMINANTS Melodic

383

dominant, 385 dominant, 386 Sequential treatment of secondary dominants, 387 Secondary dominant of the dominant (V/V; V/V), 388 Approach to dominant of the dominant, 389 Resolution of dominant of the dominant, 390 Use of dominant of the dominant, 391 Dominant of subdominant, 398 Uses of dominant of the subdominant, 400

Harmonic

Dominant the

25

significance

significance

of

the

secondary

the

of

secondary

Uses of dominant

of the supertonic, 404

of

supertonic, 405

CONCLUSION OF SECONDARY DOMINANTS

411

Dominant

Uses of of medi-

dominant

of

submediant (V jvi; V/VI), 411

of the submediant, 412

Dominant

Uses of dominant of the mediIrreguant, 418 Dominant of the subtonic, 423 lar resolutions of secondary dominants, 424 Deceptive ant (V/iii; V/III), 417

Other irregular resolutions, 430

resolution, 425

Se-

quential use, 434

26

TONALITY CHANGES

439 Melodic modulation, 440

Modulation, 439

Less

tionships of keys, 445

Other

27

common

key relations, 450

aspects of tonality change, 452

PROCEDURES OF TONALITY CHANGE Modulation by tion,

Rela-

465

pix'oi

chord.

Modulation

461 Pivot tone modulaby chromatic inflection, 466

Enharmonic modulation, 469 changes, 472

461

Mutation, 478

More abrupt

tonality

There to

is

a certain marvellous order which belongs

the nature of

harmony

in general;

every instrument, to the best of

its

in

this

order

ability, participates

under the direction of that faculty of sense-perception on which they, as well as everything else in music, finally

depend. Aristoxenus,

The Harmonics, Book

II

^.Vf^l

»\

Basic Properties

7 orii

Notation of Tone

and composers, we deal with patterns of organized sound. Any pattern of musical sounds has four properties pitch, which As performers,

listeners

:

may

be described as high or low;

quality;

and

intensity,

described as loud or soft; timbre, or tone

rhythm, or tone duration. In this chapter

we

shall

review some of the

important characteristics of two of these properties, pitch and rhythm. Characteristics of

We

Rhythm

often respond to music by participating physically in

tapping our

feet,

pulse.

Rhythmic

we

are carried

pulse can be

compared

of a watch or the throbbing of a heartbeat. In a sense, rhythmic

pulsations, like heartbeats, indicate "aliveness,"

rhythm.

rhythm through

dancing, or snapping our fingers. In doing so

along by a characteristic of rhythm called to the ticking

its

We respond

easily to

pulses are not periodic,

it is

and music comes

rhythmic pulse when

more

it is

alive

through

periodic, or regular.

difficult for us to react or participate

When

through the

physical responses mentioned above.

Rhythmic

grouped (or metered) by acknowledging one of a series as a mental accent or "more important" pulse. These groupings are generally made in the form of pairs, or threes, or fours. Any grouping, however, is possible, and units of five, seven or more beats per group can be found in Western pulses (or beats) are usually

music. Beats, then, are usually regularly recurring pulsations, like the ticks of a

metronome, which have a precise speed (tempo). In the three melodies shown as Ex. 1-la, Ex. 1-lb and Ex. 1-lc, twelve periodic beats have been grouped differently: first in pairs, second in threes, and third in alternate groups of two and three. Perform the melodies at a moderate tempo (M.M. = 80 per beat) and note that it is through our acknowledgement of accented (strong) beats, as indicated below each melody, that we perceive each successive group.

2

BASIC PROPERTIES

Ex.

AND NOTATION OF TONE

1-1.

^ ^

^ w

^^

r w

S

S

w

w

^w

S

Ww

^ w

S

The accent

w

w

w

w

w

s

*

S

w

w

particular grouping of beats within a composition is

S

w

is

called meter. Metric

the impetus or inflection created by the accented pulsations of strong

Unaccented beats are called weak beats. In Ex. 1-la the ordering of beats creates the pattern strong=weak {S=w), and the pattern in Ex. 1-lb is S=w = w. The irregularity of Ex. 1-lc results from alternate groupings o£ S = w and S—w = beats.

w.

Our

perception of meter

accented beats. In

is

not limited to the recognition of accented and un-

many

fact, in

compositions our comprehension of meter results

more from the grouping of melodic pitches or chords than from the mere ordering of strong and weak beats. To understand better this aspect of rhythm and meter, us reconsider the term beat.

let

Basic Durations and the Beat

A beat

is

understood to

last until

a next beat occurs. But

if

we imagine

beats as

view one beat as continuing until the next beat occurs. However, if we regard the beat as only the beginning of a regularly recurring time span, then we can more accurately describe the total instantaneous pulsations or

time span

from one beat

ticks,

then

it is

difficult to

beginning of the next as a

until the

basic duration.

Further-

more, the various durations used in a composition can be related to the basic duration. Meter^ then, is more accurately described as an ordering of basi c durations into groups of two, three or four units per measure, or whatever pattern the composer may wish to establish. Basic duration refers to the time span from the articulation of one beat to the next, and this unit is usually represented in notation by one of the note-values shown in Ex.

Ex.

1-2.

1-2.

Basic Durational Signs (note values

Whole note

=

Sixteenth note

o

=

Half note

J)

Thirty

= J -

)

Quarter note

second note

=

^

=

J

Eighth note

Sixty -fourth note

=

J)

= ^

,

S

BASIC PROPERTIES

Pulse or

beat

AND NOTATION OF TONE

(1)"""" *)

duration («

Basic

1

i

1

1

f

f

f

f

^

by the quarter-note.

* Basic duration represented here

We have noted several processes that are involved in creating meter.

First a pulse

of a particular tempo or speed must be established.

And

beats must be organized into periodic groups, each of

which begins with a strong

second, the successive

(or mentally accented) pulse.

Meter

is

a basic kind of rhythm, the rhythm of pulse, or metric rhythm.

It is

im-

portant to note, however, that rhythm also occurs in the form of accented and

unaccented, long and short durations which organize melodies, accompaniments,

chord patterns and other parts of a musical texture. These varied patterns of duration in most melodies communicate metric organization to the listener. This can be seen in the melody of Ex. 1-3, which is shown without a meter signature. Bath

and

the distribution of long

J

IJ

J

IJ

J

J

J

short notes

and patterns of durations

IJ

IJ.

J

IJ

J

IJ

three's

u.

J

J

in

created by the pitch line, reinforce our notion of a triple meter.

As a

rule, then, the structure of

a melody (or other parts of a musical texture)

confirms the metric organization denoted by the meter signature.

l-3a. Beethoven:

Ex.

^

Symphony No.

I.

{»

(»

(>)

3,

(>)

(>)

(>)

^

t

(Theactualmetersignaturefor the melody in Ex.

1-3

f When

is I).

^

(>)

a conflict occurs

between the accents of melody or chords and the metric accents, syncopation results. By notating the melody from Ex. 1-3 in ^ meter, a conflict is created between the implicit triple meter of the melody and the metric accents {S=w) of the notated meter. This is shown in Ex. l-3b.

Ex.

l-3b. Renotation of Ex. l-3a.

S

S

(w)

w

S

Syncopation)

(

S

iB:

in

tw)

S

w

S

i (

Sync.)

(S)

w

S

w

J

J

^ %v

^

(

S

J

I

(Sync.)

S

w

S

w

^

J

J T (

Sync.)

(

1^

w

)

m

4

BASIC PROPERTIES

Other

AND NOTATION OF TONE

placement of high or low notes, or the emphasis created by the use of dynamic accents such as /or szf, or >, frequently reinforce or agree with metric accents. When they do not, syncopation results.

The

factors too, particularly the

strong beat has an importance to rhythmic structure

greater than a simple description of

is

suggests. In fact, the strong beat

is

and musical form

position in a duple or triple

its

that

measure

often a rallying point for rhythmic patterns,

phrase beginnings, or the initiation of larger musical sections. Furthermore, strong beats are important in relation to cadences, melodic decoration, and many types of harmonic progressions.

Rhythm

occurs in

many

ways. Meter

is

one form of rhythm

in that

it

involves

duration. In addition, any aspect of music that possesses duration, such as succes-

melody, the duration of a chord, the time span or the total duration of a large section of a symphonic

sions of pitches that constitute a

occupied by a clarinet

movement, levels of

solo,

creates rhythm. It

is

the coordinate activity of both large

and small

musical action that produces the total effect of rhythm in music.

Meter Signatures; Establishing the Basic Duration's Length and Grouping

The

rate at

which basic durations occur

in given meters

is

usually indicated

by

an appropriate designation such as Allegro (fast) or Adagio (slow) or other descriptive words. Since these terms, which are generally chosen from Italian, French, German or English, are not precise, composers also often assign a metronome marking. The metronome is a clock-like instrument which divides the minute into a precise number of beats ranging from thirty to two-hundred. By indicating a metronome speed, (M.M.= 120, or M.M. = 80)^ the composer can set the desired tempo accurately for performers.

The

number of basic durations per measure

is

shown

as the

upper part of the

meter

The lower part, a number such as 2, 4, or 8, represents the basic duration.'^ For example, the number 2 represents a half note; 4, a quarter note; and 8 in-

signature.

dicates that eighth notes equal the basic duration.

numbers are

1,

2, 3,

Meter signatures whose upper

or 4 are called simple meters.

The

prevailing note-values

in simple meters generally represent divisions or multiples of the basic duration

by two,

four, or eight.

The

ruple simple meters are

page

An

conductor's beat patterns for duple, triple and quad-

shown

in the

diagram of simple meters

at the top of

5.

interpretation of the meter signature

example, a

fast

simple triple measure such as

is

\,

Allegro molto,

or conducted "in one," in other words, with one

equal sub-pulses) per measure.

And

often subject to the tempo.

may be

For

interpreted

main pulsation (divided by

three

may be

per-

a duple or quadruple meter

formed "in one," or "in two." By the same token, an extremely slow simple measure may be divided into twice as many beats as are indicated by the signature, where do

to

so facilitates the performance.

1

M.M.

-

We

stands for MaelzeVs metronome. important exceptions to these statements

shall note

when we study Compound

meters.

4 4

BASIC PROPERTIES

Number

Usual

Common

Basic

AND NOTATION OF TONE

Beats

of

Duple

Triple

2

3

Measure

per

Durations

J;J;J)

Grouping of Strong (S) and weak (w) beats

Quadruple 4

J;J;J>

J;J;J)

w

S

S

w

S

w

1-^ Conducting

Patterns [3

Notation of Rhythm

Notating rhythm involves the use of the following symbols: 1) a note-head, o • that is written on the line or space of the pitch to be expressed 2) a notestem, (for all durations except whole notes) which is formed by a straight line ,

,

;

,

that joins the note-head at the

note-head on the

staffs,

J

f

,

left

a

3)

,

or right, depending

from the note-head, J

farthest point

flag,

\

which

upon the

location of the

joins the note-stem at the

or double, triple or quadruple flags, J^ J^ J^

depending on the duration desired. Flags are frequently replaced by beams, J

J

= J J

which are used

mally employ

Beamed

to join series of similar durations that

flags.

notes are associated primarily with instrumental notation, while the

use of flagged notes

is

indigenous to vocal music, where the flag

shown

tones that occur with single syllables of text, as

Ex.

1-4.

would nor-

is

used for notating

in Ex. 1-4.

Schubert: Longing for Spring.

m ^^ Mur

-

^

mur- ing

^^^^

3

^Fl^fc^

i

i

bree/.

-

"T'pL^

es

^

^^m

r

P

Soft

flow

^

p -

ing

by

,

±1

i

' If the note head is located above the third line of thestafT, its stem usually points down, or hangs below the note head. The opposite is true when the note head is written below the third line.

M>

,

BASIC PROPERTIES

Continued.

1-4.

Ex.

J'

AND NOTATION OF TONE

I

I

Sweet

>

your

are

h kiss

i

m

your

y

^^=^

5^

33^5

I

p

r Balm

es

sigh.

^r=f

m

Flags are always used for isolated notes or where single durations of an eighth

note or

are preceded or followed by quarter, half, or whole notes (or their

less

equivalent

rests).

See Ex.

1-5.

1-5.

Ex.

^ c;>^

^j^

^^

Beams help

l

pyp^py yj)|j

'' d

^

^a

m"

the reader to group note patterns according to basic durations.

group of patterns shown obscured by illogical beaming. In the

J^yyyj) »

first

in Ex.

1-6,

the location of beats has been

1-6.

Ex.

(J)

(J)

(J)

(J)

(J)

(J)

(J)

(J)

w

s In Ex. 1-7 the same patterns are

beamed

in groups that reveal the meter's beat

structure.

Ex.

1-7.

^ (J)

(J)

(J)

(J)

(J)

^

A

(J)

(J)

(J)

i

general guide for notation

is

to avoid

beaming more than

six notes together,

more are needed to consume the equivalent of one basic duration and further, beams begin on the beat unless the notes they join are preceded by a rest unless

;

sign.

.•<

T

•

i'

•>

>

.

AND NOTATION OF TONE

BASIC PROPERTIES

1-8.

Ex.

s^

MIZ

r[_rr

When

possible, avoid

i

u xLium^r

'

^

mixing flagged and beamed notes, except in notating vocal

music.

1-9.

Ex.

Better

Poor

'Pc;cp

"^r

i

r

ppbt

h 'PULs

\

r

pu^

Absence of tone is indicated by rests, and each of the basic durations discussed earlier has an equivalent rest symbol. Rest equivalents for each basic Rests.

duration are shown as Ex. 1-10.

1-10. Basic Durations

Ex.

Note value

and

their Rest

Name

Rest

-

—H-

Equivalents

-^

Breve (or double whole -note)

_Q_

Whole

1 1

Half

note

Quarter note Eighth

A 1 Rests

note

may be

note

1

Sixteenth note

I

Thirty - second note

f

Sixty -fourth note

used in the same situations as their corresponding note-values,

with the following exceptions: 1)

Rests are never tied.

2) Half-note rests are not used in J meter. 3) The whole-note rest may be used for convenience to indicate a rest in less

4)

The

any meter, except

in those

meters

in

full

which the whole note

is

measure equal to

than a complete measure's duration. notation of rests, like note values, should permit clear understanding of the

metric organization.

BASIC PROPERTIES

Ex. 1-11 clarifies the use of

Ex.

i-n.

(a)

9 4

(b)

g

-

J 7

^

rr

{r

better

J.

II

I

J.

II

J)---

better

written

I

mediately after a note-head

clearly written

^yl

II

{r

and

Ties

'

a-

),

Slurs.

J.

il

The

J)y]{

rr

augmentation dot

|

J)y I jJ)J

||

r

(

r

•

),

rr r)

placed im-

extends the duration of the note by one half of

normal duration. This means that o

tion dots are not used if they

J.

|

"^

written

rrr r)

r

J

^

I

more

J)J

Augmentation Dots,

its

rests.

I

(c)| })l J)777|

AND NOTATION OF TONE

J could also be written as

would prolong a note

into the next

J.

Augmenta-

measure

v

4

J

a-

).

In such a situation, and where a continuation of sound between two notes of the

same pitch

is

sought,

notes of

identical ical

with the

slur,

pitch:

pitch

which

AHfc

is

ties

^

are used.

j{

,

ZBt

The

tie

is

a curved line which connects two

.The

tie

should not be confused

used to indicate a smooth connection of two notes oi different

^

Ex. 1-12 illustrates several notational signs and principles of clear notating.

Ex.

1-12. Beethoven:

Sonata for Violin and Piano, Op- 23,

II.

I

BASIC

PROPEHmS AND NOTATION OF TONE

I

^

J

n

N

m

:

i=a:

^

^

^^^Ht

^

i

yt

5=fc=5

i

^

JJ^

5 iM {/:

y

j)

^^ w

^^T"

^

^^

#_^:-

^?

1

^ ?r

pSii cresc.

S

J^

? ^^^^

1

CTt?5C.

-^^

I

if.

B i^ ^?F

y

P

^f

U m^^

i* jg^^^

?

^ffi

*

= £5

^^f

W

^

1

70

BASIC PROPERTIES

AND NOTATION OF TONE

1-12. Continued.

Ex.

*^

^

decresc.

i|t^ ''

^

decresc.

S

^Ht *pt

—

«:

^

f:

fe

^^-fe^

f

i>i5

3

c

J

^ -^ J^i^l

^

5^

^

>>f!

£

VjJ^ilJ i

^i*

#

I -hiHr^

-^^^^

Compound Meter

We

common

have noted that the

divisions

in simple meters are duple. Since in a simple

tion

by three (the

triplet)

3

'

above the beam, or by

a.

not a usual one,

is

—

and multiples of the

basic duration

meter the division of the basic durait is generally shown by writing a 3

J) J) J) bracketed 3 above the stems

if

a

beam

In contrast to simple meters, triple divisions of the basic duration are

is

not used.

common

to

meters called Compound Meters.

Compound a dotted

meters, those calling for a triple division of the basic duration, have

note as

shown here:

the basic duration, as

(Common)

Basic Durations

and

in

their

Compound Meters

Normal Divisions

J.

J~7

J)-

«

«

J.

J

J

J

d

Compound

meters, like simple meters, are called duple, triple, or quadruple,

depending on the number of basic pulses per measure. The family of compound meters can be shown as

2,

3

X ing the

number

shown above

(..,

J^

J.,

signify-

.^)

of beats per measure and A' representing any of the basic durations

(as

dotted notes).

Meter signatures for

primary)

with the upper numbers

or 4

division

compound time

are actually representations of the

of the basic duration, rather than the

number of main

basic duration, as in simple meter signatures. For example, a

first

pulses

(or

and

common compound

BASIC PROPERTIES

AND NOTATION OF TONE

II

meter signature is |. This signature would seem to denote a meter of six basic durations per measure, each of whose value equaled the eighth note. While such an interpretation can be made, it does not present an accurate picture of general performance practice and rhythmic interpretation. This is true because in most

acknowledge two, not

instances, except in very slow tempi, performers

pulses in

meter, with each basic duration as J-

|

,

(or

note as a division of the main pulse (basic duration). and note the analysis of its rhythm shown below.

its

equivalent)

Read

six,

main

and the eighth

the melody that follows

1-13.

Ex.

Note the

essential

grouping of each measure into two main pulses (duple). The

and are in fact a division of the Only those eighths that fall as the first or fourth (eighths) of a measure correspond with the main accentual bases of the measure. It can be seen that the signature |, which accounts for the total num-

eighth notes divide each basic duration by three basic beat rather than a primary level of accent.

ber of eighths that occur in a measure of

|

meter, actually refers to a grouping that

from dividing each basic duration by three, thereby producing a total of six eighths (or their equivalent). Six-eight meter could be more effectively shown as 2, and has been by some composers. results

f we apply the same reasoning to other compound meters we note that | is triple compound meter, easily grasped as 3, and g is a quadruple meter underIf

a

n IH!

stood as

Any

4.

dotted note can serve as the basic duration for a

compound

r The most common compound meter

signatures are grouped below:

J.= basic duration 6

Uf)

8 if) h—

if)

r

6

'iif)

basic duration

9 4

12

})

4

f)

16

=

2^

basic duration

'il)

16 Vp-/

'HI-) 16 \p

meter.

:

12

BASIC PROPERTIES

AND NOTATION OF TONE

Sub-divisions of the Basic Duration

Although the primary division of the main pulse the sub-divisions of the basic duration, that

triple,

is,

in

compound time

divisions of the

is

usually

primary

divi-

sion, are generally duple. Triple sub-divisions regular,

of the basic duration are called iras are triple divisions of the beat in simple meter. The first four measures of

the melody in Ex. 1-14 contain regular (duple) sub-divisions of the basic duration, while the second four measures illustrate both regular and irregular sub-divisions.

An

analysis of the

rhythmic content of the example shows

basic duration =

primary division =

J-

regular sub-division — J J J J J J J J J J irregular sub-division =

J

J

J

j5

JT2 JT^ fH J72 JT2 J^

1-14.

Ex.

Moderate

^m. 3

J

/»!

1

3

i

J ^ ** J * J

$

X i

-

^

Notation of Pitch

from the sustained, periodic vibrations of a flexible body such as a string, a column of air, or a vocal cord. Pitch is indicated by symbols, most familiarly the first seven letters of the alphabet, a b c d efand g. These letter-names represent Pitch results

the different lines

By

itself

and spaces on the

the musical staff

meaningless. However, by placing a clef sign at

edge, a specific letter-named pitch

left

treble clef

sign

is

$

G

that designates the pitch g^

in

The

on the

the treble clef.

~9

B

For example, the tone that is known as a^

(v.p.s.)

designated for each line and space.

its

staff.

1-15. Notes on the staff

Ex.

is

actually an elaborate script

second line of the

*

is

five-line staff:**

D

results

D

^ C

from a vibration rate (frequency) of 440 vibrations per second

BASIC PROPERTIES

The

Ex.

bass clef specifies the

Notes on the

1-16.

13

AND NOTATION OF TONE

note/ for the fourth

staff

in

line of the staff.

the bass clef.

FGABCFEDCBAGFE The

question

may

more than one clef. If our musical pitches, there would be no such need. How-

need

arise as to the

system were limited to only seven or so

for

ever, the capabilities of hearing are such that a

used in most Western music.

broad range of pitches has been are used, each em-

Consequently, a number of clefs

ployed to represent pitches in particular areas of the pitch spectrum, or gamut. The gamut of pitches most used in music is shown in Ex. 1-17, which illustrates the "Great"

Ex.

staff.

1-17.

4..

n

jLU

r>

The mid-point broken

f^

p

-2g

of this

which

staff,

line that represents

middle

either staff are called ledger

lines,

and bass clefs, is a segments line above or below

joins or links the treble c,

or

c^.

Added

and they are used

to notate pitches

which

lie

beyond the staff area of a particular clef. Although the treble and bass clefs are most used, other clefs are needed for the notation of some music. They are known as "movable clefs," or as the "family of

74

BASIC PROPERTIES

Using these

c clefs."

Four

c clefs

are

possible to assign

c clefs, it is

shown

middle

c

AND NOTATION OF TONE

any

to

line of the staff.

in Ex. 1-18.^

1-18.

Ex.

Tenor

Alto

Mezzo soprano

Soprano

i

t

Musicians have developed a useful terminology for pinpointing the various pitches of the gamut. This

amounts

to

grouping the pitches of the pitch spectrum Each segment begins with a

into seven-note segments, called "octave segments."

C and

includes

all

possible pitches

C and the B seven notes above. With lowest C [CC) on the piano, AAA and BBB

between

the addition of the two tones below the

segment called "Sub-contra"), the different seven-tone segments are named Contra (CC-BB), Great (C-B), small {c-b), prime or 1 (c' or c^ b' or b^), b" or b^), triple prime or 3 (c'" or c^— b'" or b^), double prime or 2 (c" or c^ (the partial

— quadruple prime or 4 (c"" or —b"" or c'*

the five prime segment, c'"", or

c^.

—

The

b*).

highest note on the piano begins

This nomenclature

is

illustrated in notation as

Ex. 1-19.

1-19.

Ex.

The seven-tone segments of the pitch spectrum. c4- b4

;2. b2 ;1.

bl

^

c5

5 — — — I — I

-»'

TT"

*

middle c

o

P

331 J

c-b

^ ^ ^

C-B

Small

Great

J AAA -BBB ^CC-BB

Sub-contra Contra

Accidentals.

Sharps

(

ff

)

or

flats

Any of the (

|>

),

notes of the

double sharps (x

gamut may be preceded by accidentals. ),

or double

flats

(

b b

)

are placed im-

mediately before the note head and indicate slight pitch modifications. Sharps inmost often found are those that place c^ on the third and fourth lines of the staff. These are the alto and tenor clefs, and they are used for the notation of parts for alto and tenor instruments (or voices) such as the viola, cello, and trombone. ^

The two

c clefs

BASIC PROPERTIES

AND NOTATION OF TONE

dicate a raising of the natural note

natural note

is

to

raising of the note

by two

by one

half-step, while flats indicate that the

be lowered a half-step. Similarly, double sharps indicate a

by two

half-steps,

and double

flats

are used to lower the note

half-steps.

Natural signs accidentals

Ex.

15

(

J]

)

are used to cancel previous sharps or

may be found

in Ex.

flats.

Proper use of

all

1-20.

1-20.

When measure

accidentals are used, they are understood to continue throughout the in

which they appear without being rewritten. Therefore,

all

of the/'s

that recur in Ex. 1-21 should be performed as/' sharps.

Ex.

1-21.

')^v'r»rrr

Furthermore, accidentals govern only those level at

The

Ex.

which they are introduced; they do not

result of the passage in Ex.

1

-22(a)

is

notes

^m

clarified in version b.

(b)

^

occur

on

the

pitch

affect pitches in different octaves.

1-22 (a)

that

i=F

)

»

^^^^a\

BASIC PROPERTIES

16

AND NOTATION OF TONE

Intervals

An

Numbers are used names encompassed by any two pitches. Thus a fourth denotes an interval that spans four different letter names of the staff; for example, c' up tof spans four letter names, c' d' e and/', and a down to e spans four letter names, a' g' and e' Intervals may be described as melodic, which means successively sounded tones, or harmonic, which means sounded tointerval

is

the spatial relation or gap between two pitches.

to describe the total

number of

letter

f

.

gether.

Who/e and Half Sfeps. The half step is the smallest difference of pitch commonly employed in Western music. The half step interval is easily observed by locating those white keys on the piano that have no intervening black keys. The relation between these pairs of keys, e-f and b-c is called a half step^, a minor second (m2), or semitone. The relation between pairs of white keys separated by black keys comprises a whole step, or major second (M2). Thus although the numerical name of an interval describes the number of different lines and spaces spanned, and this is easily relatable to the positions of two pitches on the staff, it does not account for the exact size of the interval. This can be checked by comparing the sound and total number of whole and half-steps in each of the following

intervals,

^

both of which are fourths: •i

(2) ^*^(i) The first of these two intervals is one half step smaller than the second, since it consists of a total of two whole steps and one half (or five half steps), while the second interval spans three whole steps (or six semitones). To describe intervals

more

/

1

accurately, musicians use the terms perfect, major, minor, augmented

minished.

The

abbreviations for these are

and

di-

shown below:

Perfect-

Major- -M minor— -m Augmented-

-Aor( + )

d or Doubly Augmented Doubly diminished

diminished

The term

perfect

is

(o) .\.\

or

dd or

(

++

(oo)

applied only to unisons (primes), fourths,

fifths

and

octaves,

while the words major and minor are applied only to seconds, thirds, sixths and sevenths. Augmented

and

diminished are applied to certain modifications of

any type

of interval. As a synopsis of the preceding discussion, the following chart

may

prove useful for reference.

The half step from e'f is more accurately called a diatonic half-step, which means that different note names are employed in its notation. These same pitches in other instances may be notated as e' and e' sharp. This notation differentiation calls for using another name, chromatic half step, for a relationship that is identical in sound to that of e' and/'. By placing sharps or flats in front of notes on the staflP, their pitch is raised or lowered by one chromatic half step. The various available pitches of our musical gamut can be notated different ways, that is, spelled enharmonically, and ournotational practices are usually determined by specific musical contexts, as we shall note in Chapters 3-8. *

;

BASIC PROPERTIES

;

AND NOTATION OF TONE Major

Octave (8^'') Unison (prime)

Seventh

Seventh

Sixth

Sixth

Fifth

Third Second

Third Second

chromatic half

Intervals

Enlarged by

Enlarged by ^/g step* becomes augmented Reduced by ^/^ step becomes diminished;

Two

Minor

Perfect Intervals

Fourth

* All

17

^/g

step

becomes augmented Reduced by ^/g step becomes minor;

Intervals

Enlarged by

^/g

step

becomes major; Reduced by ^/g step becomes diminished:

steps.

any interval. First a generic classification must be made, based on the number of letter names spanned. This is easily done by noting the relative positions of two notes in terms of lines and /or spaces on the staff. These are illustrated in Ex. 1-23. processes are necessary for the precise identification of

1-23.

Ex.

m

=^

^

33: ^cn

or

II

-O-

jCH

~rr^

331

33:

-e-

331

5th£

33:

-e-

JOZ

8thj

7ths

6ths

-o-

TT-

zaz

jcr

jOT =ai

-e-

331

4ths

3rds

2nds

3x:

xn

3

8

Note that seconds are notated on adjacent lines and spaces; thirds span two lines or two spaces; fourths span two lines and a space or two spaces and a line; fifths span three lines or three spaces; sixths span three spaces and a line or three lines and a space; sevenths span four lines or four spaces; and octaves span four lines and a space or four spaces and a line. Having determined the generic classification of an interval (as shown in Ex. 123), a more precise description, such a.s perfect, major, minor, augmented, or diminished, can be made on the basis of the number of whole and half steps involved. This is illustrated in Ex. 1-24.

Ex.

1-24.

Major and minor 33:

33:

M2=l

m2:

H

tT

M3 = 2

33:

m3 — lH

33:

M6 = 4Hor m6 = 3 P5 plus

1

whole steps

plus 2

halfs or

P5 plus

I

H

331

M7 = 5l^or P8 minus

V^

2!/2

plus 3, or

m7-2\i P8 minus

plus 1

2H

or

.

.

BASIC PROPERTIES

78

Ex.

AND NOTATION OF TONE

1-24. Continued.

Perfect IXC

331

e

-o

P4

Unison or Perfect Prime

=

P5

2 Vo

=

3

H

P8=5

whole -steps two half steps

plus

Tritones (TT)

tmr Xt: + 4

3X:

=3

o5 = 2 whole -steps plus 2 half steps

whole steps

Exercises

Additional materials are contained in Materials and Structure of Music 1

2.

Practice drawing treble Identify the small,

3.

4.

1, 2,

names etc.) of

and bass

Workbook, Chapter

1

clef signs.

of notes written in both

clefs,

indicating the specific octave (contra,

each note.

Locate the different note and

Name

I,

rest

symbols in a composition.

the equivalents of different notes in smaller denominations of note values. For

example,

how many

sixteenths equal a dotted half note?

beamed

5.

Correctly rebeam patterns of incorrectly

6.

Transcribe a vocal melody of many individually flagged notes into correct instrumental

notes.

notation. 7.

Identify the notes that occur in each part

8.

Use Ex. 1-11-1-17

9.

Compose

on successive strong beats

in Ex. 1-1.

for interval identification.

eight measures of

rhythm

in

2

nieter, trying to avoid the repetition of

any

measure's pattern. 10.

Make

11.

Play any note on the piano (within your voice range) and sing fourths above and below the note played. Apply the same procedure to the practice of other intervals.

12.

1-1.

Write the following intervals above and below

g^:

+6, m3, M2, p8, "5, M6, "7, M7, +8, mlO, +4. Transcribe Example 1-14 into j^g and ^ meters. p5,

13.

a neat copy of Ex.

M3, m7,

04,

Tonality

In Chapter

1

2

our discussion of meter showed that music can be

grouped into regular units of time, or "metered." In this sense the patterns of weak and strong beats form a framework within which groups of tones are organized into rhythms. The total range of pitches we use in music can be ordered in a similar way within still another kind of framework, in this case called tonality. If music were made from only one continuously repeated pitch, the need for such an organizing scheme would not arise; melody would derive its charm from rhythmic play alone. In fact, some very simple music does incorporate a relatively limited set of pitches, thus reducing its attraction primarily to rhythmic motion. The two very primitive melodies of Ex. 2-1 illustrate such a narrow choice of pitch ingredients.

Ex.

2-1.

Taulipang melody (after Hornbostel). From Curt Sachs, The Rise of Music W. W. Norton & Company, Inc. Ancient World, New York

the

in

:

i_/0 IJ J JrJ

Ex.

2-2.

JIl

r

r

r

New

York: W. W. Norton & Company,

r-^ u

u

clear that in each of these melodies one pitch

melody

1, f

in

"^^""X Rise

i:

^

of

Music

in

the

Inc.

r^

emphasized so extensively becomes a point qf^focus^around which the

melody 2) that it other pitches are more or less decorative. Just {a in

ff** *

Vitoto Indian melody (after Bose). From Curt Sachs, The

Ancient World,

It is

J^J^

jo:

is

as all the dots in Ex. 2-3 point to the 19

20

TONALITY

last

dot to the right,

all

pitches in these simple melodies converge toward one point

of focus; in music, this point of focus

is

called the

tonic,

or center of tonality.

2-3.

Ex.

In the melody of Ex. 2-1 the pitch a is stressed, for it is both the beginning and ending pitch, as well as the pitch of longest duration. The numerous g-sharps clearly perform a more decorative role as pitch filigrees related to their more basic neighbors, the

The melody first

and

last,

a's.

of Ex. 2-2

and

is

organized with

c

heard more often than

it is

as its

its

tonic, or focal pitch.

two

associates, b

and

C is

a.

heard

In other

dwelt upon as a kind of ho me ba se^ a frequent point of departure and return during the course of the melodic unfolding.

words,

c is

These examples are simpler in structure than the melodies that we associate with our Western musical heritage. By our melodic standards they are a bit dull in terms of pitch resources, and they move within a pitch range that is narrowly restricted. (The wider melody of Ex. 2-2 covers a span of only a minor third, a' c".) Nonetheless, the more complicated melodies of our own musical tradition reveal identical principles of organization. Note the repetitions and emphases (in time and pitch) that are partial causes of the respective tonics of the melodies in

—

Ex. 2-4.

Ex.

2-4a.

German

folksong.

^

i=i

i Ex. 2-4b. Irish folksong.

^

3

21

TONALITY

Ex.

2-4c.

Gregorian Chant

The melodic

:

Responsorium, Libera me

(first

two phrases).

excerpt of Ex. 2-5 begins and ends with the same pitch, /'. But

unlike the simpler melodies of Ex. 2-1, 2-2, and 2-3, this its first

and

last

melody does not confirm

pitch by frequent repetitions, nor does the tonic have excessively

greater durations than other pitches.

And

yet, the

melody does not require a

full

playing to convince us that/ is the tonic pitch.

Ex. 2-5.

Mozart: Sonata No. 12

in

F,

(K.

332),

I.

i ^3

JH

^''i'^^

^ i

r

1

^

This leads us to the conclusion that something about tones in a melody, in addition to accents or durations or position as

first

or

last,

pitch-focus in melody. This further source of tonality

can create

lies in

this

element of

the interval relations

between the tones of a melody. In their movement in time, the various pitches create a tonal frame work, a kind of "flooiL2Xld_ceiling," within which the melodic parts will all sound as related elements of the tonal design. Sorne^itches are basic to this framework like the beams of a house, while others are more important as the decorative overlay.

In the Mozart melody of Ex. 2-5 the longer and metrically stressed notes seem more important to the overall contour of the whole melody. The first pitch, /', is the beginning of the melodic pattern;

it

performs the

vital function of

"leading the

Here the composer's problem is similar to that of the painter who wishes to compose an effective picture both must immediately attract the attention of an audience and, at the same time, ensure that listener" into the melodic organization.

:

this first attraction is the

To

beginning of comprehension.

achieve this immediate goal the painter usually organizes his canvas into

forms that "point" to the focal areas of interest. Regardless of which area of the painting we look at first, we are always led back (if it is a good painting) into the picture-plane by the formal arrangements of lines illustration of this attention-focusing

and forms and

colors.

A clear

can be seen in the reproduction shown in

Ex. 2-6 and the analysis of linear forces that reveals this painting's main linear scheme of organization.

22 Ex.

lOUAlHY 2-6.

The Last Supper, Leonardo da Vinci

DIRECTIONAL FORCES OF MAIN LINES

:>i'

—

23

ONALITY

The composer

ushers the listener into a suitable framework of pitch reference

he "auditory picture-plane"

— by

beginning

his

melodies with patterns that

Melodies that begin with a downbeat pattern most frequently )egin with the tonic, while melodies that begin with an up-beat figure frequently )egin with some other pitch, but move to the tonic without delay, often on the first stablish a tonality.

aetric accent.

Regardless irst

of the relation

of the

few pitches usually make clear

all

first

pitch to the melody's tonality,

the

framework that

will

or a part of the pitch

erve as a basis for the remainder of the melody.

;x.

2-7a. National Anthem.

m (a)

EI

f

f X.

2-7b. Comin'

P

Round the Mountain.

I

#J.#

X.

2-7c.

Italian

folksong

c)

The las

idea of a pitch framework within which the tones of a

still

another

facet.

Notice that the metric

stress

we

melody are organized

associate with thef^ of meas-

Mozart melody (Ex. 2-8) invites us to accept this pitch as an important )oint of arrival within the whole melody. It acts as the basic high point of melodic notion. Though actually higher, the g^ of measure 3 is rhythmically less forceful md thus sounds like a mere upper neighbor to the more important/^ that arrives n measure 5. ire 5

Ex.

of the

2-8.

Mozart: Piano Sonata No.

12, (K.

332),

I.

24

TONALITY

The pitchy forms Mozart melody returns to

its

is

the bottom of the pitch framework of this melody,

essentially a pitch line that forms a

original point of departure. Its

and

so the

path from/' up tof^, then

framework of activity

is

^

t

/ assumes

an important function within this succession of tones. This particular framework, combined as it is with f as the first and last pitches of the melody, creates a tonality that unmistakably bears f as its tonic. We shall refer to this relationship, formed by the tonic and the highest and lowest For

this

reason alone,

structural pitches of a melody, as the tonality frame

.

Pitch Roots

Within a melody certain special groupings of pitches can confirm or deny a particular pitch as tonic. Just as the words "I am going home" take on a quite dif-

meaning when rearranged to the order "Am I going home?" so the tonality of a melody is afifected by the way in which pitches follow one another and by the rhythms they form. Although both melody (a) and (b) below contain the same pitch materials, they represent different "tonal meanings" because they are organized in ways which make C the tonic for the first melody, F the tonic for the

ferent

second.

Ex. 2-9a.

Pitch material

Melody "a"

Melody

The

I

^e^

o-

o

^^^

f3^

-•p

#

^>

^ IZZ

particular intervals formed between pitches sounded in succession produce

qualitative effects that influence tonal organization.

The

octave has the unusual quality of sounding like the same pitch duplicated

at different high-low levels. It

is

this peculiar effect that leads us to

repeat note

25

TONALITY

names of tones at every octave of the musical staff, so that the thirteenth note of any series always has the same name as the first. For instance, if at the piano we begin with any key and play every successive white and black key, the thirteenth key will always have the same note name as the beginning key.

Ex. 2-9b. Octaves.

Other

intervals share this quality of pitch identity in lesser degrees than the

octave; the octave

is

the only interval to bear notes of the

representation of the decreasing mutual identity of pitches or harmonic

series._

and

process,

struments.

it

A

same name. found

clear

in the ove rtone

This natural order of pitches functions as a part of our hearing

operates as a part of the tone production of almost

When we

characteristic, for the

hear a tone,

"tone"

is

we

actually recognize only

in reality a

obvious features of

its

its

all

musical in-

most prominent

complex sound pattern composed of

we hear only

several different elements. In a sense,

A

is

a generalized

tone, for

the

less

constitution escape our attention.^

tone D, for example,

when played on most musical

instruments,

is

really

only the most prominent part of a scheme of pitches that follows the pattern of overtones illustrated in Ex. 2-10, the natural harmonic

2-10.

Ex.

Harmonic

series

above

series.

D.

^1>¥^ I

S TJ

1

Fewer or more parts (or partials, as these accompanying sounds are called) are present in the make-up of a tone, depending upon what instrument produced it. A violin normally produces a tone that contains more partials above its fundamental pitch than a saxophone or a flute. But the pattern is duplicated in a greater or lesser fashion by any musical instrument,^ and except for unusual cases, we re'

With training one can learn

pitch than the note by which *

Only pure

to recognize

we name

some of

these other parts of a tone that lie higher in

it.

tones contain one simple pitch element,

and they are quite rare

in music.

—

26

TONALITY

cognize only the lowest (or fundamental) as

members

the pitch

of the tone. These additional

of the harmonic series affect the qualitative aspects of instrumental and

vocal tone, controlling the

tone color

or timbre by their presence or absence

and

rela-

tive strength.

This pattern of pitch relations represented in the harmonic series is imposed upon our every experience of musical tone, and its particular formation (the way the various parts are ordered in relation to one another) has

many

interesting

world of sound. The harmonic series of a single tone is itself a kind of "pitch framework," for the fundamental member of the series serves as a nucleus,

parallels in the

or

tonic, for all

of its accompanying parts.

we impose

In listening,

to tonal organization.

and, in so doing,

the structure of the harmonic series as one kind of guide

That

we have

is,

we mentally gauge

the jumble of incoming sounds

recourse to the patterns that are intrinsic to tones them-

harmonic series. We have already noted the unique quality of the octave, the way its separate parts fit together in a relationship that suggests a mutual identity; for this reason the t^v•o parts even bear identical note names. The second interval that occurs "in the harmonic series after the octave, the perfect fifth, shares this mutual identity of its parts to a lesser degree. It is not difficult to hear this interval as two separate pitches, even when played simultaneously. But next to the octave, the fifth is the simplest of all pitch relationships. It is not so simple as to sound like a single tone, but it is simple enough to create a strong effect of tonal focus, this quality causing its lower tone to act as the fundamental pitch of the interval. selves, the relations of the

2-1

Ex.

1.

Pitch

roots.

(a)

(c) (Ty

^

E

The

first five

? Root

Root

partials of the

harmonic

series create five different intervals, in-

cluding the perfect octave and the perfect

2-12. First five partials

Ex.

fifth.

intervals.

M.^

fl

m

and

Root

"^

p.5.r ^^ [^

-

J

^M.G

8'ca

Since the fundamental pitch of the harmonic series

whole pattern,

the root pitch

for any one of

is

the focal point for the

these intervals is the

fundamental pitch of

its

27

TONALITY

series.

This means that

we tend

context,

if

we hear one

of these intervals apart from any extraneous

to regard the fundamental of the series

which the interval belongs as

to

melodic (successive) or harmonic (simultaneous), each of these intervals implies a root that can operate in melody. When

Whether the

the interval's root.

interval

combined with rhythms, these

is

interval relations create a pitch

framework of

melodic organization.

The perties.

intervals in Ex. 2-13 are

arranged

according to their

Note that turning each interval upside down produces

plement: the inversion of the perfect the major third third.

in pairs

is

its

is

also revealed in the

com-

inversion

the perfect fourth; the inversion of

the minor sixth; and the inversion of the major sixth

This similarity

pairs shares with

fifth is

its

inversion pro-

common

the minor

is

root that each interval of the

inversion.

This root property of musical tones can best be illustrated by separating each of the five elementary intervals

Ex.

and showing

their separate root effects.

2-13. Interval roots. inr\

Root

Root

Root

xnt*t

:2±

FTT

to-

^

L-e-

^f-

£>

Root

Root

Root

Root

Root

rn t-o-

C8

i

[8

or

i

We should remember that this root effect operates with more force for the octave, the perfect

fifth,

and the

the harmonic series

perfect fourth than for

itself

is

any other

intervals.

Implied within

a dwindling relationship to a fundamental pitch; the

higher in the series an interval appears for the

first

time, the

weaker

is

its

root

above the fifth partial become increasingly negligible. For this reason, melodies that span a range of less than a perfect fifth or perfect fourth rely most heavily upon rhythmic details (such as repetition, duration, and accent) to produce an effect of pitch focus. As can be seen in Ex. 2-13, even the major sixth and minor third are subject to two possible root analyses, depending upon their position within a group of tones. As isolated intervals, the first root possibility is more probable, but in a musical context, melodic emphasis on the upper tone of the major sixth or on the lower tone of the minor third can impart to those tones a significance that outweighs effect.

The

roots of intervals that

lie

their effect alone.

Interval Quality

Mozart excerpt of Ex. the importance ofyas the tonic.

Returning reasons for

Ex. 2-14.

and Melodic Organization

to the

Mozart: Sonata No. 12

^ ^^

in

F,

^

(K.

2-5 (page 21),

332),

I.

we can now

see other

—

28

TONALITY

From its first skip, this melody traces a pattern that reinforces / as tonic; each new tone of the entire first two measures confirms this relationship to / as root tone.

Ex. 2-15.

Analyses of Ex. 2-14.

P.

5

M.3

M.3

These inner relationships within the pitch framework of/' c^ pre-establish the basis for this melody's pitch organization. After the first two bars any digressions (such as the b-Jlats and e's of measures 3 and 4) are heard as subservient in their relations to f as tonic. And then the return of/ in the seventh measure is like the closing of a full circle, for it comes as the return and reconfirmation of the fundamental pitch from which the melody originated. Other melodies reveal these same characteristics of pitch organization to lesser or greater degrees. The relative simplicity or complexity of any melody is determined to a great extent by the clarity with which the various pitches have been organized in relation to a tonic. Some simple songs of widespread use hymns, communal songs, children's play chants and the like are even more tenacious than the Mozart example in their adherence to a tonic. (Sing through the first six measures of America for such a sample.) More complicated melodies are comparatively vague as pitch organizations around a tonic, avoiding rhythm and pitch patterns that could confirm and intensify the focal role of any single pitch. Sing or play through the melodies of Ex. 2-16 as samples of this less definite kind of pitch organization in melody.

—

—

Ex. 2-16a.

Theme and Four Variations. (C) 1947 by Reprinted by permission.

Hindemith

:

B.

Schott's Soehne, Mainz.

(tonic?)

^

i^iJ-

^F

»r

iTCrP

^P

pitch frame

Ex. 2-16b.

m ..if,i

Bach: Well-tempered Clavier

]

l

I,

Fugue XXI

in

B-flat

J1^jJ1 J^SClLi^ l

Major.

g

29

TONALITY

Mozart: Piano Sonata

2-16c.

Ex.

^^ Melody

Major, K. 282.

E-flat

gf

p of Ex. 2-16

(a)

in

is

or

g/

i

ambiguous because no pitch

of focus for the whole melody. After the

initial

is

emphasis of

W'

^'r

Efr

singled out as a point c

(by repetition at the

octave with the fifth-fourth forming g in between), no pattern confirms this opening tonic.

Melody

(b) contains a different

problem, for here

it is

possible to find

two plausi-

The numerous soundings of/ draw our attention to it as a possible reference pitch, but b-Jlat is also very much in evidence. B-JIat is the intended tonality (we know this because of what happens in the remainder of the ble tonics,

or f.

b-JIat

piece), but the patterns of the this pitch as

Melody focus. Is

there

first

few measures are not decisive in establishing

a tonic.

it b-Jlat

would be

some question about the pitch of Heard with the accompaniment provided by Mozart

similar to (b), for again there

(c) is

or

is it e-Jiat?

little

out of context,

question, for e-fat predominates within the

this short

the perfect fourths,

b-flat'

e-fat^

cannot convince us that

Once we have heard

much

easier for us to

as

tonic.

its

Many

first

measure. But

passage dwells upon b-fat to such an extent that even

—

only with the entrance o^ a-fiat in the ble possibility.

is

last

pattern that

e-fat

b-flat is

is

made

the tonic. It

is

a very negligi-

melody through measures 3 and 4 it is hear the beginning notes within a framework that has e-flat this

other melodies, like the Mozart melody of Ex. 2- 16c, do not by them-

selves create

an altogether clear

tonality.

with a chordal accompaniment that

Such patterns are normally associated

fulfills,

with the melody, the

total pitch

Such melodies usually make clear a focal pitch at some point within their courses, but often only at the end or at some location well within their interior structure. So even without the chordal accompaniment, once we have become familiar with these tunes we do not have to hear their total span to realize their orientation.

pitch orientation.

When

rhythmic and intervallic emphasis of a particular pitch are combined in

melody, a sense of organization

results

where

aimless,

random

successions of tones

might otherwise prevail. The effect can be engaging, for musical tone by itself can be an object of beauty, but the whole might add up to nothing that reveals a scheme of organization

:

the compositional technique in such a case does not

form. Tonality provides this organizational basis for

all

communicate

of the pitches that comprise

man's range of hearing. When we sing, play, or listen to music, tonality is one of the most important form-giving elements, helping us to orient our tonal "thoughts" into comprehensible images. We shall learn about other agents of musical organization as our study progresses, but of all those pertinent to the musical experience, tonality is most intrinsic to musical tone.

)

30

We

TONALITY

can

isolate four simple questions that are

tonal organization of a melody.

with the answers 1

2)

to

The study

What is the last pitch, and what is the first pitch of rhythmic importance (because of metric position or greater duration or both)? Is

any

single pitch

What their

4)

of any particular melody should begin

each of these questions.

made prominent because

several repetitions, or because of 3)

important to any decision about

What

its

intervals occur during the first

common is

of

its

frequent occurrence, or

its

and stresses? patterns of pitch motion, and what

relatively greater durations

or most emphasized root,

if

is

any?

and what is the highest pitch of the whole melody or its and what is the interval relationship between these and any important because of reasons covered in items 1, 2, and 3 above?

the lowest

several parts,

pitch that

Many melodies

is

incorporate at least three schemes for establishing a tonic, others

no more than two, and

still

others

commandeer every

a single tone as the focus of pitch organization.

It

is

available force to establish

the basic problem of the per-

former and the listener to recognize the various clues of pitch organization and then allow the conclusions to serve as guides to musical understanding. Three melodies of simple pitch structure are shown below, each accompanied by

its

tonality frame.

Ex. 2-1 7a. Pergolesi

ii

p^ip? c;T7[; ^r i

cj

i

^#

rr cp^'

^

Tonali^y frame

J^

J

i

J

ns

A Tonic

Ex. 2-17b.

Hungarian folksong.

Tonality frame

;z=^

*r

Tonic

i

:: :

:

TONALITY

Ex. 2-1 7c.

m

-zl

31

Scotch folksong.

—m

m m

-P

Pr

i

r

^r If

r

r

r

s:

i

i

^ Tonality frame

P

^

^

flf

I? '

Tonic

Exercises

See Chapter 2 of Materials and 1

.

Structure of

I,

Workbook for more detailed work.

Using only the given prescription, write a short melody that

A) Tonality, F Meter, :

Tonality,

A

C) Tonality,

E

B)

:

Meter,

flat:

E) Tonality,

C

:

I

Pitches

:

C

Pitches

:

Meter,

D) Tonality, D: Meter,

2.

Music

Meter,

2; Pitches

|: Pitches:

|

:

Pitches

fulfills

each of the following

^^

^ m § h

'

3

A) Find five melodies which exhibit a tonality frame of an octave, tonic to tonic. B) Find five melodies which exhibit a tonality frame of an octave, dominant to dominant. C) Find five melodies which exhibit a tonality frame of only a dominant.

3.

fifth,

from tonic

to

At random, choose relatively simple melodies from a sight-singing collection. Analyze each melody for tonality frame and the relations (step or skip) of all other pitches within the melody to that frame. Then sing the melody.

Key,

3

Mode, ani

Scale

Closely related to the tonality framework discussed in Chapter 2 are the key systems

and

Although pitch focus can be ways, the music of Western tradition has

scales of traditional music.

produced with tones in many different developed its own characteristic methods.

We

commonly speak

C

major" or "in the key of B-flat minor." In such statements we establish a relationship between particular pitches of focus (C and B-flat respectively) and particular patterns of notes (major and minor scales). In other words, key combines the factors of tonic and scale. Many different kinds of scales can be abstracted from music: There are "Hungarian Scales," pentatonic scales, whole-tone scales, chromatic scales, gapped scales, symmetrical scales, and so on, each of which has a unique combination of notes that sets it off from any other. Aiiy one of these scales is nothing more than a particular ordering of notes that can form the basis for the pitch patterns of of a composition as being "in the key of

music. If 2-5),

we

extract

all

of the notes from the Mozart melody quoted in Chapter 2 (Ex.

then order them in succession following the tonic pitch of the melody (F),

the result pitches

is

the scale

that serves as the pitch basis for this melody;

which are used

to

fill

in the span

between the outer

it

represents the

limits of the tonality

frame, /^ tof^.

Ex. 3-1.

Mozart: Sonata No. 12

zn

in

F,

f i

(K.

332),

I.

zn

? 32

s 3t

—

MODE. AND SCALE

KEY,

33

Pitch scale

The Any 1,1,

-e-

result of this abstraction

is

what we

series of pitches that duplicates the

^/a,

1,

1,

1, ^/2

—

is

a major scale. (The

The

represents a half step.)

which are major,

five

call the major scale

same pattern of

number

1

-'^'

k^

successive intervals

represents a whole step,

which are

not.

,qIxJQ^

^tiCjil

^^'/

X'CuXiiLf

JUcdL<^

l>o -

^E f

ly

^/a

note combinations of Ex. 3-2 cojntain five pat,terns

3-2.

Ex.

DnU^ KhO fJ

of F.

t>

O


(D^-

I'O

o

in: =e=fct ff"

©

i

o

11

oj^^

Q

°>"

°-

itr

© '>

O

•®

M

TT"

o

1^

1.

p ''

I'o

®

-»—1U3_ it.y

n—

^3

W^

^n

31: -e-

u

-e-

o

tt

O '-

^

O

® e1^

3

..

O

lM>

^

We

can transpose^; each of the scales shown in Ex. 3-2 so that the pattern of intervals remains the same but the initial note is always c'. In this way the similarities

and the

differences in the various arrangements

become more apparent.

Ex. 3-3.

®

A

® O

I 1

any

33"

:

:

Transpose literally series of notes

register.

"

-O-

n

o

o

331

means

to

O

O

331

$

"

j ^

"change position." In music

can be transposed

if

the series

is

^, ^o

331 331 -O-

"

O

I

m.

^o

^^

it refers to a change of pitch level. Thus, kept intact but changed to a higher or lower pitch

^^

^^^

34

KEY,

MODE, AND SCALE

Ex. 3-3. Continued.

[,0

l^o

1^"

'^Q

n

o

''^

<>

o

»

:

"

l>o

® 331

ini

^o^

®

® "or

n

.1

i^^^

Q

qD

Our

O

331

in Ex. 3-3

is

a "

C

i»

o

-e-

Each of the scales "major scales." .

331

331

o =o=n= O

scale," although half

1,

"

i>o

do not qualify

as

music reveals that certain arrangements of pitches have been most favored by composers during the past several hundred years, and for this reason we shall pay particular attention to these. We might note in passing that our musical staff, with its alternating lines and spaces, and the black and white key pattern of the piano both have a simple relationship with the C major scale literature of

pattern.

Ex.

3-4.

331

O

«>

mnn

331

°

cl

Thus a

scale of all successive notes beginning

automatically creates a

major

cessive white keys of the

scale pattern

piano from

C

on

on the

dl

el

C and

staff of

fi

gl

ai

bl

c2

extending up an octave

any

clef;

playing the suc-

to c automatically results in the

C-major

pattern.

The Diatonic Scale Systems begin a scale on any note other than C (written on the staff or played at the keyboard), and if we use only unaltered pitches, different kinds of scales are produced. As in major, there will still be a pair of minor seconds at some two points within the series, but they will no longer fall between the 3-4 and 7-8 notes where If

they

we

fell

in the

major pattern.

It

is

the shifting of location of these two smaller

intervals within the series of scale tones that determines the scale form.

KEY,

Ex.

35

MODE. AND SCALE 3-5.

^xfXtl fKcDMA£)J^

Major

Dorian

Ionian)

(

Lydian

Phrygian

^

^ t^/^f

^ TJ^ /

'

^^

^^^

-^^^tU^^^ V^C7)f/. Aeolian( minor) /)(rlurO

Mixolydian

i '-vur.j

Locrian ^

m

-'

•

jj^

•

n

i Each of

these different arrangements of seven notes

we again use C as a common tonic, we can mode are brought about with the relocation of If

see

is

more

called a scale or mode^

readily

how changes

of

the two half steps in relation to

the tonic note.

Ex.

3-6.

Ionian

(

Major)

Dorian

n

o=9=

o

ZSSl

*

Phrygian

XT

I.O

«i

Q

'^

^o- 3x:

Lydian

o-

Mixolydian

Aeolian

"

-e-

o

^^t°

"

l>o

^n ^o

g

I

I

j ^

(

Minor)

.U

..

oJ:-.-^°

"

Locrian

i>

is

o

t'o

..

2 The word modi is derived from the sa me wo r d root a s mood. Each of the traditional mode names of Greek origin Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian. In most instances

the

:

word mode

is

interchangeable with

scale.

'^

— —

36

KEY,

Since scales "1" and "6" of Ex. 3-6 are better

we

shall henceforth

known today

MODE. AND SCALE

as major

and

minor,

drop their impressive Greek names in favor of the more

familiar. Itjs significant that six of the seven

modes contain a

perfect fifth interval

between

and their fifths. As we can recall from our study of the tonality frameChapter 2, the diminished fifth is not an interval that is conducive to a

their tonics

work

in

mode

strong root effect. For this reason, the Locrian

more

mode"

as a "theoretical

(i.e.,

not used

traditionally has

in music),

and

it is

been regarded

rarely found as

the pitch basis for a composition.

The melodies

of Ex. 3-7 are labeled according to the

making certain modal character. each,

Ex.

3-7a.

fM

i

Greek

:

to

Hymn

JT

produce

mode

used. Sing or play

pitches accurately in order to recreate the true

all

to Seikelos.

r

T^r

i

fii^^LEJ

IP^

Mode: Mixolydian

I

t

pflj

f

1^^

^

Icjj'ffiN'^

P'J

a

zzi

oaz

Ex.

3-7b. United States

^

^ $

•

Folksong.

^

*

:

^

w

J) 1

w

t

m

(!;iJ

—w

-0

J

1

t

^

^

^ *

d

m

*

'

i

Mode: Dorian

Ex.

3-7c. Spain

:

Chant to the Virgin.

^

m£

f

i I

f

37

MODE, AND SCALE

KEY,

m

^^^^

W

^

L/

i'

i

r

Lf f i

Mode: Natural Minor (Aeolian)

*

.

•

^ z^l

^'

have not always created melodies that consisted exclusively of the pitches from any one of these scales. In this sense, scales or modes

Composers and

folk singers

are really basic patterns that are often altered in various the person using them. For instance, the melody in Ex. 3-8 notice that the seventh scale note

3-8.

Ex.

Dufay

:

is

raised a semitone in

By

essentially Dorian,

measure

but

six.

(ii)

P ^^ p i

^

is

to suit the taste of

Chanson, te /cor s'endorf.

(h

i-

ways

^^ u i,^ nA ? ^

^P la

i.

i

raising this note one semitone, the

melody

line leads

with even greater j

impetus into the tonic pitch, D. This strong melodic relation— the melodic half- / gives this seventh scale degree the name "leadingjtone^"|/ step below tonic pitch Two modes contain this relation between their seventh and eighth notes without

—

To

note alterations: Major and Lydian.

modes would require

contain the leading tone, the remaining

the raising (by sharp or natural accidentals as the case

may

member. Without this change their seventh degrees distinguish them from the semitone step of the leading

require) of the seventh scale

are called "subtqnics," to

tone

— tonic

When

relation.

the seventh degree of the Dorian

tern very similar to the major its

Ex.

lower half-step

falls in

mode

mode

results. It

is

is

raised

different

by one half-step, a patfrom major only in that

a different location.

3-9.

1

^

Y .,

o

o

o

t^'^

Major

i

j

o

^^

:xsz

:^^fe

Dorian

with raised 7

'

^

38

KEY,

This scale

is

better

known by

still

MODE, AND SCALE

another name, melodic minor.

It shares the

minor second placement between pitches 2 and 3 of the Aeolian mode, but it is different in that its other minor second occurs between 7-8 rather than 5-6. This whole scale, then, consists of the interval succession of 1 | 1 1 i. A third kind of minor scale results if the seventh note of the Aeolian (natural

—————— 1

minor) pattern

is

raised a semitone to create a leading tone. This

from the other modes discussed

differs

in that

it

new

1

pattern

contains three minor-second inter-

vals rather than the usual two. Such an arrangement leaves an unusual interval, the augmented second, between 6-7,

Ex. 3-10.

4

A-

o

-&

m melodic

^

XE

^^-

331 -o-

xn

"O"

The

°

o

o

Aeolian

O

O

O

33:

Aeolian (Natural minor)

y

Harmonic minor IxJUMci

(.th^l^ .loL^

Melodic .minor

+2

/i7q

"cr

^iK

JW^

fourth scale of Ex. 3-10

is

and

occurs frequently in the music most familiar to us.

natural patterns,

it

traditionally called harmonic minor.

Along with the

important to remember that each of the modes derives its unique character from (1) the intervals formed by the separate pitches with their tonic, and (2) the It

is

between any pitch and its immediate predecessor and successor. For this profit from a growing acquaintance with the different intervals that form the scale types discussed thus far: major (Ionian), natural minor (Aeolian), melodic minor, harmonic minor, Dorian, Phrygian, Lydian, and Mixolydian. intervals

reason

we can

Ex. 3-lla.

m.:

Major

^^ M2 M3 TT

-O-

:7^-^

3x:

ZZZ.

P4

One

rf\l

m2

ZESl

^

Natural minor

P5

M6 M7

minor

tradition regards melodic

the ascending form (as

shown here

^^ ^S M2 m3

_Q_

zss.

Z^L

P5

m6 m7

33:

-^z

P4

two different scale patterns, one what we shall call natural minor.

as actually consisting of

in Ex. 3-9), the other

iw«-

)

KEY,

39

MODE, AND SCALE

Harmonic minor

Melodic minor

m3

M'2.

P5

P4

M2 m3

M6 M7

P4

P5

Phrygian

Dorian

m2

-^»3-

*

o^o

V

M2 m3

P4

°

*

-

ir^

M2 M3

zz:

M6 m6 Mixolydian

m2

o

" z^

m2 mS P4 P5 mG m7 P5

Lydian

o h;

m o ^^ ?JT,,^l_^^

TT

311 fro-

m6 M7

m2

m2

A

ni2

+2

>

P5

+4

-&-

M2 M3

M6 M7

P4

P5

M6 m7

Terminology of Scale Degrees

In addition to the of

all scales

are

named

total scale system.

a

C major

scale

tonic,

which

in a

is

way

the central tone of any scale of pitches, the tones

that classifies their particular function within the

This gives us an additional

name

for reference. Ex. 3-1

and the various symbols which are commonly used

lb shows

to represent

each degree.

Ex.

3-llb.

C Major

scale

jj

VI

IV

Submediant

Subdominant

Supertonic

I

(

Tonic 331

-o-

3SZ I

To nig

This except o[ seven

Mediant

Dominant

Leading tone

in

V

vn

applied to every scale or mode, no matter what

set of

names

when

the seventh degree

is

is

is

its

structure,

not a semitone below tonic in this case the pitch ;

called subtonic rather than leading

tone.

The name for each scale degree is derived from its functional relationship tonic. The set of definitions that follows explains the distinction of each name it

relates to the scale set.

Tone of focus for the scale Dominant: The tone a fifth above the

$

Tonic:

tonic

Tonic

i Dominant

to

as

.

40

KEY,

Mediant:

The

tone between (the

"medium"

MODE, AND SCALE

or "halfway" tone) the

tonic

and

its

dominant

Dominant

Tonic

Subdominant :

The

tone a

fifth

Mediant

below the tonic (The under-dominant)

$ T^ "^o"'^

Submediant: its

The

tone between (The

Subdominant

"medium"

or "halfway" tone) the tonic

and

subdominant

Tonic

Submediant

E±S

$ F^

Subdominant

The next tone above tonic Leading-tone: The tone a semitone below tonic Subtonic: The tone (when present) a whole step below Supertonic:

tonic

Each of these names is a normal part of the trained musician's vocabulary. We shall use them even more when we deal with chords. At that time we shall use both the numerical distinction (such as I (for "one") and V (for "five")) and the functional distinction, such as tonic chord (or pitch) and dominant chord (or pitch) Key Signatures

The

notation of music developed concurrently with the gradual adoption of our

major-minor scale systems.* One adaptation of music writing to these scales has been the development of a shorthand method for previewing the pitches encountered in a composition. Such is the essential function of the key signature that appears at the beginning of many compositions. These collections of sharps or flats (or their absence) indicate the alterations of the "natural" note system that must be made to achieve the desired pitches. Without sharps or flats the musical staff" re* Most of our current music notation practices were established during the seventeenth and eighteenth centuries. Earlier music requires considerable deciphering to be made readable by modern performers.

)

KEY,

41

MODE. AND SCALE

presents a set of notes that renders a major scale possible only from C, a natural

minor

Ex.

.

scale only

from A.

3-12.

^

O

m A

C Major

o

O

331

ini

Minor

(

natural

«

TT

ICC

ZJJZ

Since the lines and the spaces of the staff have "built-in" half steps and whole steps, untransposed modes result from unaltered successions of pitches. A beginning

on any note other than

C

or

A

will

produce one of the modes, Dorian, Phrygian,

Lydian, Mixolydian, or Locrian. (See Ex. 3-5.) A composer writing a composition for soprano voice based on the natural minor scale could,

by pitch

alterations, shift the intervals of the unaltered

C scale

so that

minor results. The required alterations are those which produce minor seconds where they occur in the pattern of natural minor, between 2-3 and 5-6.

Ex. 3-13.

Minor

Major ~0"

331

~CT~

(

natural)

~n-

o

l^o

^

"

l

»i

I'o

"

As a convenience to the composer and the performer, the three flats {B-Jiat, E-Jlat, and A-Jlat) required to make this shift of pattern can be indicated as a "signature" at the beginning of the line after the clef sign. This relieves the composer of inserting necessary alterations every time these notes occur within the

melody.

Ex.

3-14.

In the same way, the key signature of three

mode from

a scale that begins on the note

flats

E-flat.

can be used

to

produce the major

42

KEY,

MODE, AND SCALE

Ex. 3-15.

E Phrygian

o

9

o

The order pattern;

it is

Et Major *

irc

o

1

o

«>

^^\

°

o_,,.

,.

^^

331

which flats or sharps are placed in the key signature follows a set based on the sequence of pitch changes required to produce a relocain

tion of the scale.

Using the unaltered mode based on F, one alteration is needed to create the major scale the lowering of B to B-flat. Since this is the first flat demanded in the notational system, it is always the first flat to the right of the clef sign of any signature containing flats. Ex. 3-16 shows the successive alterations required to produce major scales from the natural notes of the musical staff. :

Ex. 3-16.

xn

~rr ZJJC

IS

jCC -e-

P

T>

O- 331

A

It

o

~XT-

O

^>

"

v\r

t>

B-flat

12

4

3

-

o 9

im

9

etc.

5

the addition of sharps for the creation of major scales, the series follows

a sequence by

fives.

The

sharp; the third G-sharp;

first

and

sharp alteration required

F-sharp; the second C-

is

so on.

12

FGAB CDEF GABC DEFG Ex.

?

^1

9

is

BCDEFGABCDEFGAB With

E^ o o

331

o

=o=a=

^

TT e-

introduced, E-flat follows; A-flat next; then D-flat and progressive series by fours is established that can be represented as:

Notice that after G-flat.

*

-o-

3

etc.

4

3-17.

33:

i»

o

" O

^ yu

p

o

n

O

xn

3X1

o LI

O

33= =e=33=

331

i 33=

-o-e- 33=

T^

<>

O

~n~

tl

o

33=

31=

=n=

»«

o

-

KEY.

43

MODE, AND SCALE

This

has historical significance as the circle of fifths, a circular scheme that pictorially represents the system of keys for our

series of pitch akerations

which is major-minor

scale system.

Ex. 3-18. Circle of Fifths.

>— /.^^\> circle

/''r

q/-

*

AV,

rD

3HA

-3b

61

H Db

6b

Two scales which have

Cb

the

same

tonic but

which do not contain

identical pitches

on every scale degree are called parallel scales. For instance, the keys of B-Jlat minor and B-fiat major are parallel keys. On the other hand, two scales (or keys) which contain identical pitches but do not have the same tonic are called relative scales. Thus G minor and B-fiat major are relatives, and D major is the relative major of

Ex.

B

minor.

3-19.

Parallel

scales

1^

te:

Bb Major

'

i

^

^l,.^-

-''"'^^

Bb Natural minor

Relative scales

M

m

3

G Minor

'

Bb Major

i2L D Major

'>

.11." B Minor

»'

44

KEY,

Since double sharps

(X )and double

flats

(b

l>)

MODE. AND SCALE

are not generally used in key

is extended no further than seven sharps and seven flats (for C-Jiat major or A-fiat can be continued until the original pitch,

signatures, the system of keys normally (for C-sharp major or A-sharp minor)

minor). But the progression by

fifths

spelled enharmonically^ as B-sharp,

The key

is

reached.

signatures of our music are usually derived from the diatonic scale struc-

music based on the pitch resources of some other scale does not readily fit our traditional signatures. A composition that makes free use of the twelve tones of the chromatic scale gains little of practical use from a key signature. If tures.

As a

result,

used, the composer

and the performer are kept busy staying abreast of alterations

and, ultimately, their frequent cancellation.

3-20. Chopin: Valse,

Ex.

Op. 64, No.

3.

Compositions based on scales unlike the traditional modes might conceivably use signatures that look strange. The melody in Ex. 3-21 incorporates such a scale,

and the composer fabricated a former the pitch materials

Ex.

Bb Db

Scale

^

be expected within the composition.

Cradle Song, Violin Duets, No. 11. Copyright 1933 by Universal Edition; renewed 1960. Copyright Reprinted by permission. assigned to Boosey & Hawkes Inc.

3-21. Bartok

^i (|

to

special key signature that indicates to the per-

^°

:

^

& renewal

^ r

y

l9-=-

' ^°

Enharmonic tones are those which bear different note names but which have the same pitch. For F-JIat and E, A-fat and G-skarp, B-sharp and C are all enharmonic pairs.

example,

—

KEY,

45

MODE. AND SCALE

Modulation and Mutation foregoing discussion of keys, modes, and scales must be amplified somewhat to account for the pitch organization of many melodies. For the sake of variety, more than one pitch framework is often used within a composition.

Our

The word modulation refers to this shifting from one another. Thus we can say that a modulation occurs at the initial tonic of C replaced by the new tonic of G.

pitch focus, or tonic, to section

"Y"

of Ex. 3-22,

Ex. 3-22. Russian folksong.

^=zi—

xi

"^•icrcircrcJ

^

V

f

r

V

Tonic

Sections

II

i

TO^

J 11

^^

Tonic

"X" and "Y"

both

utilize

simple scale materials within their respective

boundaries, each incorporating only four different notes. It following the focus on

C,.

is

the

new

focus

on G,

that constitutes the modulation or change of key.

change of tonic. On the contrary, we can best describe the pitch organization of Ex. 3-23 by noting that a common tonic, F, persists throughout. The change of mode from minor to

Change of mode alone does not achieve

the

same

result as

major at section "Y" represents mutation rather than modulation. In this case, mutation refers to scale change as distinct from tonic change. In this example the contrast is affected by a change to the parallel major scale.

Ex. 3-23.

Swedish folksong.

^^ ^^nnm^^ jt

nn^ z-

s

Pitch frames

P

j

^

\S-}i

^P

£

"r

^m

^^ ^ \[j

^

46

MODE. AND SCALE

KEY,

—

Modulation is closely allied with the sectional divisions the phrases of musical I'brm which we shall discuss later in Chapters 4 and 5. For the present, however, we can observe that the melody of Ex. 3-22 illustrates this formal division by shifting tonics halfway through the melody. In a similar way, Ex. 3-23 is sectionalized by the change of mode the mutation that occurs after measure eight. It is this psychological shift from the old tonic to the new that makes modulation an element of variety, for only the relation of the original tonality to another establishes a condition of change. Either one without the other would represent merely one particular tonality, and thus provide no contrast. In establishing a new pitch focus, the same techniques of repetition, duration, metric placement, and strong interval embellishment (fifth or third above, leading tone relation) are used. The melodies which follow incorporate these various methods of establishing a new tonic. It is interesting to see that several techniques can be combined, as in Ex. 3-25, to create an immediate and unmistakable shift of

—

—

—

pitch focus.

Schumann

Ex. 3-24.

An den Sonnenschein, Op.

:

^—

36, No. 4.

Bb major

I

I

m£m

-&

X2I

m m

I

pr

pr cJ

m.

If P^

r

—F

m

n

^

r

r

Ex. 3-25.

Chopin

^ u

A

:

— Bt

major

wnr

gr

•

H

J-

J'^

u

Madchens Wunsch.

^

g

^

^ iEt J

^s>s it

\± A

I

e

J

I

J

^-

,

Ji

minor

rzs

£

J

^

u

major

S

J'J

f^

^

c

r

i

r

^

H

¥

r

t

major

i

i

major

^

i^^ ^j^ _l

47

MODE, AND SCALE

KEY,

It

how

would be brief, as

ter that

is

unrealistic,

however, to regard

key changes. In

we

this sense

all shifts

are dealing with an organizational mat-

subject to relative judgments. Pitch focus

chological response to tone patterns, so

of pitch emphasis, no matter

is

itself

a product of our psy-

reasonable to assume that one person's

it is

reaction might be slightly different from another's. For instance, one person might regard the "Y" section of Ex. 3-26 as an interesting diversion within the tonality of

D; another might hear

Ex.

3-26.

German

the passage as a definite modulation to the

tonic of A.

chorale.

J

^Ji

r r p

As

new

i

j^J

p J

J j']

i

^

^

modulating if the ap parent shift of tonic is^c onfirmed by at least two c onsecutive sections of the melody.^ Thus the melody of Ex. 3-27 does not contain a change of key; the emphasis on E-flat in the bracketa general rule,

we can judge melodies

as

ed section represents emphasis on the dominant within the tonality of yl-flat. On the other hand, the melody of Ex. 3-28 modulates, for the emphasis continues long enough for the new pitch frame to be established clearly in the listener's mind.

Ex.

3-27. Beethoven: Piano Trio,

\

1,

No.

^

fi'^^cS-

^' } Pvpv

Op.

>

I^r |

pv^P

1.

^' i

^cjcj-

^m

r^CfrTTJ

i

&r

rJ3

J

• We shall make our definition more preci.se in Chapter 4 by regarding ihe phrase, with cadence, as the unit of measurement for modulation.

^

its

attendant

—

J

#

48

MODE, AND SCALE

KEY,

Ex. 3-28.

German

chorale

A:-

to

-

Valet

:

-

will

-

-

dir

ich

geben.

-confirmed

-

>-

-

Some melodies use a modulatory scheme to create a series each new section creating a new reference point. These transitory occur between sections of clear tonal focus, the variety as

compared

to the definite,

D

back to

of shifting tonics, modulations usually

of tonics creating a tonal

shifts

unchanging pitch frameworks of the beginning

and ending sections. Once again, it is quite possible to hear such melodies as organized around a single tonic, the changing pitch frames representing changing stress upon different pitches belonging to the single overall tonality. In cases where a beginning and ending are clearly grounded in a single tonality,

more accurate

^

±=R

j" 10

perhaps

Gigue.

:

W jn

is

to favor the latter interpretation.

Ex. 3.29. Froberger

H

it

J'

j

J

^r^^r/exf i

i

^

s

nsj r i

r

^r^^r,!;

!

—

0^

15

p

i

gsf M'U ^HHf PLJ r

i

r

Br

rJr

^^

20

^P 25

I

^

frame of

e'

I

e^.

^-

S)

i

5

The melody

—

I-

w

j

^LLT

leading tone

—tonic

r

Peg

m

5

30

t*f^

in Ex. 3-29 contains a beginning section

The

i

((/-sharp

e)

based within the tonality

pattern in measure eight

the final substantiation of this tonic before a change occurs, in the section

is

marked

1

J

—— :

KEY,

49

MODE. AND SCALE

"X." This second section revolves around the pitch frame of ^^ g', with emphasis on the fifth of d^. From measure fifteen through seventeen d and /-sharp are emphasized by repetition and by the leading tone created by the sharped c. Measures eighteen and twenty relate these two pitches (rf and^-sharp) to a new pitch frame based on a tonic of 5. Thus section "Y" brings a new tonic to the fore, followed by a return (Section "Z") to the beginning tonality frame of e' e^. We can digest this tonal

movement

into a simple diagram.

Section

"W"

"X"

1-8

9-14

B

E

Tonics

Overall Pitch (Principle Tonic:

"Z"

"Y"

14-20 21-30 E_

Frame

E

Exercises

See Chapter 4 of the Materials and Structure of Music

Look

I,

Workbook for more detailed work.

and find examples of Dorian, Aeolian (or natural minor) Phrygian, Mixolydian, and Lydian scales. Copy the total r~-^elody and then show the pitch frame and scale in notation after the melody. [2. Write a melody according to each of the following prescriptions ^-^ a) Six measures long, range d d' in bass clef, tonic D, in Mixolydian mode. b) Four measures long, range from g g', tonic C, in major mode. e^, tonic E, in Phrygian mode. c) Four measures long, range from e' 3. Find examples of melodies which begin and end clearly in the same key but which contain 1.

in a collection of melodies (for sight-singing, perhaps)

—

— —

a modulation to another tonic within interior parts.

F

beginning and ending tonic,

4.

Write a melody eight measures long that emphasizes but stresses C at some point within.

5.

Transpose relatively simple melodies in major or minor keys to new pitch levels. (For example, transpose at sight a melody in the key of B-flat major to E-flat major.) Play at the piano. Practice the same procedure with other instruments.

6.

Practice writing every possible major scale, beginning with

7.

Practice spelling scales orally.

8.

Write the proper key signatures

for all

major and minor

as

C and scales.

ending with

B

as tonics.

Melodic

4

Cadences

A

fundamental characteristic of

human

behavior

is

our inabihty to

peak level of attention or participation in any activity. Whether in work or play, our patterns of involvement are normally marked by periods of successive intensity and relaxation. Such behavior is required for maximum efficiency, whether in reading a book or in physically more taxing pastimes. Even our speech reflects patterns of rise and fall, slow and fast, motion and rest, hard-accent and soft-accent, all of which, when combined, transmit more effectively what we wish to communicate they create the cadence of our phrases and sentences. The result is an organization of sounds into meaningful language. The cadence in music is an adaptation of these same points of pause amidst activity that gives form to the unfolding of tonal ideas. Even if composers did not mold such articulations of movement-repose into their music, listeners would seek them as aids to the listening process. A continuous series of identical clicks is heard as grouped into accents of twos or threes; and melodies areheard as patterns of tones grouped around certain structural rallying points. The cadence is that point in melody that provides momentary pause to the onward flow of musical pattern or, at the melody's end, signals permanent conclusustain a

;

sion. It

is,

therefore, a sign for the listener of relative degrees of termination;

separates one melodic unit from another. Like the written

and periods of speech, the cadence

is

commas and

it

colons

a heard signal that helps us organize our world

of tones into comprehensible forms.

The cadences

named according to the roles they play in tonal melody alone we shall discuss only two basic types:

of music are

ganization. In regard to

or-

the

denoting a partial or total cessation of melodic activity; and the progressive cadence, marking a break in tonal flow but with the suggestion of continuaterminal cadence,

tion.

Compared with

the punctuation marks of language, the terminal cadence

resembles the period, while the progressive type

is

more

like the

break in a sentence

marked by a comma. 50

MELODIC CADENCES

51

The Beethoven melody in Ex. 4-1 contains each of these cadential gressive at the midway point in measure four, terminal at the end.

Ex. 4-1.

Beethoven: Symphony No.

types, pro-

J

IV.

9,

m

-|

^m

r

If

r

r

r

r

\

/^'

'

Progressive cadence

s

^ 1

r

r

I

f

r

^

i

r

^5'-'

J$>

Terminal cadence

Rhythm and

pitc h

com bine^t o produc e

the two segments of the (

J-

J J

melody

the c ad ence effe ct. Although each of

in Ex. 4-1 closes with the

same rhythmic unit

the two cadences create different expectations because of the positions

)'

of their cadence pitches within the melody's tonality. foreign to the d— a frame established

in

The

of measure four

e

measures 1-3. Since

it

is

does not create

an effect of repose, it sets the stage for continued activity. By contrast, the d of measure eight, as tonic of the melody, renders permanent conclusion a logical consequence. In addition to the increased note durations in measures four and eight, another

rhythm confirms the arrested motion at these two cadence points. Notice that the pitch contour of this melody consists of a two-measure shape that rises gently in measure two, falling to a low point at the beginning of measure three. aspect of

^

Ex. 4-2.

m The same shape

is

repeated in measures three and four, creating a balance of

melodic contour, a musical statement modeled from the repetition of a two-measure unit.

The

continuation of this pattern into measure four, combined with the

contrasting longer durations (dotted quarter and half), impHes that the close of a definite musical section has

been reached.

Ex. 4-3.

^m

r

r

I

f

r

r

I

f

^

—

52

MELODIC CADENCES

While these rhythmic groupings create the cadential it is

caesura

— the pause

effect

the cadence pitch that determines the kind of punctuation.

and informative

experiment with other pitches as cadential notes in the middle of the Beethoven melody, to observe the punctuative effects It is interesting

to

produced by different relations. Since the second four measures duplicate the first four (excepting the cadence pattern itself), separation of the two by a terminal cadence produces a monotonous, disjunct effect, as illustrated in melody a of Ex. 4-4. Play or sing each of these versions to observe the contrasting cadential effects.

\v- ^.c-^ •>

<^..^

(e)

T-^

rr

i

f

rr

i

fpr

etc.

With the exception o[d a.x\df-sharp, the alternate cadence pitches perform about the same role as e of the original. They imply, in varying degrees, the continuation of melodic flow. However, all would not be successful choices for this melody because some, such as /-sharp and g, destroy the two-measure shape established as a pattern of contour in measures one and two. Cadences frequently

lie

at equally

spaced locations within a melody, thus giving

a simple continuity to the flow of tones. But

all

melodies do not follow the same

four-measure pattern clearly stamped into the fabric of Ex. 4-1, and some melodies are notably free of the regularity imposed by phrases of equal lengths.

Melodies "a," "b," and "c" of Ex. 4-5 have balanced pattern lengths; but melodies "d," "e," and "f" deviate from

this regularity

of formation.

The

last

two

examples are interesting because their cadences establish unbalanced melodic units as the basis for melodic form.

M MELODIC CADENCES American folksong,

Ex. 4-5a.

^

^^j^^

H[

1(3)

—w »— =gfe=^

-0

J J J

^ ^^^ i '

^

Ex. 4-5c.

P

i 1(3)

i

w

g

W

U

Op. 100 (Scherzo).

^^

^(4)

r

r

If

r

(4)

^

:

n(3)

$ Ex.

^

'

Vj J •!

t

4-5d.

German

Ex.

g

Ij

(3)

r

?^^ 1(3)

German

'jTil fL''

folksong.

I

4-5e.

1(3)

'nj ^

^ ^g

r

Mikrokosmos, "Staccato and Legato," Vol. V. Copyright 1940 by Hawkes Son (London) Ltd. Reprinted by permission of Boosey & Hawkes Inc.

Bartok

&

r

i ^?

4-5b. Schubert: Piano Trio,

Ex.

*

"2^

J J

J. I

53

i

r

^ n{3)

J.

^J^

f^^^^^\

^^

;

(3) (a(l>

\

.

m

(3)

3 1(3)

I

folksong.

1(3)

t rrrnrrrr

i

1(2)

(3)

rrMrrrrirrrrirrHr^ 1(3)

1(2)

rrrrirrrirrrr rrrrirrHrrrr i

1(3)

r i

rrrrK^

54

MELODIC CADENCES Brahms

Ex. 4-5f.

f $

Haydn Variations

:

^

i[^

i

(theme).

^^

r

1(5)

- »

(5)

ti ic-Zcj

r

rj^

f

i

ucj-

The

^^

1(4)

nmrJ

If

^

M' F m

P

^"ir/ i

r

l

w

^

(5)

U^^if

patterns that span the distance from one cadence to the next are called

phrases.

This unit of melodic form will be discussed in greater detail in Chapter

but no

discussion of the melodic cadence could be clear without

its

nature.

We

melodic phrase

might turn is

to

language again

for

comparison

some

7,

attention to

to note that the

similar to the "clause" or "phrase" of the sentence.

And

like its

language counterpart, the musical phrase can usually be reduced further into smaller units called motives. For instance, the third phrase of the melody of Ex. 4-5d consists of the

rhythm :(

]t

J

J

J

J) and

its

immediate

repetition,

both squeez-

ed into the span of three measures.

The Brahms-Haydn melody measure phrase

(Ex. 4-5f) yields a similar result in that the five-

units can be reduced to two-part units, the

first

unit of three

measures, the second of two. In this case the divisions are represented by

different

patterns rather than the repetition of a single motive.

Ex. 4-6.

repetition

motive a

motive b

reason a break occurs between the patterns of measures three and four which, in a limited sense, is a cadence; only after hearing the continuation of measures 6-1 1 can the listener decide that the important melodic units are five

For

this

MELODIC CADENCES

55

measures long. The combination of the two phrases resuhs in a ten-measure section.^

Perfect and Imperfect Terminal Cadences

As we noticed

earlier (page 52),

it is

the particular pitch at the cadence that

determines the cadential effect by implying or denying continued motion. A strong progressive cadence forcefully suggests continuation, while a strong terminal

unquestionably marks

The

most appropriately fulfills this latter function, while its scale relatives a major or minor third or perfect fifth above can also, under most circumstances, imply closure to a limited cadence

finality.

tonic as cadence pitch

degree.

The

third cadence of the

Brahms-Haydn melody

caden ce. Since the ultimate pitch d is

is

in Ex. 4-5

preceded by the tonic

the root of this melodic relation B-flat

—

d,

is

an

B-flat,

imperfec Uerminal

and

the cadence pattern does not un-

And

yet,

it

motion has concluded; such a cadence

lies

in the never-never-land

equivocally

demand

continuation.

weak p rogressive cadence a.nd^tjtrong terminal

The cadences a,

the perfect

It

fits

cadence.

above tonic

d.

In measure four the a acts as a point of brief

into the frame of the D-tonality (since the tonic,

lation d'

such as

e,

melodic between the

also does not suggest that

of the melody in Ex. 4-7 are similar. Here there are two based on

fifth

— a), so

since B-Jlat

it

D,

is

rest.

also the root of the re-

demand resolution to the same extent as other pitches, Compare the relative intensification of this cadence when

does not

c-sharp, or g.

these other pitches are substituted for

a.

Play or sing each version several times

to realize the precise cadential effects.

Ex.

4-7.

^ ^m

Original

O

I

p

Revised with

cjf

(

^^

g

^

it.

m

\

Pr

i

-e-

This combination of two phrases separated by a progressive cadence and ending with a terminal cadence is sometimes called a. period. ^

_

56

MELODIC CADENCES

Ex. 4-7. Continued.

Revised with g

m

^

?z==®^

Revised with

:^ ^

e

£^

P=:^

we

^

ways accompanying chords and melodic activity in other parts can emphasize or weaken the cadential effect of a particular pitch. This is one of the ways chords can add variety and alter the function of pitches within a melody. Without chordal underpinnings a melody must depend on rhythm and pitch relations within its tonality frame to create the available nuances of cadence, which act as form-giving elements. In a later chapter

shall discuss the

Transient-Terminal Cadences

hovered tightly within the orbit of a single tonality frame and the foregoing discussion of cadences would suffice for all music. But since melodies fluctuate in their obedience to a single pitch focus,^ some cadences

If melodies always scale,

many

momentarily create the effect of closure, and yet they do not meet the other specifications demanded by our definition of the terminal cadence. The middle portion of the melody in Ex. 4-8 pauses momentarily on d, a tone made prominent by its leading tone, c-sharp. If the initially established tonality were d, then this would be a simple terminal cadence. But since G is the tonic of the tonality frame (g' d^), the pause on d does not represent a perfect terminal

—

cadence.

Ex. 4-8.

German chorale

is

^

:

muntre dich, mein schwacher Geist

Er

m

We shall call such a cadence transient-terminal. d

is

interpreted as

be associated with

^m ^^

^ Only

if

a modulation from the tonality of

G

full

the motion to the cadential to the tonality of

D

can

it

termination.

Transient-terminal cadences can occur on any degree of a scale other than tonic.

^

The

dominant (5)

is

one of the most common, as

illustrated in Ex. 4-8.

See the earlier section of Chapter 3 that deals with modulation, pp. 45-49,

Other

57

MELODIC CADENCES

way

pitch degrees that frequently function in this

and the submediant. Each of the melodies is

melodic structure

to

4-9a.

German chorale

^

:

^

Valet

al

rrr f i

Ex.

4-9b.

Irish

')

&cr

£j^a:' r r

will

ich

dir

by

its

its

leading

successive repetitions.

geben.

3JI

n

r

p-

mf

^

wm

r

i^^rrr r^^

r

r

^7 MC;^^

^i^p

'

folksong.

i![

'^^'^r

s

is

established as a pitch of emphasis, either by association with

tone, with pitches a fifth or third above, or

Ex.

one transient-terminal cadence. the way each of these "temporary

in Ex. 4-9 contains at least

Of particular importance tonics"

are the subdominanl, the mediant,

r

i

r i

^m

j:?^^

^-^

^=^

mmm

h ium

Submediant

S

'

Ex. 4-9c.

1i

m

f

M

r

p

\

i!

^

John Dunstable: Soncta Maria.

^

*—^r

J-

^N-

JJJ1 Dominant

S

58

MELODIC CADENCES

Ex. 4-9d.

Handel

:

Air with Variations (Var. 3).

m^

tariejt

^m A

more

m

m

Mediant

^

m

p

and precise classification of cadence patterns must can be added to the rhythm and pitch elements that

detailed discussion

wait until harmonic features create the cadential effect.^

the terminal (both perfect

The

and

present limitation of basic types to the progressive,

and the

imperfect),

comprehension of the usual patterns found

in

transient-terminal suffices for

a

melody.

Cadences and Musical Style

As we have

seen, the

cadence

is

a fundamental determinant of musical form.

It

punctuates melodic flow in a way that suggests momentary or ultimate pause, thus contributing a kind of gauge to the forward propulsion of tonal motion.

Operating

in

combination with the pitch patterns of the musical phrase,

it is

a key

element in the organization of music. Since

it

does perform these unique

made

posers consistently have

roles, it

is

not surprising to find that com-

use of individualized cadence patterns in their

music. Stereotyped formulae can be found, used repeatedly by one composer or

by a group of composers who share a common musical heritage. These cadential "cliches" run the gamut from the strong terminal cadences in music of the eighteenth and nineteenth centuries to the actual suppression of cadential effect in some works of the twentieth century. We mentioned earlier that the cadence acts as a "signal" in musical form. Like the other signs of everyday raised

eyebrow

life

— the green

light,

the siren, the

— the melodic cadence can function

at the other extreme, as a

ture contains melodies

weak

waved hand,

as a clear, absolute signal, or,

symbol or hint of musical organization.

whose cadences operate

the

Music

litera-

at both of these extremes, as well

as at levels in between. It

is

not difficult to follow the melodic structure of some fourteenth century

music, for instance, because

many

of the outlining cadences use a specific scale

formula, 7-6-1 as their pitch content.

Ex. 4-lOa. Ciconia

m *

:

Et

in

terra pax.

U 7

6—1

This further discussion appears in Chapter 17.

59

MELODIC CADENCES

Amor

4-lOb. Landini:

Ex.

J)lJ

4-10c.

Ex.

£

^H

Machaut

^^

dal tuo suggetto.

:

i5

—

7

6

Mes

esperis.

1

^ 6

7

1

Although the name "Landini cadence" (after the fourteenth-century Italian composer) has been coined for this pattern, it was actually used as the common property of many earlier and later composers. In music of the sixteenth century the fusion of a set rhythm and pitch formula provides the cadential basis for

many

compositions, particularly the choral sacred

music of Palestrina. Ex. 4-11 shows this pattern, a rhythmic syncopation combined with the 7-1 scale degrees, both as a terminal and as a transient-terminal cadence.

Ex. 4-1 la. Palestrina: Vestina

a)r

colli

i

(Kyrie).

°

»r

Pitch:

Ex. 4-1 lb.

Palestrina:

Ex. 4-1 Ic.

Lassus

m

$

:

In

dominicus quadragesima.

Cantiones, No.

1,

*5ii

The use of these established

"signals" of cadence goes

"rhythmic pause" of the cadential

effect as

we

somewhat beyond

discussed

it

the

mere

earlier; their repeated

"road signs" of musical form. The use in music established appearance of a conventionalized pitch-rhythm pattern reinforces the mere dura-

them

tional

and tonal ingredients

as the powerful

in differentiating the parts of

melodic form.

60

MELODIC CADENCES

Bach, Handel, Haydn, Mozart, and Beethoven shared as common property the perfect terminal cadence of 7-1, the leading tone resolving to tonic, with a weak-

power of this simple pitch-rhythm pattern to confirm tonality relations that makes it a significant cadential formula in the entire history of music. Aside from its frequent appearances in music written by composers of the classic and Baroque eras, this cadence pattern can be found in the bulk of popular and community music whose most conspicuous features are simplicity of tonality and phrase organization. One special adaptation of the 7-1 figure became a cadential trademark in the music of Haydn, Mozart, and Beethoven, whereby the usual weak-strong rhythmic placement of the two parts of the 7-1 pitch pattern were regrouped into a strongweak relation of syncopation. The leading tone of such a cadence is suspended from a preceding weak position, thus delaying resolution to the tonic pitch.* to-strong metric location. It

Ex. 4-1 2a.

is

Haydn: Piano Sonata No.

^m Ex. 4-1 2b.

the

1

(Adagio).

strong weak

JH 7

1

Mozart: Piano Sonata No.

16,

K. 533.

strong weak

In our

enough

day, some composers have used certain cadential patterns frequently

to justify their identification with the composer's personal style. Since

harmony it is

own

plays a crucial role in determining the character of most recent music,

increasingly difficult to identify cadential patterns as melodic formulae alone.

However, composers whose music emphasizes melody use melodic cadences of some uniformity.

Ex. 4-1 3a.

Hindemith

:

Theme and Four

as a

Variations. (C) 1947 by

B.

dominant ingredient

Schott's Soehne, Mainz.

Reprinted by permission.

^ weak

^±

strong

Upper leading -tone cadence

'

This delay

is

further enhanced, as

we

shall see later in

Chapter

17,

by the underlying chords.

:

61

MELODIC CADENCES

Ex.

4-13b. Hindemith

:

When

Lilacs

Last

in

Dooryord Bloomed.

(C)

1948 by Schott &

by permission.

Co., Ltd., London. Reprinted

^g

S

t

Upper leading-tone cadence

Ct:

It

the

seems

clear, then, that in addition to

cadence can be elevated recognizing

its

role as a

its

to a position of significance

determinant of form, the

and

individuality, thereby

contribution to the "personality" of a particular work, the works

of a single composer, or even the compositions from an entire era of music-making. In this latter role the cadence is a prime element that suggests, perhaps in a more direct

way than

utterly

other musical elements, the peculiar flavor that makes one melody

and uniquely

from another.

different

Exercises

See C:hapter 4 of the Materials and Structure of Music 1

.

I,

Workbook for more detailed work.

Write several melodies, each of which fits one of the following schemes Compose other melodies with similar characteristics. (a)

Key,

Meter

D minor

3

terminal cadence

transient-terminal

cadence on

A

(d)

(b)

Key,

A major:

transient -terminal cadence on F"

Progressive cadence on G*

(c)

Key,

G

terminal cadence (A)

Mixolydian:

terminal cadence

Progressive cadence on F

(G)

2.

Copy

3.

Write one- or two-measure fragments which a variety of keys, major, minor, and modal.

several complete chorale tunes from a collection such as the 371 Bach Chorales. Using only the melody as a basis for determination, name the cadence types.

Example:

4.

L-t y -

-/

* i

ttj

"w

illustrate

each kind of cadence type. Use

transient-terminal cadence in D-major

Analyze the melodies of any chosen composition for scales. Having determined the tonic pitch for a passage, arrange the pitch materials in an ascending scale that begins with the lowest note and extends to the highest. From this determine the basic scale.

Forma/ Characteristics

5

of Melody:

The Motive

and Phrase

In Chapter 4

we saw how cadences impose form on

tonal ideas

by

one melodic unit from another. In this sense cadences form still another kind of musical framework. The span between cadences is "filled-in" by various related and contrasted melodic patterns. Even in the most complex melody, these

setting off

patterns are

combined

to create recognizable units

between the cadential bound-

aries.

Since music takes place in time,

a pattern

is

we hea r

musical patter ns in successioa. At times

repeated immediately; at other times a

tern stated earlier;

and

at times a pattern

is

new

changed

unit

is

followed by a pat-

slightly or a great deal, there-

by creating a variation. It is t his succession of discrete tonal units or sectionsjhaj; produces form in music. Such a description of musical form is very general; however, a close look at several melodies will show what is meant by musical form. The terminal cadence in measure 6 of Ex. 5-1 divides the whole melody into two smaller sections. These two sections complement one another tonally and rhythmically, even though they '

are not of equal length.

mimi^

ac^icj^'

IKfcii ^

^cxjic^rrj

mxiK

Ex. 5-1. America.

4

^ 9

}iVf'

e 10

r

r

r 11

If

'5 12

13

14

two melodic sections is a phrase. As each unit is succeeded by another, the unfolding of the melody takes place and its form is delineated. As Ex. 62

Each of

these

FORMAL CHARACTERISTICS OF MELODY: MOTIVE AND PHRASE

63

need not be of equal length; however, each of the phrases off by a clear cadence. Not until we count the measures do we become aware

5-1 illustrates, the phrases is

set

of unequal phrase lengths.

formed from successive statements of smaller patterns, each of which is two measures long. Thus, just as this melody is made up of two sections, so each of its phrases is made up of smaller units called motives. These motives are simple rhythmic patterns such as those seen in measures 1 and 2 Both phrases of Ex.

(

3

(

4

J J

and 4 J

J

J

gives

J

and the

I

I

J-

5-1 are

)•

J^J

J-

^^^ immediate

prominence )

settling

is

repetition of these patterns in measures

to the motive. In

measures 5 and 6 a new pattern

introduced which, because of a longer duration at the end

on

phrase to a terminal cadence.

tonic, brings the first

The

phrase contains three two-measure units, two of which are rhythmically alike. The third unit contrasts somewhat with what has gone before, completing the first

rhythmic design of the phrase.

The

motive at the beginning of the second phrase establishes a strong bond between the two phrases. In this case the phrase does not end with the statement of the contrasting pattern, but continues for two more measrestatement of the

initial

Because of the particular rhythmic and tonal points of emphasis that have been established, we might expect the melody to halt on the first beat of measure 12 on the pitch g. However, the dotted rhythmic figure is preceded by a new patures.

tern as well as a pitch motion

up

to d; consequently,

more music

is

demanded

to

complete the phrase.

The prominence

of the rhythmic pattern (J J J

ing force of this tune. In

unfolding of the

melodies

this

is

initial

many

|

J.

melodies a short pattern

/^J)

is the

may form

the basis for the

musical phrase and subsequent phrases as well. In some

not as easily observed as in the tune America, and in

short unit or section

is

essential bind-

still

others no

repeated (see Ex. 5-2). However, some characteristic pat-

tern usually appears as a formal binder.

Ex. 5-2.

Beethoven: Piano Sonata No.

*e:r:=

s

13,

II.

tef |

Motive Structure motive

Op.

f|fr.s'

'y-M'i^

A

8,

is

fv rr:!]i^ i

midiiK. -f^yTAcJUk^ .Uct(i^XL^A.

ni^ami^

a short a nd di stinctive melodic pattern, often characterized by

rhythm and pitch design. Because of its brevity, the motive is easily recognized and frequently plays an important role in the organization of a melody. Both_pitch and rhythrn produce the distinct qualities that characterize a par-

simplicity of

ti cular

factor,

motj vg. Either the pitch or the rhythmic structure can be the dominating or both can be combined and equally important. The motive illustrated in

64

'FORMAL CHARACTERISTICS OF MELODY: MOTIVE

Ex. 5-3 does not have a noteworthy rhythm, and yet

its

AND PHRASE

pitch outUne forms a strik-

ing pattern of great melodic potentiality.

5-3.

Ex.

Mozart: Symphony No. 41, "Jupiter," -o-

On

ux:

331

IE

rhythm

K. 551,

dominant feature of the motive shown in Ex. 5-4. As is frequently the case, this motive has an upbeat beginning, its first real stress falling in the second measure on a relatively longer duration. Here, as in the other hand,

many

passages of music, the motive

importance and contributing

its

the

is

Ex. 5-4.

Beethoven

:

is

to musical continuity.

Symphony No.

5,

I.

Cs

pi

/7\

In Ex. 5-5, repetition of the motive

whole phrase

up

is

restated immediately, thereby establishing

until the

change

F^

(

at the cadence.

The

restated at different pitch levels until the

etition at different levels gives

prominence

I

to

JV

)

forms the rhythm of the

pitch pattern of step-down step-

approach to the cadence. This repthe rhythmic figure and makes the

motive the organizing feature of the phrase.

Ex.

5-5.

Still

Bach

:

Brandenburg Concerto No.

3,

I.

another factor gives shape to the Bach phrase. Notice the

—

— —

octave {g g'), and the fifth {g the phrase unfolds rhythmically,

d').

The

filling-in

of the

sketch in Ex. 5-6 illustrates that while

dominated by a melodic pedal on g', and balanced by the descent from d' g. The introduction of c'-sharp and the change to ascending motion momentarily shifts the emphasis from G to D, creating a transient-terminal cadence.

Ex. 5-6.

it

is

FORMAL CHARACTERISTICS OF MELODY: MOTIVE AND PHRASE

In

many

melodies the motive's pitch pattern

65

when

varied

is

it is

repeated-

emphasis created by the repetition of a particular rhythmic pattern compositions based on dance forms. Such an emphasis

motive

J

(

^n

JV J

J

Here a new

in Ex. 5-7.

)

J

(measures 6-7; measures

the close

(

J J J

J\l)

J

I

motive receives

5-7.

Ex.

Pachelbel

m

*t

:

less

n

pr

11

this

motive

^

irjr

J^

12

13

r'cJitnrpr is

14

i

^fr

rhythm of the is

first

Piston:

15

m

five times.

i

may

\

J

)

shorter, three beats instead of four.

Symphony No.

4,

(C)

I.

c

—g

is

16

1^

occur. Ex. 5-8

repeated. Notice that the

it is

part of the motive {\

petition has six articulations: the fourth,

5-8.

the

^^

repeated hnth pi trh and rhythmic changes

also that the restatement

Ex.

pattern

m

m

shows some changes a motive might undergo when characteristic

new

made more prominent,

is

emphasis by appearing three instead of

,

a motive

this

see,

assumes greater importance in the second phrase by

i«t

When

introduced to bring about

Sarabande.

1

ffr

is

typical of

is

created by the rhythmic

is

we can

14-15). As

being stated twice. Notice also that as initial

figure

The

filled-in in the

is

retained. Notice

However, the

re-

restatement.

1953 by Associated Music Publishers,

Inc.,

New

York. Reprinted by permission.

Piacevole

43d:CUt^5 '

(

i St ,

,

^^--

m

^

Sometimes a motive and a phrase are the same. as in Ex. 5-9,

Ex.

5-9.

such a merger occurs,

a motive has the significance usually attached to a phrase.

Schubert

Allegro

When

:

Symphony No.

5,

I.

66

FORMAL CHARACTERISTICS OF MELODY: MOTIVE AND PHRASE

Subsequent£e£etitions^Fa_niotive generally appear in the_same metric position, but deviations from such a plan may occur, as in Ex. 5-10. The repetition of the

an interesting example of variety created by rhythmic relocathe repetition of the motive begins on the second instead of the first beat.

five-beat motive tion;

Ex. 5-10.

is

Prokofiev: Violin Concerto No.

2,

By permission of the International Music

I.

Company, New York.

Allegro moderato

ri'Tr'^r

r

r^

i

Phrase Structure

and

Earlier in this chapter

perties of the musical phrase,

in

its

At a

organization.

and the

vital role

we

discussed

relatively short

is

and

some pro-

which the motive frequently plays

larger level of structure, the phrase

agent of form. Thejnotive

An

preceding chapter

in the

is

is

also a distinctiye

usually a sub-unit of the phrase^

examination of music shows that there are numerous

possibilities for construct-

ing phrases.

A common is

marked

type of phrase structure

off rhythmically

is

seen in Ex. 5-11.

Each of the four phrases

by a tone of longer duration and a

rest

(J.

Jv

7

)

When

the two elements of greater duration followed by rest are combined, a rhythmic cadence is unquestionably established. Therefore, at the beginning of measure 5 we recognize, in retrospect, a complete rhythmic structure, a phrase.

The this

succession of shorter rhythmic figures shapes the entire phrase. Notice that in

melody the

shortest durations occur in the

first

measure of each phrase, and

that the second longest duration occurs in the second measure.

Ex. 5-11.

German 1

•Ui'^Jf

melody.

folk

mm ___

2

^

'

*-j-»

^

8in J

i^

i

j

j'^Jj

JH-' ^^12-^^V .

j3

1

^^

^^

udJ^'^^^^ *

*•

s

^^

10

)Y'

E=5 ^4

j5

jg

FORMAL CHARACTERISTICS OF MELODY: MOTIVE AND PHRASE If the

measures of the

first

phrase are considered separately,

has a different rhythmic arrangement. the phrase,

8 J^ J!!]

e.g.

I

67

/T]

I

The J

J-

we can

see that

each

design of each creates balance within

il J

J^JTi

I

J-

/^

;

measure

1

is

measure 3, and measure 2 has longer durations in common with measure 4. Even if this phrase is performed without the assigned pitches, we recognize it as a complete rhythmic structure; nothing else is needed to complete it as a balanced rhythmic design. As we saw in Chapter 4, cessation of activity does not by itself cre ate a cadence. In Ex. 5-1 the first part of each measure always contains a longer duration, and an upbeat precedes each durational accent. The rhythmic motion from a lesser to a greater accent also occurs between measures, as from measure 1 to the durational accent of measure 2. Considered in this light, the phrase is grouped rhythmically by groupings of two's. Phrase grouping of this type occurs so frequently that it is considered to be the norm. By this criterion, the phrases illustrated in Ex. 5-12 would have to be considered "abnormal," although in their context they are perfectly normal. similar to

1

Concerto for Oboe, String Orchestra and Percussion, I. (C) 1957 Inc., New York. Reprinted by permission.

Ex. 5-12a. Alec Wilder:

by Associated Music Publishers,

(

J = ab. 92)^'^'^^

S

ii t; Oboe

ft

Tnf

r r

cJt

Ex. 5-12b. Bartok

:

I

^ ^'t^"

r

ii

'^

^ ^ ii

^^ afiOM^y^ r^iUAi-

^

s;

^

u

z

331

r

/

Mikrokosmos, V, "Boating." Copyright 1940 by Hawkes & Son (London) by permission of Boosey & Hawkes Inc.

Ltd. Reprinted

Allegretto

J=116

U U

^^?

J^y_

^^^

t'f

hd\

68

FORMAL CHARACTERISTICS Of MELODY: MOTIVE AND PHRASE

Ex.

5-1 2c.

Schumann: Symphony No.

JL66

Larghetto

Ex. 5-1 2d.

1,

Trouvere song: Virelais, Or

mm

la

iruix.

r

1

^m

J

which

is

A

.

rrl J^J

For example,

arts.

of Ex. 5-11 without a change of pitch, straight line,

^

i

We often speak of a melodic

Pitch factors also influence phrase structure.

an analogy to the graphic

l

we can

if

we perform only

represent

its

the

"line,"

rhythm

pitch contour with a

complete rhythmic structure

still

remains; how-

most of us would agree that such a phrase is comparatively dull, that not really a melody. When changes of pitch are added to our performance a ever,

it is

dif-

wavy line, with the high points, low points, final note, etc., delineating a melody. The pattern set up by a succession of different pitches influences the general shape of a phrase. The old expression "What goes up must come down" also applies, broadly speaking, ferent kind of "line" results. This line generally corresponds to a

to

melody. In the

first

phrase of Ex. 5-1

1

the highest pitch occurs very near the beginning.

As soon as the highest point is reached a descending pitch motion takes over. The contour of this phrase can be represented by a wavy line which has one predominant arch, _*-*-~* A more precise representation of the phrase contour .

" ~"^ would include other segmental waves, «*— The rhythm of the second phrase in Ex. 5-11 is identical with that of the first phrase. However, a change in pitch structure is made so that the cadence tone now becomes d. The change is accomplished by interrupting the descending motion with a minor third skip, then descending to tonic. This, together with the rhythm, .

delineates the phrase.

Using the same rhythm type of phrase relationship

manner 1

3

two or more successive phrases is common. This caWed parallel phrase construction. Phrases related in this

for is

melody by restatement of similar material. In the melody of Ex. 5only the rhythm of the first phrase is retained in the second every pitch is difunify a

;

ferent, i

^

.

•

IL

.Up CiiJkl

(_

-

-

«

—

:-_

V ._

„ ^u w -0_^Jw .

ti u>till>rY\

69

FORMAL CHARACTERISTICS OF MELODY: MOTIVE AND PHRASE Ex.

5-13. Brahms: Quartet No. 2,

Op.

31,

Allegretto con grazia

-fJr^^^rJ^ijJr'-'ncrcjcj-

^

i^ji'i^jinu

J"""

^

^j^

^lI'iili

In Ex. 5-14 both phrases are four measures long. Since most of the second phrase differs in is

rhythm from the

first,

this

called contrasting phrase construction.

phrase creates a contrast. Such a relationship

The two

phrases together form asymmetrical^

structure because both are of the sam,e length.

it>/U^^^

^

MjrtJL 5-14. Beethoven: Piano Concerto No. 3,

Ex.

Op.

C

37,

Allegro

ji't 8

J.

I

r

i^BE

^

In Ex. 5-15 the phrases vary in length. This means, simply, that some phrases is achieved by combining phrases of unequal proan asymmetr icoL structure.

are longer than others. Balance portions, resulting in

,

.

(J

i

Ex. 5-15.

Hovhaness Prayer of Saint Gregory, for Trumpet and String Orchestra. Copyright 1952 by Peer International Corporation. Reprinted with permission of the copyright owner. :

^ g^j i

i

^m

^

70

FORMAL CHARACTERISTICS OF MELODY-. MOTIVE AND PHRASE

Formal

units containing phrases of equal duration (as Ex. 5-14) are

for they create

an

common,

understood musical form. In Ex. 5-16 both phrases are four measures long. Moreover, each phrase is a complete rhythmic unit. However, the phrases are dependent upon one another tonally; a terminal cadence does not appear until the end of the second phrase. easily

Beethoven: Piano Sonata, Op. 31, No.

Ex. 5-16.

^ ^4^

3.

i^#

rf

i

f f

i

tfrnrp

Both phrases in Ex. 5-16 form a musical period. In a period, two^£more£hrases_ are joined by avoidinjg an implication of finality at the close of the_interior phrase or phrases. In Ex. 5-16 this

accomplished by the progressive cadence at the end phrase. The two-phrase formal unit, then, is understood when the terminal cadence appears at the end of the excerpt. Many melodic periods consist of only two phrases. However, this is not always of the

is

first

the case. In Ex. 5-17 three phrases combine to form a period. Each of the phrases contains similar melodic elements. Since the second phrase does not have a strong

rhythmic

Ex. 5-17.

close, there

is

no suggestion of

Beethoven: Symphony No.

^te Formal

^

8,

finality until the

end of the third phrase.

I.

r^*^ /

^

M'

T

'^r

j)yj^

'f

sections consisting of four or

more dependent phrases occur

frequently.

is The emphasis on first beats by dynamic accent in measures 5 and 6) estab3 lishes a pattern suggesting that the phrases will probably close on a first beat. Contrary to our expectations, the first three phrases end on beats other than the first. The statement of the fourth phrase satisfies our expectations by coming to a close on the first beat, completing the rhythmic design of the melody. Even though each of the phrases in Ex. 5-18 is a rhythmic unit, a larger formal unit is not heard until all four phrases have been stated. Not only are the first and third, and the second and fourth, phrases rhythmically similar, they are also alike in pitch contour. Notice the subtle pitch changes in the last phrase which provide variety and aelay the arrival of tonic. The second cadence (measure 8) binds the

In Ex. 5-18 each of the four phrases (by duration in measures

1

and

;

of equal length.

FORMAL CHARACTERISTICS OF MELODY: MOTIVE AND PHRASE

71

by closing on supertonic. Each of the phrase pairs forms a period. In this example, however, the two periods are dependent upon one another both tonally and rhythmically. Such joining of phrase pairs is often called phrase pair to the

first

a double

last

beriod.

Ex, 5-18.

Haydn: Symphony No.

93,

I.

Allegro assai

^

^

10

11

u m

r

^

16

15

14

13

12

w

m

We

have seen that certain typical cadences mark off the phrase as a formal unit, that a motive frequently dominates the unfolding of a phrase, and that each phrase is a particular kind of pitch and rhythm structure. These distinctions apply to phrases in general. However, any phrase of music is heard as a unique structure, even

if

many

of

its

elements are similar to those in other phrases

we know. As we

music we are probably aware first of the "highs" and "lows" of the pitch motion, the contour of the phrases and their relative balance rather than their exact listen to

lengths.

produced by the rhythmic placement of the high and low pitches. In the first phrase of Ex. 5-19 the pitch apex is in measure 4, the highest point of the entire melody. After this highest point the predominant pitch motion is down to tonic. The phrase forms one broad arch that includes several smaller waves. Notice that the pitch apex is the dominant scale degree, which is important Phrase contour

is

in creating tonality.

Ex. 5-19.

^

Trouvere song: C'esf

P^

^

P r

S^

la fin.

i

^ a

^ r

pi

pg:

^ rir

c;-^

r

ir

^ V

^

r

i

rrcf ^r i

^m

^

72

FORMAL CHARACTERISTICS OF MELODY: MOTIVE AND PHRASE

The contour

also contrasts with the

arch of

this

this arises

type

is

first

phrase because of

common

less

its

length and

than that produced by the

from the resulting ascending motion

inflection raises a "question," similar to

when we

The second phrase

of the second phrase forms an inverted arch.

its

A

range.

first

phrase

;

phrasein part,

cadence pitch. This rising the way the pitch of a spoken word rises to the

ask a question, producing an expectation of something to follow. Notice

also that a progressive

cadence

combined with

used. Thus, ascending contour,

is

progressive cadence, results in anticipation of continuation.

In Ex. 5-20 the pitch apex appears at the beginning of each phrase. However, both phrases differ in contour and range. Considering the number of waves in the line,

it is

Ex. 5-20.

The tern

is

"complex," each phrase consisting of several secondary arches.

—

Tansman: "Berceuse," Pour les Enfanfs 4th Set. (C) 1934 Eschig, Paris. Renewed 1962. Reprinted by permission.

five-tone

melody

by

The wave

in Ex. 5-21 forms another type of contour.

characterized by descending motion until the

rise to b

Max

Editions

(measure

pat-

which

5)

is

The appearance of the highest basic pitch (b) The opening of the phrase outlines a d) However, the tonality of the excerpt is E. The

the highest point in the phrase.

coincides with a change of tonal emphasis.

D

tonality (the perfect

E

tonal center of

phrase and

e

a

—

.

created by using

b,

the

dominant degree,

apex of the

as the

as the final pitch.

Mikrokosmos, IV, "Playsong." Copyright 1940 by Hawkes Reprinted by permission of Boosey & Hawkes Inc.

Ex. 5-21. Bartok Ltd.

is

fifth,

:

& Son

(London)

i The arch formed by highest pitch

is

the phrase in Ex. 5-22

is

a

common

one. Notice that the

reached around the middle of the phrase and that

this

dominant scale degree. Notice also that the leaps centered around 2 and 3 slightly disguise the tonality of a.

Ex. 5-22.

^'^J

Brahms: Salamander, Op. 107, No.

1^

^

r

r

i

r

r

c

pitch

in

is

the

measures

2.

^

r

r

c/c/i-^

i

—

FORMAL CHARACTERISTICS OF MELODY: MOTIVE AND PHRASE

The

possibilities for different types of

illustrates

other possibilities.

Ex. 5-23a.

J.C.

Bach: Symphony

^

St.

:

rr

m ^

Bloch

I^

$

:

LT

J

I

^

0^

0* 4

"• '

W

m ^=^

i^^

Copy-

IV.

5

By permission of the International Music Company,

I.

York.

r>

#

ZZl

^ Ji.j

Maschera

i.r3

i

/3

i

k\jX'.*iC

i

^

pjp-^ jjjJOT i

Mozart: Concerto for Two Pianos,

rji:j'irr

^:

i m

Canzona.

.-

I

Jiij]::^

Safe

heiligen Gebeine."

^^ fern

String Quartet,

-f>i'tfUL4->C

m

l

^

Ex. 5-23f.

ihr

'ii"iiiJi]uiayiii^i"JjjlL"jiy

Ex. 5-23e. Florentio

jjj

John Passion, "Rohf wohl,

^m

i

Concerto Grosso for String Orchestra with Piano Obbligato, by Universal Editions. Used by permission.

^ New

-^

If

:

'ii'i

5-23d. Ravel

Ex.

[J-

^g right

II.

A 4^r\

U^U

5-23c.

phrase contour are numerous. Ex. 5-23

n n

m

Ex. 5-23b. J.S. Bach

Ex.

B-flat,

in

73

\

i

rf

K. 365,

n.mrrn

p aj'J jjJ

III.

r[:; i

i

i

r:£;

i

riiJ

m

i

f

.

.

:

74

FORMAL CHARACTERISTICS OF MELODY-. MOTIVE AND PHRASE

Ex.

5-23g. Beethoven

^^

Symphony No.

:

la

3?t^

8,

I.

m p^^^ .n n

^W

I, :i^^^

i

Generally, the apex of a line will be a pitch that

is

the dominant, the tonic, or the mediant scale degrees.

^

basic to the tonality frame

Other parts of the

scale also

appear as highest points, but they frequently have clearly decorative relationships to pitches that are basic to the tonality.

Pitch climax

As a phrase

also associated with the contour of phrases.

is

unfolds,

the pattern of motion to the highest pitch directs our attention to that pitch. In a

manner of speaking, pitch apex or in

energy

is

of music. line the It

is

the "energ)'" of the directional pattern opposite, the low point. Since

its

usually followed by release,

The

we know

concentrated in the

that a "build-up" of

expect the same to happen in a phrase

pitch apex and the low point, then, are important factors that out-

contour of a phrase or section of music.

impossible to exhaust

composition presents all

we

is

new

the possibilities for constructing phrases, for every

all

solutions.

However, certain principles are present

in

compositions. 1

A

2.

The

by a cadence. The stress patterns produced by rhythm and pitch generally reinforce the meter of a phrase as indicated by the meter signature. phrase

is

a rhythmic-pitch unit

marked

off

length of phrases, considering only the

In part, the length

is

number

of measures,

determined by tempo; more precisely,

it

is

is

variable.

completely

influenced by our psychological span of attention. Certain phrase lengths pre-

dominate,

e.g., in

two measure phrases;

a slow tempo,

four or more. Other phrase lengths, such as three, 3.

The shape or contour of a phrase pitches. The apex and the lowest

in

five, etc.,

a faster tempo, are also possible.

the result of the placement of high

is

and low

pitch of a phrase are usually either the tonic,

mediant, or dominant.

Exercises

For more detailed assignments see Materials and 1

2.

Structure

of Music

I,

Workbook, Chapter

5.

Perform each of the examples in this chapter. Listen for the larger formal sections. Isolate the motive, or motives, and describe the rhythmic structure and pitch structure of each motive found.

Use

several of the motives contained in examples cited in this chapter as the principal

unifying factor in two-phrase melodies. 3.

Devise three or four original motives.

Then

use these motives to organize original three-

phrase melodies.

and analyze the phrase structure of songs by Schubert, Schumann, and Brahms. Describe phrase lengths, pitch structure, and rhythmic structure of the melodies selected.

4.

Listen to

5.

Find examples of melody in the literature lel

for

your voice or instrument containing paral-

phrase construction, contrasting phrase construction, and period construction.

FORMAL CHARACTERISTICS OF MELODY: MOTIVE AND PHRASE 6.

Listen to the

first

movement

of Mozart's

Symphony No. 40

75 in

g minor, K. 550. Compare

the prominence given to the initial motive with the use of the motive in the

ment of Beethoven's Symphony No. 7.

first

move-

5.

Find examples of melodies in a collection such as the Harvard Anthology of Music in which motive repetition, phrase repetition, etc., play a small organizational role. Describe how unity

is

achieved.

The

6

Extended

Melody

In a broad sense, a melody

may

be regarded as the joining together

of several phrases. One-phrase melodies are possible; however, most of the melodies

we hear

are longer.

The

principles of repetition

and

contrast, briefly

men-

tioned in the preceding chapter, form the core of our musical experience in

extended melody. Repetition of a musical unit produces emphasis, but

when

carried

on excessively

constant repetition can be boring. For this reason, contrasting ideas usually

mark

off the various parts of a melody, thereby contributing to musical balance

and

variety.

Contrast and repetition are opposites. In between these two extremes changes

can be wrought that combine features of both. In other words, rhythmic and tonal patterns can be varied to produce contrasts that are still within the bounds of similarity.

The

possibilities are infinite, as

Repetition.

phrase units.

The

A

simple

way

Schumann: Dichterliebe

^^m fci

More

shall see later in the chapter.

of extending a melody

is

to repeat

complete

repetition of the initial phrase in Ex. 6-1 immediately focuses

our attention on that phrase. In

Ex. 6-1.

we

:

this

excerpt the repetition

is

almost exact.

"Im Wunderschonen Monat Mai.'

tVLj

frequently the repetition of a pattern will contain

^^

some change, usually

two changes appear: the progressive cadence (measure 4) is replaced by a terminal cadence in measure 8, and the pitch contour of measure 7 is slightly altered from its prototype in measure 3. at the cadence. In Ex. 6-2

76

77

THE EXTENDED MELODY

Ex. 6-2.

j

Brahms: Symphony No.

"j j jj j i

i

many

In

p^J

1,

IV.

JjJj

melodies extension

is

I

Jj J ji' jj j i

j

Prokofiev: Rigaudon, Op. 12, No. (Sole ogents

:

C.

Changing the pitch

F.

is

is

3.

U

J

one of the

dif-

Reprinted with permission of Robert Forberg

New

York).

many ways

varied. Notice that the intervals are not precisely the will

J^Jj

called sequence.

Peters Corporation,

level

J

achieved by the repeti tion of a phrase at a

ferent pitch level. This type of repetition

Ex. 6-3.

l

musical materials can be

same

in

both phrases. This

always be the case when a sequence follows the notes of only one scale sequence).

(diatonic

Both phrases in Ex. 6-4 use the same motive. The

first

phrase unfolds sequen-

(The use of sequence within a phrase usually involves the repetition of a motive) The end of the sequence is signalled by the change of the perfect fourth skip in measure 2 to a minor sixth skip in measure 4. tially.

.

Ex. 6-4.

Beethoven

:

Piano Sonata, Op.

No.

2,

3.

Allegro

m

wtj *

^

CjiJ

r

i^i^U-^^

In Ex. 6-5 the motive that begins in the sequentially, spinning out

Ex.

6-5.

Mozart

m yp

'^

J

:

*

last

^

portion of measure 2

*

is

treated

an extended contrasting phrase.

String Quartet, K. 499,

I.

'

''''"' ^^r>J -^-

i

;

J

J

J

IJ-

[^

Jj

t^uur^-

mi

^^J

'

ijiju.

^

J

7^

THE EXTENDED MELODY

Ex. 6-6 illustrates a sequential section that is not diatonic. Note that the melodic pattern remains identical because the same intervals are used.

Ex. 6-6.

Carter

Elliott

Piano Sonata,

:

Used with the permission of the copyright owner,

Mercury Music Corporation.

j

^

'i

?

Jffl-^

^

##

3

mm

Repetition need not be as obvious as in the previous examples.

rhythm

tions repeat only the

Some composi-

melody of Ex. 6-7 none of the pitch patterns are exactly the same, but the phrases that have the same rhythmic shape contribute

Anon

Ex. 6-7.

f

Is

to a

/cumen

pr

p

^

i

^

f

p i

J'j

i

\

balanced design.

In.

Fr pirprjij

iif

J

Sumer

:

or motive of a phrase. In the

JJy

i

jjJ-

^ ^ i

r J

J'j

i'j

J-' i

f

j-mJ

hj

i

JiJ JJ

J'J

r|f J>J JjJ pp

i

r

Mr

pr

p

i

pr

j^

J>

^^^

^^

"

may be lengthened by adding material. One characteristic procedure is the repetition of a small melodic unit at the end of a phrase. The cadential extension in Ex. 6-8 lengthens the third phrase by reiterating the closing figure. The extended length of six measures better counterbalances the two preceding four-measure phrases. Just as melodies are lengthened by phrase repetition, so a phrase

Ex. 6-8.

Beethoven: Piano Sonata, Op.

2,

No.

1,

Allegretto

»

»

I

1

m ? te:

r

J

1

1

i

j

* #

^

r^ihi'ii

^ ^ 1

>:

it :zt

^m

—

THE EXTENDED MELODY

79

Another type of extension delays the appearance of the cadence pitch. Because of the stress pattern and the pitch motion, we expect the cadence to occur at measure 8 in Ex. 6-9. But our anticipation is deceived, for the motion to tonic is temporarily halted by afermata, followed by the repetition of measure 7 in a stretched out version in measures 8 and 9 and measures 10 and 11. This delay intensifies our expectations and emphasizes the finality of this section.

Ex. 6-9.

Beethoven

i

Piano Sonata, Op. 53,

I.

J

J A

may

phrase also

the lengthening

is

l^'

As in the cadential extension, accomplished by the repetition of some melodic unit, as in Ex. be lengthened by

interpolation.

6-10.

6-10. Brahms:

Ex.

j('f >):.r

The

[j i

Symphony No.

r

J

J

I

3,

y-j

J

J

M

'

^

—

P m

rcrr irfrr rrr

1*

^ pTTI

i

i

f^

dependent upon previously recognized phrase lengths. Thus a phrase built from motive repetitions or a phrase in which a motive fragment is repeated is not necessarily an extension by interrecognition of this type of phrase extension

is

polation.

As can be seen first

in Ex. 6-1

1,

interpolation by sequence

phrase establishes the phrase length

we

is

another

possibility.

The

expect to hear continued, but the

sequential repetition of this initial pattern extends the second phrase considerably.

Ex. 6-11.

Wagner:

Die Meistersinger, Prelude, Act

80

THE EXTENDED

MELODY

Succeeding phrases may also be shortened, as in Ex. 6-12. Again an expectation of a four-measure phrase has been established however, the second phrase is only three measures long. In this case the compression results from the "mosaic" block statement of the motive of phrase one in the second phrase. This type of com;

pression

is

called truncation. Since truncated phrases result

from shortening phrase

duration, the effect of compression will be understood only

have been previously established, and to an earlier phrase.

Ex. 6-12. Schubert: Piano

Sonata

Andante

iim

j^ii

\

ijj]

\

in

A

if

if

the phrase lengths

the truncated phrases are easily relatable

Major,

II.

m ).m^ \

\

jf Vi ji^^m i

another type of compression occurs when the close^^£qne phrase is t he be-^ ginning of the next phrase, as in Ex. 6-13. Such phrase interlocking is called _elision._ Still

When

phrases elide continuity

is

produced by negating a cadential "breathing

point." Elision also creates a shorter total time span for the interlocked phrases

than when a separation occurs between phrase endings and beginnings.

Bach: Sonata No. 3 for Flute and Harpsichord,

Ex. 6-13.

II.

Confrosf. Successive repetition of a single musical pattern provides rather

limited possibilities for extending a melody. Generally, the repetition of a

phrase unit

makes

is

"interrupted" by the introduction of a contrasting pattern, which

later restatements of the initial pattern

more

by

Ex. 6-14.

slight

first

changes in rhythm, and by the transient-terminal cadence.

Beethoven: Symphony No.

^

and welcome. by a change of con-

interesting

In Ex. 6-14 the second phrase forms a contrast to the tour,

first

2,

II.

h^ x

P

r

iLC/

i

p

r

rt

^m 1

r-

irijir

^

^ r

THE EXTENDED

MELODY

81

1

* ^ *

c/'^Pto \ui^

» ^ *

The

third

'rn

P r^rr l

l

and fourth phrases are

i

^ {nj

r

c/^ g

\

i

B'

r

repetitions of the

i

first

two.

Pa

C-££l

[rrr

l

r

^^ The two

part se-

quence of the fifth phrase contrasts with the preceding phrases, and the sixth phrase adds still further variety to the whole melody. For convenience, a letter system of diagraming is used to designate the various parts of a melody. If we call the first phrase of the preceding melody a, the form representation of the total melody would be ab ab cd cd' There are four sections, .

each resulting from the combination of two phrases. Since each of these sections forms a larger unit, it is helpful to "reduce" the diagram to its lowest common denominator, A A B B' a b Variation.

understood.

Of

a b

c

d

c d'

In their simplest forms, repetition and

greater interest are those melodic

elements of both,

procedures which combine

gradations of contrast and repetition brought about by

i.e.,

varying the materials.

contrast are easily

The

fourth phrase of Ex. 6-15

second phrase. By inverting the perfect

is

obviously related to the

measure 3, the resulting perfect fourth produces a change of pitch contour in measure 7. Note also that some of the pitches in measure 4 are eliminated in measure eight to create a clearer cadential motion. As a whole, phrase four is a variation of phrase two.

Ex. 6-15. Schubert:

Andante

Impromptu, Op. 142, No.

^ ^^

We

fifth in

fc

3.

^m S

1 r

^

have already observed that phrases

1 r

Ex. 6-16.

like the first,

II.

Andante un poco mosso

^

have the same changed. In Ex. 6-16 the second

is

but the pitch structure

Schubert: Trio, Op. 99,

0-

in parallel construction

rhythm, but the pitch structure frequently phrase begins

0—0 M

zz

is

a variant of the

first

phrase.

— THE EXTENDED MELODY

82 Notice that each of the phrases

is

four measures long, containing a three-meas-

ure and a one-measure extension. Both measures 4 and 8 are varied by simple elaboration and are thus variants of measures 3 and

Some forms

of varying a

6, respectively.

melody normally occur when melodic

units are re-

peated in the later portions of a melody. In Ex. 6-17 both the pitch and rhythm patterns of the phrases are slightly ornamented, producing a

more

active variation

of the initial statement.

Ex. 6-17. Le

Begue

Bouree.

:

#—(^

yfc^F^

p

m. 1-4

—^ Lj

7^^

/|*

P m

f^K

m

^ ""Tr

^ M f M f '— f

rrrrrr

f

rr

u »

f * ^ lt r

a^

^ \

^J

^ !

i-»—i^id •••••• §

\'

^ h

13-16

Frequently only parts of a phrase are varied in a later appearance. In Ex. 6-18 the approach to the final cadence of the excerpt is the same rhythmically in both versions.

However, the varied version contains figurations not hinted

at in the

original.

Ex. 6-18. Satie: Fifth

Nocturne. (C) 1920 by Editions

Max

Eschig,

Paris.

Renewed 1948.

Reprinted by permission.

^m "m r

^

E &.

*

#

^^^^^^^^^

^

F

r

P

r

r

p^

s

^

^m

In variation movements melodic embellishment sometimes becomes the principal procedure of melodic organization. Ex. 6-19 shows typical changes a phrase

might undergo in a variation movement.

THE EXTENDED

Ex. 6-19.

n^

83

MELODY

Beethoven: Symphony No.

it

5,

II.

^

^^

rj^n

WmT^

a greater or lesser extent these procedures of variation could be used in any composition, either forming the basis for an entire movement, or appearing less

To

any event, the relation of a variation to the original is usually apparent. However, the embellishments could reach a state of complexity in v^hich the original melody is no longer recognizable. In some melodies rhythms are varied by changing the durational values of all or parts of a phrase. In Ex. 6-20 the pattern of measures 9-12 is an augmented (lengthened) version of the preceding patterns in measures 5-6 and 7-8. consistently as an extension procedure. In

Ex.

6-20. Beethoven: String Quartet,

,y The

ii^f'f

i

Op.

18,

No.

2,

IV.

Pm

pattern that begins in measure 11 of Ex. 6-21

version of the pattern that begins in measure

5.

If the

is

a diminished (shortened)

tempo remains the same,

augmentation lengthens a phrase; conversely, diminution shortens a phrase.

Ex.

6-21. Beethoven: String Quartet,

Op.

18,

No.

2,

iV.

84

MELODY

THE EXTENDED

Sometimes a melody is extended by inverting the whole or a part of a phrase. The rhythm of the pattern that is inverted might remain the same, but its intervals are reversed, ascending motion duplicated by descent and vice-versa, as in Ex. 6-22a and b.

Ex. 6-22a. Bartok:

& Son

Mikrokosmos, Vol. IV. Copyright 1940 by Hawkes by permission of Boosey & Hawkes inc.

(London)

Ltd. Reprinted

112

3

4

•

i jj u jj

I

j^

J J J J J

j)^

m

^f p I

I

,

^f

r> m

^

I

or cjij Inversion

Ex. 6-22b.

Brahms

:

A German Requiem.

t-

gi

^J N

W

J|J Inversion

Since change of contour creates only pitch contrast, the inversion of a pattern easily recognized. Notice that only the first portion of Ex. 6-22a

is

inverted.

is

Note

measure five is a partial augmentation of measure 2. (This excerpt is noteworthy for yet another reason; it contains only eight different notes.) Variety of phrase structure frequently is produced by mutation. In Ex. 6-23a, the fourth phrase repeats the third phrase in the parallel minor key; the third phrase in Ex. 6-23b also is in the parallel minor. In the latter, mutation coincides with the also that

beginning of a new section, while in Ex. 6-23a phrase repetition

Beethoven

Ex. 6-23a.

m

:

i

P

i

r

If

involved.

Piano Sonata, Op. 53, Rondo.

Mr

^^ j

is

r

i

r

h

\

>

pn>

^

^

r

MT

r

m

p

0-

M

m.

r

If

85

THE EXTENDED MELODY

6-23b. Schumann: Carnaval, "Reconnaissance."

Ex.

i)

)aTCjfiOI^

Changes of tonality help to intensify our awareness of form. In Ex. 6-24 the first and last sections are in G, while the middle section is in D. This change of tonal focus, plus other aspects of phrase contrast, delineates the form. In fact,

it is

probably more accurate to say that the tonality change coincides with other contrast-producing elements, such as the change in contour and pitch motion. As is often the case, the return to G provides unity, even though earlier melodic material is

not restated.

Ex.

m

6-24.

Weber

r

^

:

pr

Feldeinwarts flog ein Voglein.

^^^

r

r

^

f

i

fr

Change of tonality frequently is introduced at that a new formal unit will follow. The return

^

m

the end of a section, announcing to the original tonality

and the

restatement of the opening material coincide in the following excerpt, vividly delineating the form.

86

THE EXTENDED MELODY

Ex. 6-25.

Schubert

Der Alpen Jdger.

:

j^^ Our awareness

f J

i

j)

of musical form

new formal

the statement of a tial to

i

is

aided

its

when

unit. Generally,

an extended composition than

center provides variety with

/^^^ to a short

i

r

i

^

a change of tonality coincides with

changes of tonality are more essen-

melody. In either

case, a

new

tonal

new focal point.

Exercises

For more detailed assignments see Materials and 1.

Extend Ex.

6-1

for four

Structure

of Music

more measures. Use one of

I,

Workbook, Chapter 6.

the procedures discussed in the

chapter. 2.

Find examples in music and change of tonality.

3.

Write a melody that has as

4.

Listen to kosmos,

5.

/

6.

your instrument or voice that contain sequence, variation, its

basis the

rhythmic structure of Ex.

6-7.

analyze the phrase combinations of various works from Bartok's Mikro-

Volume IV.

assignments as the basic unifying factor of a three-phrase melody. Create variety through the use of the procedure of inversion. Write an experimental melody four phrases long that contains no repetition of pitch or

Use one of the motives invented

rhythm 7.

and

for

for previous

patterns.

Listen to the

describe the

first

ways

2, No. 3. List and which Beethoven varies the motive and the phrase lengths.

movement of Beethoven's Piano Sonata, Op.

in

Basic

7

Melody

In the aspects of

melody

—

last five

drawn to various and motive that constitute cadence, phrase,

chapters our attention has been

tonality, scale,

—

the organizational procedures and materials.

melody and reduce procedure

We

many

its

It

is

now

possible to study the full

total pitch structure to a skeletal outline.

Through

this

melodies can be seen as elaborations of essentially simple tonal

fundamental outlines basic melody. The pitches of a basic melody differ from less structural pitches because they receive, special emphasis through their placement and function. In other words, the total pattern of tones is formed so that some individual parts are more important plans.

shall call these

than others.

an automobile of all its parts except its motor and drive mechanism, its chassis and wheel assembly, and, strictly speaking, an automobile still exists. The thousands of additional parts are in varying degrees elaborations or ornamentations of the core, the fundamental mechanism. No one would seriously advocate a return to such "fundamental autos," but clear knowledge of any object car or melody begins at the basic structure. The tonality frame discussed in Chapter 2 is one kind of drastic melodic pitch reduction, representing the pitch order around which a melody is organized. In this sense, many melodies could have the same tonality frames; it is the varied "elaborations" of the frames that create the uniqueness and the charm of particular Strip

—

—

melodies.

The Mozart and Beethoven melodies

in Ex. 7-1 not only share the

frame types; they also resemble one another in the way has been elaborated.

this

common

87

same

tonality

pitch nucleus

88

BASIC MELODY

Beethoven: Piano Sonata Op.

Ex. 7-1 a.

2,

No.

1,

I.

^

S?ES

j.rirrx^Dli.i rrir^t^i^

^

The

to the

melody,

its

SH ? 'IWiC

K. 550, IV.

a basic level of pitch organization, serving as the which melodic activity takes place. is,

therij

second higher level of organization, the pitches that determine

melodic shape constitute

total

^

^

i^

fe

?

tonality frame

tonal outline within

i

3

^

Tonality frame

fS

Mozart: Symphony No. 40,

Moving on

i

3

^^ Ex. 7-1 b.

5

i

basic melody.

By shape

important high and low points,

its

is

meant

the general sweep of

beginning and ending, an d the im-

portant junctional pitches in between.

Ex. 7-2a.

i •-'

Beethoven: Basic melody of Piano Sonata, Op.

1,

I.

m^

m

;z:

() Mozart

:

Basic

melody of Symphony No. 40, 3

The

No.

y

2^

Ex. 7-2b.

2,

5

4

K.

550, IV.

6|,^r^

third (and most complicated) level of melodic organization

pattern, complete with the rhythmic

life

7

is

8

the full-blown

that creates the wonderful illusion of

1

89

BASIC MELODY

Here the tonaHty frame has been fleshed in with the patterns that link basic pitches together and form the interesting relationships that make true melody. Look back to Ex. 7-1 and compare the whole melodic patterns there with the reduced forms of Ex. 7-2. These latter abstractions are mere skeletal outlines of their parent melodies. For the present we shall view with greater interest the melodic skeleton, shifting our attention in Chapter 8 to the vital elaborations that create the final product. moving

tones,

the experience of music.

Melodic Terminal Points

From t

he

As end-points of what

last.

aries of

The

heard, these tones are the structural

is

first

melody.

last pitch

sound heard, ferred.

and time bound-

the standpoint of basic melody, the most important tones are the

Thus

it

is

particularly fundamental to melodic design because, as the last

offers

the final

an ultimate point to which all preceding pitches can be repitch in most melodies is tonic. When it is not, the pitch is.

usually a nieml^er of the tonality frame, the dominant or the mediant.

The

we saw

Chapter 2, it helps to lead the listener's attention to the tonality frame within which the whole melody will operate. The first pitch of melodies beginning on a metric accent is first

pitch

is

the beginning of melodic pattern

with the dominant and the mediant as

generally the

tonic,

ever the

pitch of the

first

with another

as

;

member

downbeat beginning,

it

is

in

lesser possibilities.

What-

usually linked immediately

of the tonality frame, thereby leaving no doubt as to pitch

orientation.

Ex. 7-3a.

Dufay

:

Mon

amy

chier

(Ballade).

Tonic beginnings

d:

W

Ex. 7-3b.

£ JM

Schubert

aa ^

:

Symphony No.

^

J

545,

K.

^

C:

b:

J J,i

Mozart: Piano Sonata,

^M Ex. 7-3c.

J

8

in

J

I

Ji

J

j

J)

W

1

I.

b minor,

I.

m

5

90

BASIC MELODY

Ex. 7-36.

Hindemith: Third Piano Sonata,

1936 by

(C)

I.

B.

Schotfs Soehne, Mainz. Re-

newed 1963. Mediant beginnings

S

L/

^^'

P

Mozart: Piano Sonata No.

Ex. 7-3e.

m

16, K. 331,

I.

*4

ic:i;r

p

^

<^>

\

^'r

p

i

r/r

r

A:

Dvorak

Ex. 7-3f.

:

^^

Symphony No.

5,

p

II

^

^F *

#

Db:

Ex. 7-3g.

de Lantins

Puisque

:

voy (Rondeau).

je

Dominant beginnings

if Ex. 7-3h.

^

^

1

Schubert: Symphony No. 8

\ri^

fiiir-

\

.

^

1-

{

in

IJ

B Minor,

i

1>

.

f

^

I.

fii^j

—

—

Melodies with weak metric beginnings the anacrusis or upbeat pattern do not often start with tonic. Rather, their first sound is usually the dominant, the mediant, or, in rare instances, the leading tone. This first pitch is then followed on the first strong beat by the

tonic

or another

member

of the tonality frame.

Ex. 7-4 show various ways in which the anacrusis melody initiates

Ex. 7-4a. Liszt:

j^'l.

Hungarian Rhapsody No.

' I

J

)

J3

IJHRML^

J^'J

liJ

If

The its

tonal pattern.

9.

^y

\

^

PJ

rJ'J

excerpts of

p

BASIC MELODY

Telemann

Ex. 7-4b.

(Ih

91

{',

!)

j)

:

Fantasia for Harpsichord No.

a iiism^^

h

^

Shostakovitch

Ex. 7-4c.

m

New

^ :

7,

Copyright by Leeds Music Corporation,

(C)

I.

^

Piano Sonata No.

fr^[lJ^ still

Symphony No.

m

**

In

:

^m

York, N.Y. Used by permission. All rights reserved.

Haydn

Ex. 7-4d.

1.

l

6,

m

rO^'^

r^

l

I'

II

II.

c^3

other melodies the

first

immediately. In association with other parts the relation

accompanying chords

(as in

made clear might be made clear by

tone's relation to the tonality

is

not

Ex. 7-5). But in terms of pure melodic structure,

the delayed establishment of tonality can create a degree of tonal suspense for the listener.

Ex. 7-5a.

This

particularly true in melodies like

is

of Ex. 7-5.

Copyright 1949 by Boosey & Hawkes Inc. Copyright assigned to Aaron Copland. Reprinted by permission of Aaron Copland, Copyright Owner, and Boosey & Hawkes Inc., Sole Licensees.

Copland: Concerto for

(Di

Clarinet,

F

lS^

i

I.

^ i

m

r

S Ex. 7-5b.

(c)

i

4

+

¥

'+•

S

i

¥

i

T

^

Chopin: Etude, Op. 25.

k^ w^ * Ab:

Ex. 7-5c.

Bortok Ltd.

:

Concerto for Orchestra,

IV.

Copyright 1946 by Hawkes & Son (London)

Reprinted by permission of Boosey

& Hawkes

Inc.

92

BAS/C MElOOy

The cadence It

is

pitches at phrase endings are also basic Hnks in the tonal chain.

not an exaggeration to think of the cadence as a point of respite at which the

can take stock of what has preceded, instantly forming an impression of the important tonal events that have led to this point in the melody. The role performed by cadence pitches is basic, then, to the total organization of the melody. listener

At this point we can make a rudimentary analysis of melody by abstracting the first and last pitches and all cadence patterns to reveal a great deal more than the tonality frame.

Brahms: Intermezzo Op. 117, No.

Ex. 7-6a.

^^

I

1.

J J

*^

r

s^

Reduction to terminal points

Ex. 7-6b.

is;

^

Barber Schoo/ for Scandal, Overture. Reprinted owner, G. Schirmer, Inc. :

4. Ex. 7-6c.

1

-

Vivaldi

ZZI

I

^

i

Violin Concerto in

:

__

L-"

C Minor,

by permission of copyright

m

f=m

W

'^-

- -L____j3

i

III.

(b*)

To make

our search for basic pitches more penetrating

we must

study units

smaller than the phrase. In addition to the terminal pitches, others are basic

because

of:

(1)

their positions as parts of the overall

relatively great duration,

and

melodic contour,

(2) their

(3) their favored metric position.

Melodic Contour If we regard a

we

melody

see that the resultant

pitches, the highs

as a line that

wave

weaves through points on the musical

possesses height

and depth. Like the

first

staff,

and

last

and lows of melodic motion are impressive parts of melodic shape.

BASIC

MELODY

93

In_melodies where a succession of peaks and valleys ar e basic.

linine; pi tches

The Samuel Barber melody

and bottoms of emphasis are incorporated that was first attempted in Ex. 7-6.

Ex. 7'7. Barber

School for Scandal, Overture. owner, G. Schirmer, Inc.

(

formed, the resultant out-

when

:

into the basic

Reprinted

by

melody reduc-

permission

of

copyright

Partial reduction)

The g follows

of measure 6

is still

lower.

not a low point of the immediate pattern, for the

is

The g

is

structurally important, however, because

of a step-p rogression formed between the low pitch of measure 5

As one is

'

"

of Ex. 7-7 becomes clearer as a basic structure

these tops tion

is

~^

level in this brief

descending

(a)

stair-step, its basic role in the

e

that

it is

part

and the

final/.

melodic shape

established.

Thi s does not mean that every step relation in a melody automatically forms a sierra gression. On the contrary, step-progression refers to delayed ascending or descending motion by steps that outline the contour of the line over the whole or a large segment of the phrase.

Almost any melody contains a step relation of some kind between some two or more pitches, but this alone does not warrant recognition as a determinant of basic

To achieve the status of step-progression such a pattern must create a recognizable uniformity within the pitch design, an obvious linking of highs and lows that controls the melodic progress from one melodic segment to another.

structure.

Ex. 7-8 through Ex. 7-12 clarify the function of a step-progression within a melodic form.

The

circled notes of Ex. 7-8 establish a clear line of ascent

portion of the pattern.

The

thus avoiding

e

J.

S.

a sizable

mere decorative another. Bach did not dominate his line alto-

of measure 3 overshoots the conclusion of the ascending pattern,

monotony and

stressing the pitch d as the beginning of the following

part of the melodic shape.

Ex. 7-8.

for

successive steps in other parts are

motions, activities which lead from one basic pitch to allow this rather strict and obvious ladder of steps to gether, for the

by step

Bach: Well-tempered Clavier Book

I,

Fugue

15.

94

BASIC MELODY

These tracings of pitch by delayed

steps

form the backbone

for

many

melodies,

either in their entirety or in isolated parts of their total structure.

As such, they lead the listener to expect to arrive at a highest or lowest pitch (depending upon whether the line ascends or descends), and in most instances this pitch of "arrival" will be a part of the tonality framework or a pitch that rhythmically "leans" on a

member

of this group.

In some melodies the step-progression forms a periodic ascent or descent clearly allied with metric accent, as in the Bach melody of Ex. 7-8. In others its contour is

more

subtly

Ex. 7-9a. Lully

imbedded

:

in the pitch motion, as in (b) of Ex. 7-9.

Overture to Alceste

s

^'

v^ rrfP V i

vpn J3^r

i

P

¥

S^tep "pro-

gression

Ex. 7-9b. Palestrina

:

Kyrie (Vestiva

i

Colli).

331

i

lH

ZUZ

-or

-O-

P

fe

m Ex. 7-9c.

m Still

^z

J.

Strauss

:

Emperor Waltz.

r^

==¥

other melodies display partial ascent or descent by delayed step relations

without forming a clear step-progression as such.

The patterns marked with brackets

BASIC MELODY

95

in Ex. 7-10 are

fragmentary; none adds up to a structural pattern that controls

the ascent or descent of the whole line.

Glazunov

Ex. 7-10.

r

The

i

:

Carnival Overture.

^rn w

r

i

zzi

fe

^r

W

highest pitches of the smaller groupings in measures 2

a regular

way

to the

apex of the

line,

the a of measure

5.

Even

important high pitch (because of its repetition in measure

by delayed

and 4 do not lead if^

6), it

is

in

heard as the most

too

is

not reached

steps.

The ascending

probably a structural feature in more melodies than the descending, but the same organization can be found as a falling pattern in enough melodies to justify recognition. In many cases the low pitch of a line step progression

is

will return after intervening patterns, creating a

mild form of pedal or "drone."

This kind of repetition serves as a structural ground over which the melodic motion freely unwinds, as in Ex. 7-1 lb.

Ex. 7-1 la.

Bach: Well-tempered Clavier Book

Ex. 7-1 lb.

Bach: Invention

Ex. 7-1 Ic.

Handel: Organ Concerto No.

^m Step

-

proijression

in

3

I,

Fugue

11.

Voices, XV.

4,

Op.

4.

m m

96

BASIC MELODY

The

pitch basis of the melody in Ex. 7-1 Ic

is

clearly a double step-progression,

moving in contrary motion to the lower. The combination of two such distinct step-lines can create the illusion of two separate parts if the lines have a distinct separation of range. The Bach melody in Ex. 7-12 is typical of such the upper pattern

"one-line counterpoint."

Its

step-progressions descend.

Ex. 7-12. Bach: Invention in 3 Voices,

No.

3.

^^^^^^^m Step progression

,s^^^jr-aj,=a "-:^

Implied parts

''pf^cj

1

^

Like two wires suspended in space, the delayed steps formed by these two lines

frame the pitch activity sandwiched in between, which in

this

excerpt

is

relatively

negligible.

The

pitches that constitute a clear step-progression are significant parts of the

melodic shape and are, therefore, parts of the basic melody. When no step-progression is evident only the peaks of melodic motion can be regarded as basic pitches,

and then only when

their metric location

and duration favor them over

their

neighbors.

Duration and Metric Locations If other elements are equal, a tone that sounds longer than those

around

or

will

more attention. Even when metric accent coincides with one pitch, another by will be regarded as more important if its duration is considerably greater

attract close

it

if it acts as

the cadence point for the phrase.

Ex. 7-13. Tchoikovsicy

:

Symphony No.

f"''^JJj J-i!

Basic

melody

5,

j:

II.

SP3=5 i

97

BASIC MELODY

embodied in the same pitch, the impressive nature of that pitch is reinforced. Such coupHngs of organizational functions produce a simpHcity of structure that reduces the Ustener's problem of

When

greater duration and metric accent are

understanding, because rhythmic

Ex. 7-14a.

Bach: Passacaglia.

'):

melody

Ex.

7-14b. Brahms:

QI

ni

i a: Basic

stress coincides

? .

i

r

-^u- r

Symphony No.

2,

Op. 73,

with metric

stress.

^^

i ^'

P"

I.

measure of the Brahms melody of Ex. 7- 14b shows how repetition within the measure can confirm a pitch's basic role. Obviously, repetition without intervening pitches is a simple extension of duration, for no other pitch competes

The

third

But repetition within the immediate pattern (of approximately one measure), even after intervening tones, also emphasizes the returning pitch. The Beethoven melody in Ex. 7-15 shows arabesques of eighth notes moving for attention.

around the repetition of the pitches that 2.

Ex.

fall

on metrical accents

in

measures

1

and

Because of their subsequent return these pitches are confirmed as basic.

7-15. Beethoven:

Symphony No.

5,

Op. 67,

Basic

melody

In highly ornamented music, consisting of a broad range of rhythmic values, some pitches act as pivots around which others skitter as orbitings around a mother

98

BASIC MELODY

planet.

Repeated returns

basic for the pattern.

to a single pitch as the rallying point substantiates

The melodies

some pitches that are

in Ex. 7-16 contain

because of their extended durations

;

it

as

basic

others are fundamental because of this con-

centration of neighbors around the one pitch.

Bach: Well-tempered Clavier, Book

Ex. 7-16a.

S Bassic mel(ody

.ff

Ex.

I

^a P m PP W-

^[Jrfj

r

:

f

s

i -^

.

rrfr

T

\

Concerto Grosso.

s

? •

S3

'ei

=

W)

7-16b. Corelli

Prelude 10.

—*-

J/

\

I

I

.

^ -pz.

I

^

^^=

^^i=^

and the tonality frame reveal the organization of pitches within a particular melody in its barest form. As we have seen, the two are quite similar, the tonality frame itself a maximum reduction of melody to the tonal nucleus of overall structure. In the following chapter we shall examine the various ways basic pitches are As dual representatives of basic

structure, the basic melody

linked together to create the logical tonal flow that characterizes the successful

melody. Naming these

links elaborations or decorative patterns

importance. Melody

as

basic structure.

The

is

much

the manifestation of

its

separation of basic from decorative

is

no indication of lesser

decorative overlay as of

is

made

for

its

purposes of un-

derstanding rather than for the establishment of a standard of musical values.

The

pattern (a) in Ex. 7-17 by

itself would interest

used as the basis for the pattern shown at

melodic statement that

(b),

it is

seizes a listener's attention

no

listener for long.

But when

transformed into a dynamic

and begs of continuation.

BASIC MELODY

Ex.

99

7-17. Beethoven: String Quartet,

^

Basic melody

t)^

Op.

18,

No.

I.

Melody

P^

=^^

1,

?

^

*

m

^

Exercises

For more detailed assignments see Materials and 1.

Select a

number

of Music

I,

Workbook, Chapter

7.

of melodies six to eight measures in length (collection of sight-singing

melodies, violin sonatas, songs, etc.).

below each the accompanying melody.

2.

Structure

Copy each melody on manuscript

melody.

On

staff

Make up

several basic-melodies, assigning one pitch to each

line of

paper, leaving

the blank staff plot the basic pitches for

one blank

measure of any meter. framework as a basic guide, add other pitches in a variety of rhythms which make a full and logical melody that you can sing or play. Be sure that the basic pitches are preserved as the dominating elements in each measure. Using

this

Follow the same procedure as in

3.

but improvise (by singing or playing) the patterns around the selected basic pitches. Be sure to keep a steady tempo in your performances.

4.

Abstract basic pitches from any melody or use basic pitches from melodies shown in chapter and create new melodies which use these as a basis.

5.

2,

this

Write a melody that corresponds to each of the following basic contours. Use any key, meter, and scale desired.

(a)

(b)

(c)

Make up

other contour patterns to be used as guides for melodies, and analyze the con-

tours of melodies found in literature. 6.

Find several melodies which clearly incorporate a step-progression (or step-progressions) as a

7.

main

Have

feature of organization.

a friend play a melody for you. Measure off the

melody and

of bars contained in the

plot the basic pitches of the whole pattern. Don't try to get every pitch at begin with the first and the last pitches, proceed to the highest and lowest, and then in other pitches as they become known.

first; fill

number

Melodic

8

Elaboration

we saw

In the previous chapter reveals the pitch organization in

its

that reduction to basic

simplest form.

Few melodies exist

in

melody

such bare

most melodies the skeletal structure is a support for the distinguishing pitch activity by which we recognize melodic individuality. The pitches that are the overlay of the melodic skeleton are elaborative; they decorate and link together the basic pitches. Distinct melodic patterns are created by the linking activity of these decorative pitches, and various types are identifiable by their particular relationship to the basic melody. outline. In

The

basic pitches of marjy melodies (particularly those of the Classical period)

are decorated by disjunct tonal activity, such as successive thirds. In Ex. 8-1,

and

b-Jlat

are the basic pitches. Because of their metric positions and lesser dura-

tions, the notes Jlat

share

the basic

Ex. 8-1.

f^-JIat

e-fiat

marked

*

decorate the basic

as root; thus, they create

e-JIat.

In

this

example both g and

b-

the effect of extending the duration of

e-flat.

Beethoven: Symphony No.

^

;z=

f

3,

Op. 55,

I.

^m

Decorative pitches such as those in Ex. 8-1 are

Basic melody

basic associates;. th.ty

elaborate

and from a basic pitch. The basic associates often occur in weak metric positions, and they generally are shorter in duration than the basic pitch with which they are associated. The simplest form of melodic elaboration is created by repeating a note. In Ex, by skipping

to

700

MELODIC ELABORATION

101

8-2 the repetition of

g-JIat

emphasizes that note; however,

relative duration

its

is

not changed by the rearticulation.

Ex.

Bartok

8-2.

:

Mikrokosmos, No. 131. Copyright 1940 by Hawkes & Son (London) Ltd.

Reprinted by permission of Boosey

& Hawkes

Inc.

and repeated pitches are important aspects of melodic ganization, but they represent only two types of decorative patterns. Other,

The

basic associates

orless

obvious, decorative patterns are also significant. The sequential phrase shown in Ex. 8-3 uses two different types of melodic elaboration.

Ex.

by Edition Russe de Musique, Renewed 1952. Copyright & Renewal assigned to Boosey & Hawkes inc. Revised Edition Copyright 1952 by Boosey & Hawkes Inc. Reprinted by permission.

Stravinsky: Octet, Sinfonia. Copyright 1924

8-3.

^ n rln\^ 2

'if;

\

:

fe

>

.3

m

s^

i^

m

O

TT tot

[r;

i

\

-o-

Basic pilches :

^ k

£1

-Q_

nx tat

-O-

-©-

Basic pitches and associates

3X tnt

J

xr

^

331

U^

Basic pitches, basic associates, and their decorative pitches

In measures 3-6 the

first

note of each measure

is

a basic pitch because of its metric

As can be seen, the predominant pitch activity is a sequence of thirds. The upper note of each third is a basic associate. In the descending motion to the last note of each pattern the third is filled in. This filler tone smooths out the disjunct motion of the sequential pattern and at the same time embellishes each position.

basic pitch.

The

decorative notes (shown as

J

in the sketch) participate in a

step-progression that links a basic associate to a basic pitch.

Decorative pitches can embellish a basic melody with either of two

diflferent

types of tonal activity: (1) the decorative pitch exceeds the range of two basic pitches or a basic pitch

and a basic associate

(as in

Ex. 8-4a and Ex. 8-4b)

;

or (2) the de-

102

MELODIC ELABORATION

corative pitch remains within the range of two basic pitches or a basic pitch and a basic associate (as in Ex. 8-4c). In Ex. 8-4, and in all subsequent examples of this

chapter, the basic pitches are represented by o

the decorative pitches

by J

,

the basic associates by •

,

and

.

Ex. 8-4.

^^

J^^

xn

J.

33=

J-

331

Decorative pitches have names that describe clearly the role they play. For example, since most melodies use a preponderance of steps, decorative pitches called

^sing

appear frequently. This

tones

is

an apt description, because passing

tones connect two different basic pitches (or a basic pitch

Ex.

Ex.

and

its

associate), as in

8-5.

8-5.

/Ml

W

^m

^^

-o-

^

Passing tones are often shorter in duration than the pitches they connect, and they

appear in both accented and unaccented positions. Since accented tones tend impress us as more important than unaccented, thejunaccented passing tone

more common. Ex. 8-6a and Ex. 8-6b show both

types.

The

d-natural in

to is

measure 4 of Ex. 8-6c

is

a chromatic passing tone. Note that the diatonic passing tones (notes belonging

to

one diatonic

link

Ex.

scale) link

two notes a third apart; chromatic passing tones generally

two notes a major second apart.

^ ^ S 8-6a. Beethoven

-.

String Quartet,

£t

^

i

331

^

Op.

74, IV

j),n KyJ^JJ^ |

ia=

^^

^mX

s

31

^

i

MELODIC ELABORATION

103

Ex. 8-6b.

^m

m ma

i

^

F^

33:

te

Beethoven: Piano Sonata, Op. 110,

^m ^

Ex. 8-6c.

t^

t">

1>V

P^ ^ ^

TI"

U^^'iigii'

I.

^^

'^^^

pCJI^j-^p

^ "

xc

(

# )"

^^ ^

J

p

l>o

trrr

In highly ornamental melodies several tones sometimes link structural pitches

more than a third apart. Generally these linking notes are of short duraplaying the same decorative role as a single passing tone. For this reason they

that are tion,

also are referred to as passing tones (bracketed in Ex. 8-7).

Ex. 8-7.

Bach

:

"Gigue" from

Liffle

Notebook of Anno Magdalena Bach.

JJ^JJJ^

-(r&h

f>

It

^

Another decorative pitch that appears frequently is the neighbor tone} Like the passing tone, this type of embellishment can be found in both accented and unaccented positions. Step motion is again involved, the neighbor moving away (either up or down) from a basic pitch and returning to it. Neighbor tones also may be diatonic or chromatic. Since neighbor tones embellish a single tone, delayed repetition

is

more

interesting

The neighbors

{f-sharp in

involved. This emphasizes the repeated tone, creating a

pattern than simple rearticulation. In Ex. 8-8 the neighbor tones are indicated by J

measure

•

9, a-sharp in

Sometimes called

measure

1

1) in

.

Ex. 8-8b are chromatic.

auxiliary tone or returning note.

104

Ex.

MELODIC ELABORATION 8-8a. Mozart: Piano Sonata, K. 576,

If'

'i

i Ex.

^

UIU it

8-8b. Beethoven

:

-e-

III.

nc

*5

i m:

J.. J

I

.. I

Piano Sonata, Op. 90,

^^

^ -&-

331

s

nU'J

J'

l

/^ii^

xn

Chromatic passing tones and neighbor tones do not change the tonal center. Because of their brevity, the emphasis they produce is insufficient for the creation of a new focal point. If their duration were increased, a new tonal focus might result. Therefore, even if a note has the appearance of a new leading tone, duration determines the amount of influence it will exert and distinguishes a chromatic decorative pitch from a chromatic structural pitch. The frequent use of passing tones and neighbor tones does not make them more significant than other kinds of decorative pitches. As a matter of fact, their repeated occurrence only indicates that the conditions for their particular decorative role are often present. Thus, in those melodies containing structural pitches that are

a third apart, passing tones smooth the line by

filling

in melodic gaps, thereby

bringing the structural pitches into closer relationship. Similarly,

play an important part in the structure of a melody

(as in

if

repeated tones

Ex. 8-2), the effect of such

is intensified by the incorporation of neighbor tones. Both the passing tone and the neighbor tone are approached and followed by step. Although motion by step is a factor in most decorative patterns, certain types do not use this step-step configuration. Sometimes a decorative tone is given greater emphasis because it is either approached or left by skip. This added emphasis

repetition

directs attention to the decorative tone; consequently, decorative patterns con-

taining skips other than between a basic pitch

and a

basic associate appear in-

105

MELODIC ELABORATION frequently.

Two

leaning tone^

and the

different decorative pitches can be classified in this escape tone^.

Leaning tones are approached by skip and then move step. Since skips

way: the

to a structural pitch

by

tend to create emphasis, the leaning tone directs attention to the

note of arrival by delaying

it

momentarily. Furthermore, the motion by step to

the embellished tone creates the impression of "leaning," which explains the use

of this particular descriptive term.

Ex. 8-9.

* Tnr

i

za

33:

f

=QI

X-eaning tones appear in both accented and unaccented metric positions.

They

are usually shorter in duration than the notes they embellish, and the motion to the subsequent basic pitch

is

frequently in the opposite direction from the skip

that introduces the leaning tone. In all cases

it

follows the pattern of skip (either

up or down)^tep. In Ex. 8-10 the leaning tone in measure duration tone

Ex.

is

is

clearly indicated

is

1

by the notation. This

literal

8-10. Mozart: Piano Sonata, K. 284,

III

(Variation

If this type of notation

representation of a leaning

same way

XII).

1-&-

is

JOO

not used, the duration of the leaning tone

as the other notes. In Ex. 8-1

1

the basic pitches create an ascending step progression.

Sometimes called an a^jjwggMtura. Sometimes called an ecfm^^.

is

designated

by example

the leaning tones are not set apart

notation, but are notated as part of the total fabric of the phrase.

'

relative

^ ^ zaz

'

its

common.

^I:u_

the

easily recognized because

In

this

106

MELODIC ELABORATION 8-11. Beethoven: Piano Sonata,

Ex.

(iV-'^ :

(

^

P

.

«« '

*

* *

Op. 27, No.

2,

J:J .JJ..'-J -SZ_ZSZI2I

m m m m

|

•>

^4^

s

-^•^

o

*F

xt.>

=fc|P3=

Sometimes the leaning tone and the pitch it embeUishes have the same duration. \Vhen this occurs it can be difficult to difTerentiate between decorative and structural notes. However, in Ex. 8-12 the leaning tone is also the leading tone of the key, and it embellishes the tonic note.

Ex. 8-12.

Mendelssohn: Midsummer Nighi's Dream, Intermezzo.

iM

-?*-

331

rrsz

XH

XE

^

'iij^'j xc

331

r

r-

In Ex. 8-13 the chromatic leaning tones emphasize the second and third scale steps,

while the diatonic leaning tones emphasize the tonic and the subdominant.

Notice that the duration of the structural pitches varies, and the half-step relations create a strong motion to the structural tones.

Ex. 8-13.

Beethoven: Piano Sonata, Op.

14,

No.

2,

I.

jO^

i

^i=^

:^Mz

^^Sc "cr

y^=^

^=o=

f

i"

A more complex situation is illustrated in Ex. 8-14.

"cr

f

331

Here the duration of the leaning tone is greater than that of the embellished note. In measure 3, a is a basic associate o{ f-sharp therefore, even though g-sharp receives greater stress because ;

of

its

duration,

its

melodic role

is

decorative.

107

MELODIC ELABORATION Ex.

8-14. Carter:

New

Woodwind

Quintet,

I.

(C)

1952 by Associated Music Publishers,

Inc.,

York. Reprinted by permissior.

The melodic

opposite of the leaning tone, the escape

tone,

or a basic associate by skip, while the motion preceding

it

can be found in both accented and unaccented positions,

moves to a basic pitch is by step. Although it it

is

usually an unac-

cented elaboration.

,{:^^ yfcj

^l^-«lO P /sl^-

Ex. 8-15.

rin i

i=^

i

h

s

}

\

31

3X

32

33:

Like the leaning tone, the motion away from an escape tone usually involves a change of direction, as shown below. In both examples the decorative note "es-

capes" away from one important tone before moving to the next.

Ex. 8-1 6a.

Chopin: Piano Sonata, Op. 58,

i^<"ll^\,\ xn

r

r

i

Ex. 8-1 6b. Bach: St. John Passion,

L^^^utnr i^

Chorus No. 23.

^

^

^^

^^

m

i

I.

^

^S

O I 'm

r

p

Ji-

^/^

108

MELODIC ELABORATION

Sometimes, however, the motion continues in the same direction, as in Ex. 8-17. We can still recognize this as a variation of the more common pattern which changes direction.

8-17. Beethoven: Piano Sonata,

Ex.

Whichever direction the tones surrounding

Op. 101,

I.

moves, the escape tone

it it.

If not,

it

is

usually of shorter duration than

normally appears in a

less

prominent metric

position.

The

decorative patterns discussed in the preceding sections involve only one

embellishing tone, with the exception of a group of passing tones used to

an interval larger than a

third, or a third

with chromatic

activity.

The

fill

in

figure called

a neighbor group always involves two decorative tones that embellish a single basic

Both decorative notes are neighbors to the basic tone, one located a step above, the other a step below; a skip occurs between the two neighbor tones, the resulting pitch pattern forming a step-skip-step sequence. Often one of these

pitch.

decorative tones

is

unaccented, the other accented.

The neighbor groups cadence tone

is

in Ex. 8-18 embellish the

in evidence for a relatively long period of time, the neighbor groups

in this excerpt create greater tonal activity

Ex. 8-18.

r»

Haydn:

String Quartet,

.

r

!

'' i

i

.r

rrr XE

$

cadence pitch. Since the repeated

i

Op.

r rr

331

and

74, No. 2,

m

variety.

I.

r?lf f rrif r |

33:

zee

f

^.

^^EEi^ ir rrruf rrrLj r^r' i

^

#

^* 331

^

i

~cr

^

U3I

-Q-

MELODIC ELABORATION

109

In Ex. 8-19 the neighbor groups extend the duration of the basic pitches. Notice

how

closely the decorative activity of this figure resembles the neighbor tone

figure.

Ex. 8-19.

Mozart: String Quartet, No.

m

fct «4

18, K. 464,

I.

's"

i

^ ri

-tTTT

t

i.

^

331

Another type of decorative

i

^

-O-

-O331

preannounces the appearance of a basic pitch. It is by nature an unaccented pattern, almost always of lesser duration than the pitches surrounding it. The pitch motion is generally step-repitch, the anticipation,

articulation, as in Ex. 8-20.

Ex. 8-20.

J.

S.

Bach

:

Two-Part Invention, No.

fi.i,MLrr££gC/^ =^^t

SE

_Q_

-e-

i

2.

331

3X1

Sometimes the motion preceding the anticipation rearticulation pattern. Generally

when

is

by

skip, resulting in

this variation of the

a skip-

more common pattern

occurs, disjunct basic associates are also present. Therefore, the anticipation an-

nounces one of the notes that

is

contained in the disjunct

line, as

can be seen in the

opening of Ex. 8-21.

Ex. 8-21.

Beethoven: Piano Sonata, Op. 31, No.

t= B $

III.

^

S

a

xn

-^rr The

3,

suspension

is

established

by a basic pitch that passes

to

another basic pitch

or to a decorative pitch by step, usually down. In this passing process the

first

770

MELODIC ELABORATION

beyond a metric or rhythmic accent by means of a tie or rearticulation. This delays the appearance of the second basic pitch and makes the middle note of the pattern fall in an unaccented position. basic pitch, extends

Ex. 8-22.

^

i

^ The

^

suspension figure

longed by means of a

characterized by the following: (1) a basic pitch

is

is

pro-

or rearticulation; (2) this basic pitch extends past a metric

tie

or rhythmic accent; and (3) this suspended basic pitch moves to an unaccented basic pitch or decorative pitch by step.

In Ex. 8-23 a suspension appears on the first beat of measure 3. Here the suspension is created by the tied basic /. The result is an elaboration of the phrase rhythm. In addition, the entire process emphasizes the basic pitch more than if the suspension

Ex. 8-23.

had not occurred.

Hindemith: Mathis der Maler,

I.

(C)

1934 by

B.

Schott's

Soehne,

Mainz.

Re-

newed 1961. Reprinted by permission.

T

^m

i

i

_Ol

XL

In Ex. 8-24 the duration of the basic g is extended by its rearticulation on the first beat of measure 4. This delays the anticipated appearance of a different pitch

on an accented

first

beat.

The

rearticulated suspension creates an effect similar to

that of the tied suspension.

Ex. 8-24. Tchaikovsky:

Symphony No.

5,

m

5

•e-

—

"cr

33:

lU

MELODIC ELABORATION

Sometimes the motion of the suspended basic pitch to the second note of the pattern is "interrupted" by the interpolation of a decorative pitch, as in Ex. 8-25. Here the two tones of the suspension figure are separated by the interpolated leaning tones.

Ex 8-25. Bach

:

Arf of the Fugue.

r

I

$

e

i

5SX

^

ri

r

i

j

r

i

1

CjT cjf

i

^

^

1

031

-O-

^

£

"TV

-n"

r

melody alone is considered, it sometimes is difficult to distinguish between basic pitches and decorative pitches. Most melodies occur in association with other If

parts, such as other melodies or chords.

tion

When

all factors

are weighed, the distinc-

becomes more apparent. Outline of Decorative Pitches

Type Passing

Pitch

Characteristics

Appears between two different

Step-step

Tone

basic pitches or a basic pitch

and a basic Neighbor

Rhythmic

Pitch Characteristics

Motion

Accented or

un accen ted

Tone Leaning

Appears between two

Skip-step

Tone

basic pitches or a basic pitch

and a basic

Group Anticipation

Step-skip-

Step-reartic-

ulation

Two

;

or

skip-reartic-

unaccented

different neighbor

tones

unaccented

the last of

which

Accented or unaccented

Appears between two different pitches,

j^jJy:ufnJLJL

Usually

associate

elaborating one basic pitch

step

.u^iJpnQai^tlUL

Accented or

basic associate

Appears between two different

Step-skip

Tone

Neighbor

different

basic pitches or a basic pitch

and a Escape

unaccented

associate

Elaborates one basic pitch

Step-step

Accented or

Unaccented

is

a basic pitch

ulation

Suspension

Step

Involves only two pitches, the first

of which

is

a basic pitch

^ c

n

Accented

nJflUAhO

(X

MELODIC ELABORATION

772

Exercises

For more detailed assignments see Materials and 1.

Structure of

Music

I,

Workbook, Chapter

Determine the basic pitches of familiar melodies. Then use these basic melodies

8.

as the

pitch framework for melodies that you write. 2.

Use the phrase patterns from any example

rhythmic basis

for melodies that

you

Create "new" melodies by elaborating the basic melodies of any of the examples in

this

as the

write. Before writing, sketch in a pitch framework. 3.

chapter. 4.

Create an original basic melody. Then elaborate this framework, using the same basic for melodies in simple and compound meters.

melody 5.

6.

Describe

all

of the decorative pitches not identified in the analyses given in this chapter.

Analyze melodies selected from the following: Bartok, Mikrokosmos, Volumes I and II; Bach, English Suites; Mozart, Piano Sonatas; Beethoven, Piano Sonatas; Stravinsky, Sonata for Two Pianos; etc. Reduce each of the melodies selected to its basic pitches; then identify the role of each of the decorative pitches.

;

Two-Voice

9

Combinations

Our

study thus far has dealt with melody. Although

melody with a

we

usually

prominent voice or instrument (as it is quite natural how melody exists in one way or another in each voice or part of a composition, and how features of melodic organization are presassociate

to do),

it is

single

essential that

we

see

ent in varying degrees in different

styles,

forms and textures of music.

Texture

Texture meanings.

is

a word that, as used by musicians, has taken on several different

It refers to

the

number

of voices or parts in a composition or section,

each other. For instance, our next area of study will deal with two-voice textures, i.e. two-part music. But in addition, the texture of two-part compositions is often contrapuntal. Contrapuntal texture, that is, co unlerpoint, results from the si multaneo us o ccurrenc e of two or more melbut

it

also denotes the relationships of parts to

both o f whicjunajntain somejjegree of ind.ep£rideiice. more general distinction can be made among three basic kinds of textures

odies,

A

which a predominant melody chordal arrompaniment^ and polyphonic, whk hjiter-

monophonic, r,omprising_ajs ingle vo ire; homophonic, in

is_supported by an essentially ally

means "many

polyphony

is

voices ." Contrapuntal music

is

necessarily polyphonic, but the

heard as the result of rhythmically independent voices.

Rhythmic Association

The

possibilities

of rhythmic association for two combined voices are enormous,

but several basic observations can be made.

A

comparative study of the examples in this section will reveal several different kinds of rhythmic combinations, each of which represents a common treatment of two relatively independent parts. ?J3

^

*

114

TWO-VOICE COMBINATIONS

Ex. 9-1. Leonin (12th centur y):

m

^^ —5

-i^

t£Uj^\^CrUr&

^ ^ ^^ s ^ ^ fe^ ^^ ^^

P

Orflonum/ilMX^ J^Ajm [crt

o

1

1

r

i,C<

c

^

i i3

i

A

(

Ex. 9-1 contains two voices of contrasting rhythms organized in

%

meter.

The

upper part clearly predominates because of its greater activity and pitch variety. Both parts are unified through the use of recurrent patterns. This is a rudimentary kind of rhythmic association.

A

relationship of 2 to

Ex. 9-2.

Handel: Suite

A

active

VII

1

(

for

f

)

is

established in Ex. 9-2.

Keyboard, Allegro.

and more interesting upper line is accompanied by a slower paced lower voice, which by itself is somewhat dull, since it consists mainly of continuous eighth notes, outlining broken chords. However, it is a logical foil for the more active part, providing a solid tonal-rhythmic basis for the upper voice. In the second measure the lower voice momentarily assumes a leading role. A more smoothly fashioned supporting part is seen in Ex. 9-3. Here the two voices are completely independent rhythmically, and each makes a perfectly acceptable

more

melody.

Ex. 9-3. Marini

:

Sonata for Violin and Organ (two outer

Vln

rP#=^

^

^S -iS^

33=

parts).

^ ^ XE

—

—

rWO-VO/CE COMBINATIONS

115

^m^

f

P

i

^

P

In contrast with the excerpt of Ex. 9-2, the lower voice stands out as a associate of the top part, while providing a solid foundation for the

The rhythmic

tonal motion in the upper line.

more Hnear activity and

contrast between voices

is

perhaps

the most engaging feature of the example.

More voice

equality of movement occurs in Ex. 9-4,

and accompaniment

Haydn

Ex. 9-4.

Piano Sonata

:

'^^—1»

/Ts^-l

'hK

I

is less

J

[

P

[J

in

— I

distinction

between upper

obvious than in Ex. 9-1 and Ex. 9-2.

E-f)at,

^

and the

—r

III.

-f

[^ Li

Both phrases are begun by the upper part alone, and its rhythmic diversity establishes it as the more interesting. In the second phrase, however, the voices are treated imitatively, and the lower part matches the upper in activity and design for two measures. The close of the second phrase restores the original relationship

rhythm and design. attention in Ex. 9-5. Such competition

of leader and subordinate associate by contrast of

Two

equally active parts compete for

infrequent in two-voice textures, since the capabilities of our

own

is

hearing almost

two equally active voices. Although we can shift attention from one voice to another to understand essentially what is going on, the problems of doing so when both parts are equally active are many, particularly rule out the clear perception of

if

such activity

is

maintained

for

very long.

776

\^ Ex. 9-5.

Ockeghem

Agnus

:

TWO-VOICE COMBINATIONS

teidAj>-vu-

Dei.

^ ^

m

si m

V

^iiiJ"^'-

^^^^

^

^^ ^m r^ ^

^

J

fj^^^

«-

m

0-m-0

V- J j

^

i

3Z

^ s

r

^ *

p

*-n^^

I

#-^

In contrast to Ex. 9-5 by Ockeghem, a clear rhythmic distinction between two interesting independent voices can be easily perceived in Ex. 9-6.

Both parts reveal individual contours and remain rhythmically independent. Although the lower (piano) voice clearly provides a strong tonal framework [a minor) for the upper, its rhythmic individuality makes it equally important.

Ex. 9-6.

Piston: Sonata for Violin and Piano, Inc.,

New

III.

(C)

1940 by Associated Music Publishers,

York. Reprinted by permission.

^ M ^ m w^ ^s ^ ^ ^ m ^ ^ ^ ^i ^

Viol lolin

'

'lano

——

P^h ~ m

I

N

0-

-0

r^

t

•

F

^

_f

m

I

_

m

Col sva

i

5

ffs

^

7WO-VO;CE COMBINATIONS

117

In Ex. 9-6 the rhythmic separation of parts

more

readily the activity of both voices.

equally

(

ir

independence

is

When

minimized, and other

enables the listener to grasp

The_recogniti on and perc eption ., of

impo rtant, simultaneou sly heard melodies

voices have contrasting durations.

)

identical

is

made most

clear

when

the

rhythms occur simultaneously,

factors, particularly pitch association, direc-

and contour determine the degree of independence between parts. Ex. 9-7 contains a rather equal distribution of the same kinds of activity between parts. The listener is drawn from voice to voice, so to speak, by the give and take relationship which establishes the lower part as an imitator, derivative, or "bortion,

rower" from the upper. The lower voice systematically echoes the opening motive of the top voice and punctuates the movement of the continuous upper voice with octave leaps in eighth notes, followed by

Ex. 9-7.

Bach

:

Invention

in

rests.

E Minor.

.uv;

It^^Mf- f :^tm^^^

JJ^J[/ l-i

'}h;^i

The cadences

1^

^^

T=^

of this excerpt are clearly

and are always placed

m

\

marked with eighth

\

^^T

^

notes in both voices

so that they coincide with metric strength. Perhaps the

most interesting feature of rhythm in the example is the way Bach leads the voices to a rhythmic climax at measure 5. In measure 4, the lower voice, as if pulled along by the activity in the upper part, joins in the movement established by the

178

TWO-VO;C£ COMBINATIONS

top part to produce a logical and convincing rhythmic peak. Longer durations are introduced in the lower voice in measure 6, approaching the cadence at measure

and natural relaxation of activity. The opening of Bartok's First String Quartet, shown in Ex. 9-8, contains a rhythmic association somewhat comparable to the Bach excerpt discussed previously. It affords an excellent study of two-voice association in contemporary music and illustrates several of the basic principles noted in this chapter. 7,

thus affecting a coherent

Ex. 9-8. Bartok

:

Hawkes

String Quartet No. Inc.

Sole agents for

1

(opening). " Koitura "

Reprinted by permission of Boosey & (Hungarian Trading Company) in the

U. S. A.

Lento,

^"=50

1st

=tssjf

Violin

Violin

is

Vioh

m

2nd

Cello

We

^

n n

m

c.

p

#

s

^

have surveyed three basic rhythmic associations thus far ( 1 ) a predorninant meloLdy., supported by a much less engaging associate; (2) a combination, fi£.tWO rhythmically independent parts, each of which makes acceptable melody wit h one understood as a leading voice, creating a give and take relationship; and (3), two equally active parts which move in different durations. Jmitation may occur in any kind of rhythmic association, but it is most commonly found where-the voices operate in a give and take, or leader-follower plan, or where both parts are of equal interest and importance, as in the first five measures of Ex. 9-8. \Vhen t wo voices employ identical durations (note against note style), the upper part usually :

TWO-VOICE COMBINATIONS

??9

and independence of parts depends on contour, and pitch associatio n in gener aL-

prevails,

factors such as nnelodic direction,

Combination of Basic Melodies; the Two-Voice Framework

we noted

Earlier

that most melodies are unified in terms of pitch structure

a simple tonality frame. This frame clarifies the

tonahty of any single

formed by prominent pitches which are

is

The

tonic or are strong relatives of tonic.

addition o[ a. second voice generally further

and the two voices frequently create

lipe,

by

which emphasize the same strong and thirds which-are-oorjaally lound in the

intervals

vertical

intervals, particularly octaves, fifths,

tonality

frame of a single melody^as

in Ex. 9-9.

Ex. 9-9a.

Handel: Gavotte

•--'

-^^.^.H^:,S tr.

tr-

^"-^

r-F"

irr-

ff

[['

A

reduction of this Gavotte's

first

^

section to a tonality frame

is

1

y

f=f=|

-^—. —i—

r

^

r

^

shown below

Ex. 9-9b.

Ex. 9-9b.

Reduction of Ex. 9-9a to tonality frame (See same

—• ^

in

Chapter

2.).

1

fpN^

^

Ck It

O

r»

11

CI 1

1

XT 1

It

-•

l-»

1

1

O-J

S^

• -©-

in

TWO-VOICE COMBINATIONS

720

Both voices clearly move through the tonality frame of C major. The upper 1 1 th (perfect 4th + an octave) from dominant to tonic, while the

voice spans the

lower part outlines virtually the same tonality pattern. Furthermore, the two

and major thirds involving members of the same C major frame. Both phrases begin, and the second phrase closes, on members of

voices often form octaves, fifths

the tonality frame.

Not

all

melodies are as clearly and simply organized around an easily percepti-

ble tonality frame as those clarifies or

shown

in Ex. 9-9. Ho%\ever, a second voice frequently

confirms the tonality of a

less clear

upper

(or lower) part

by creating

relations to tonic that are not explicit in the activity of the single voice. In Ex. 9-10,

the tonality of the upper voice, sounded alone, seems to hang precariously between e

minor and

G

major; however, with the addition of the lower part, and

tonality frame, the

e'

Ex. 9-10.

upper part

Bach: Partita, from the

In Chapter 6

we

is

clearly heard in

Little

e

its e

to

minor.

Notebook

dealt with the fundamental outlines of melody: basic melody.

Two-voice textures can be studied by reducing the total pitch structure of each part to its basic melody. Basic melody reductions of two voices yield a two-voice framework; this framework, or "structural outline," provides a simple point of departure for the analysis, perception, and the composition of two-voice textures. The two-voice framework of Ex. 9-11, noted earlier, is shown below in Ex. 9-1 lb.

Ex.

9-1 la.

Handel: Gavotte (keyboard).

121

TWO-VOICE COMBINATIONS Ex. 9-1 lb.

A

Two-voice framework of Ex. 9-1 la.

comparison of the example with

its

reduction shows that the rhythmic ratio

of the prevailing upper part to the lower voice It

is

2

:

1

(two eighths

involves the elaboration of essentially stepwise basic pitches.

— quarter) rhythm.

The intervals formed

by coinciding basic pitches are mostly thirds. The rhythmic independence of the parts contrasts with the essentially similar rise and fall of the simultaneous stepprogressions occurring in the two parts. The dual step progression found in the lower part in measures 5 and 6 reflects the predominance of leaps in that voice, in contrast to the prevailing step motion in the upper. The high and low basic pitches of both parts are almost identical with those of the tonality frame; although this is typical of the simplicity of structure and tonal content of this excerpt, it is by no

means

the rule.

The lower

part of a two-voice texture frequently acts as a tonal support or

foundation for a more active top voice, and often creates considerably interest

than the upper

less

melodic

line.

In Ex. 9-12, the bass and violin parts of a sonata for violin and organ are shown, followed by a two-voice reduction. Despite the contrast of activity between the

two

parts,

both are organized on a simple tonal plan, and the movement

to basic

pitches frequently occurs simultaneously in both parts.

Ex.

9-1 2a.

Violin

Organ

I

Marini

:

Sonata for Violin and Organ.

^^ ^ 331

y-U^ m P fT

it-

^ r ^^ p-rrp-

?

P

^^

m^m^ s^

i

?f=p

xn

^ P

122

Ex.

TWO-VOICE COMBINATIONS Two-voice framework of Ex. 9-1 2a.

9-1 2b.

m

331

TT"

XC laz

331

331

xn

-©-

ty

33:

^^

jdl 331

TT"

^^

TT-

xc XE

-&-

While the bass Hne is an acceptable melody, it is overshadowed by the activity above. Most of the pitches in the bass are basic, while a far greater number in the violin part are elaborative.

The

contrast

is

obvious, as

a solid underpinning for the violin. This example

lower voice

is

ally sufficient

The fairly

hardly more than a framework

—which provides a

solid

reduction not only shows

is

is

the role of the bass as

typical of

— unelaborated,

many

support for the activity in

how

in which the and melodican upper part.

clear,

the violin line has been fashioned from a

simple succession of basic pitches, elaborated by scales, sequences and

between the parts which are essentially stable, e.g., octaves, fifths and thirds. Furthermore, contrasts of basic contour between the parts, as in measures 1-4 and 11-13, which are indigenous to good counterpoint, stand out clearly as structural features of the piece. The tonality of the sonata, A (aeolian), is clearly confirmed cadentially, by leading-tone to tonic and dominant to tonic movement in the bass in measures 12figurative patterns, but also reveals a succession of intervals

13.

Ex. 9-13 contrasts with Ex. 9-12 in that both voices adhere to similar basic melodies.

Haydn: Piano Sonata

Ex. 9-1 3a.

^^ I

^i^

i

^

^

in

E-flat,

Finale.

^^ ^

^ ^ ^\.

' I

,

V

I*

I*

^^

^ /

i

^

—

—

M

1

TWO-VO;C£ COMBINATIONS Ex. 9-1 3b.

723

Two-voice reduction of Ex. 9-1 3a.

S

^ somewhat more elaborate than the lower, the two voices, treated imitatively, compete for attention on a more equal footing. Both parts have similar contours and an equal number of step-progressions. Notice that the lower step-progressions of the two parts occur successively, about two beats Although the upper part

apart.

is

The syncopated treatment

of the upper line, in the

first

phrase, establishes

rhythmic identity and individuality, but a comparison of both basic melodies will show how much the two voices mirror one another. Unity of two-voice design results when both parts are fashioned from essentially alike basic melodies. Twovoice frames such as this are common to many two-part contrapuntal textures. its

The

texture of Ex. 9-14 involves considerable rhythmic independence of the

two parts (with the exception of the latter half of measure 8). The rhythmic independence, however, is balanced by an agreement of contour between the voices, seen in the prevailing descent of both parts. Although cadences are avoided in favor of continuous activity throughout the excerpt, rhythmically strong assertions

of

members

of the tonality frame occur in measures

3, 4,

9 and 10. Sing the ex-

ample, then study the reduction in Ex. 9- 14b.

Ex. 9-14a.

Ockeghem

S^

Agnus

[f^ J

J-^

-^^^

:

^ —L ^ f r

^m ^

Dei.

—rf— —

r-&^

1

0^

—

If

Uj

p\ =V ^

1

^-^

r^ -^ --'m P n U

—— —

'

p#..

r

J

J

jij] —^-^

1

\-*^

<s»-

nn

—

124

TWO-VOICE COMBINATIONS

Ex. 9-14b.

Two-voice reduction of Ex. 9-14a.

()#

O

^•

'

— —-^

5

^

•).

^,.

•„

/

/

A

m

i 1

»

The

tonal variety of the two parts

of coinciding basic pitches which are first five

1

is

•

«

•^ *

m

motion of the

1

'

*^

i>

~l m ^ • •

1

1

iV *)•

'

•

1

1

1

1

measures in the bass

of the tonaHty frame. is

S^ i~

1

reflected (in the reduction)

members

1

^1

1 1

1 9

1

1

1

*

iJ

by an

The

absence

disjunct

indicative of the leaps formed

by

same measures, but note that the leaps are comprised mostly of members of the tonality frame, a and e, and are quite stable. Step-progressions are present (but somewhat obscured) in the latter half of the example in both voices, and these contrast with the more disjunct beginning. However, the contours of the step- progressions show an essentially diflferent direction in the two basic pitches in the

parts, since the

descends a

These

fifth

upper from 6"

line

to

comprises a basic ascent from

/ to

study of the different forms of elaboration of basic

pitches in both melodies will show), result in a two-part texture

independent, while unified by tonality {A), adherence to

The

and

while the bass

.4.

factors, plus others (as a

(aeolian mode),

a,

whose voices are

common

pitch materials

similar kinds of durations.

two-voice framework, like basic melody in one

praising the structure of each voice

and

its

line,

provides a basis for ap-

relationship to the other in textures in

which both parts, to a greater or lesser degree, participate in the creation of a cohesive and intelligible musical product. As we have seen, the framework is useful for pinpointing those features of the parts which are structural, rather than decorative, and it also enables us to view those elements of the texture which hold it together.

Pitch

A

Material

glance at any of the preceding musical examples will confirm the fact that

most two-voice textures employ the same key or mode

in

both voices.

We

also seen that the addition of a second part often clarifies the tonic in a

have

melody

ambiguous. Comparing Ex. 9-15 and Ex. 9-16, we find that the tonic {A-Jlat) is strongly asserted by both voices in Ex. 9-15, but only by the lower part in Ex. 9-16. The upper voice of the latter example is apparently in E-

whose key or tonic

flat

is

(considered as a separate line), while the lower clearly establishes A-Jiat (the

actual tonic of the

Ex. 9-15.

combined

parts).

Bach: V/ell-fempered Clavier, Fugue No.

17.

125

TWO-VOICE COMBINATIONS Bach: Well-tempered Clavier, Prelude No.

Ex. 9-16.

17.

^^'

i

^n

f;rrrr

.,

rT jJj

^

any discussion of tonic, key or mode, the loweiLYQic e, because it is the to nal foundation for most two-voice works, often exerts mor e tonal force than the upper. This is well illustrated in Ex. 9-16, which is heard in A-JIat primarily because of the pull towards A-JIat created by the lower Although

both parts

must be considered

in

voice.

Two voices which possess the same note. This

is

particularly true in the

may use conflicting variants of the same minor mode with its different scale patterns.

tonic

In Ex. 9-17, D-flat in the upper part conflicts with the lower part's D-natural.

Bach: Invention

Ex. 9-17.

in

F

D-natural in the lower voice

Minor.

is

explained by the ascent of the line and the avoidance

were not altered. Considerable variety of pitch resources has been used in two melodically independent parts in Ex. 9-18. The tonality is D, but it incorporates all twelve tones of a chromatic scale, rather than a seven tone mode.

of the

augmented second which would

Ex. 9-18.

Hindemith

:

Ludus Tonoiis, Fugue

result if D-Jlat

in

E.

(C)

1943 by Schott

&

Co., Ltd., London.

Reprinted by permission.

Rhythm pattern

'

m

s

V

^^

i

p

t

^

6-

^

Tonic

jerr ^):

y

Hf -

;^

1

^ ^ ^^^ =^ p ?

sequence

^

^i \^p

\,

726

TWO-VOICE COMBINATIONS

Repeated rhythm patterns and melodic sequences create unity, and melodic interest is sustained by avoiding the simultaneous use of identical durations in both parts. Both lines reach a climactic point about a third of the way through the excerpt, and then begin a general stepwise descent to the cadence. Some composers of the twentieth century have created further independence of lines by employing two tonalities or keys simultaneously, as in Ex. 9-19.

Ex. 9-19. Bi-Tonality.

Allegro

Ex. 9-20 contains a section of a canon by Josquin des Pres, a fifteenth century

composer.

The most

pitch organization, tonics.

The

result

is

is

significant feature of this example,

from the standpoint of

that the two canonic voices consistently cadence on different

that,

although the two parts are highly unified through the use

of identical melodic material, they are delineated tonally through their adherence to different tonics,

Ex.

D

and

9-20. Josquin des Pres

P ^ i 'y-L

rrr

:

G.

Chanson.

ft

^

r

f f

P-

^

#-

m^

^m m^

m

^m

127

TWO-VOICE COMBINATIONS

^

P^

P -&

The

^^Ff

^

^

Id

m m m f

tonal separation of voices in Ex. 9-20 illustrates the

common

practice of

bringing in each contrapuntal voice in a different key, or by centering the pitch

on different notes of one key, such as tonic and domithe importance of such a technique in our subsequent study of

motion of successive nant.

We

shall see

entries

fugue and other contrapuntal forms.

Vertical Considerations

Two Voices

in

;

Consonance and Dissonance

We

have been concerned thus far with the horizontal aspects of pitches in melody. But if we are to combine melodies, there must exist a basis for the selection of the harmonic intervals that they will create. A glance at any two-voice composi-

show a variety of vertical combinations, and further study will reveal that composers employ systematic techniques for organizing harmonic intervals and tion will

successions of interval roots.

In Chapter 2 interval roots were discussed, and their relationship to the harmonic series

was

established. It

and

is

which are ^riost the beginning and caden-

entirely logical that those intervals

most often found as tial^ harmonic intervals in two-voice textures. These intervals are essentially stable, or consonant, and because of the role that they have played as basic combinations in music are described as cadential or basic consonances. It is only in recent times that composers have accepted the possibility of beginning or closing on less stable inter-

st able,

octaves,

fi fth s

third s^ are

vals.

The

perfect fourth

and major and minor

sixths

seldom occur

as cadential inter-

vals in two voices. Because of their consonant but non-cadential role in musical

practice, these intervals are regarded as decorative consonances,

voice textures

is

subject to

perfect fourth in particular

many is

and

their use in two-

considerations of contrapuntal technique.

generally afforded a special kind of preparation

The and

resolution.

We for

should not conclude from composers' general neglect of certain intervals

cadence that these combinations have no significant part to play in the organiza-

tion of two-voice music.

However, because of the tension-resolution tendency and

— —

728

1

TWO-VOICE COMBINATIONS

them as dissotiances. We ways composers have used dissonance during the history of West-

the feeling of instability that their use creates, shall see various

we

refer to

ern music. All musical intervals have been grouped below according to three sifications. It

is

essential that this

main

clas-

grouping of vertical sonorities be committed to

memory. Interval Classification.

Beginning and Cadential Consonances

Decorative Consonances

Dissonances

{Basic Consonances)

Unison Perfect

Minor Second Major Second Tritone (+4 and °5) Minor Seventh Major Seventh All Augmented &

Perfect Fourth

Major Sixth Minor Sixth

Octave

Perfect Fifth

Major Third Minor Third

Diminished Intervals.

The

two-voice composition shown as Ex. 9-21 affords a simple point of departure

for a study of the interplay

Ex. 9-21.

between consonance and dissonance.

Guillaume de Machaut: Virelais.

C

3

||>):ytFrr

Tenor

'y.2 ^^4

Bass

m^ V-

"^ J T 0ff]

1

P

n

c

-

.

m m

\

^^Lprr 7 f

$

y

7

/

r

1*

m

m^

m

#

25

f

1 1

Iff

1

M

«

. a'

r

ff

^jt, fe^

^

•0

r

1

1

r.

mm ^

TSL

p i

r

|-#

1

h

15 ''

^ [|.>:

—•

•>

^

,

^=

3 1

P

3

—

^ = t^4=J

.^e-T-"

•

M ""*

i»

—

—

—

—

^

129

TWO-VO/CE COMBINATIONS

:?:

5

[|0: ^

Eff^

f—l r r

>—

^^

-f9

V

¥r

'

4U

• P-

r#¥|

—

f

-*

^

la.

p. ^

—9

-p

consideration here

is

Ti

—

«

^

V

measures used

is

examine

first

f

i

^^

_^

-4^

this

1

T^'^44-p-

and

the interplay between consonance

nance, both of which figure significantly in the organization of ture. Let us

f— — — h

^^

«

h

ll.

M^—f^

ffffrtfrf-\

?

*

1*

^

1

Our main

f^

h

-|S»

-p

V

-?'

?:3C

:

/:

disso-

two-part tex-

the vertical combinations at cadences. These occur in

4, 9, 16, 22, 27, 32, 36,

39 and 43.

An

analysis of the cadential intervals

shown below. Cadential Intervals

in

Measure Number

4 9

Ex.

9-21. Cadential Interval Between Voices

Perfect l{^r<>T

Octave

Minor Third

16

Perfect Octave

22

Minor Third

27

Unison

32

Octave Minor Third Unison Perfect

—

36 39

Perfect Octave

43

Perfect

The beginning

intervals of

Measure Number

6

Octave

each phrase are: Beginning Interval Between Voices Perfect Fifth

13

Perfect Fifth

17

Major Third

24 29

Perfect

33 37

^t^'T-h'^yJi

Perfect Fifth

Octave

Major Sixth Major Third

!

/ ni,

q v^'TK\r(\

We may conclude generally

from the above analysis that phrase beginnings and closes are made with cadential consonances, although decorative consonances are

occasionally found at phrase beginnings or phrase endings.

We

shall see later

how

TWO-VOICE COMBINATIONS

730

dissonances too

may

be used in a similar way.

Now

reexamine the Bach

Invention, Ex. 9-7, and note that Bach appHes a similar use of the

same

e

minor

intervals.

Vocal Ranges and Spacing,

Throughout the first sixteen hundred years of Western music the organization of melody depended most upon the vocal forms that dominated that broad time span. In these early forms,

e.g.,

Gregorian Chant, Secular Song, Motets,

Chansons, and Masses, our predecessors established and developed techniques of

melodic composition that exploited the capabilities of the human voice. Instrumental melody had its origin in vocal music of the fifteenth and sixteenth centuries.

During these years vocal works were often transcribed for small instrumental groups, or vocal parts were sometimes doubled by instruments. Many of the melodic patterns we have come to know through instrumental performance are of vocal origin.

human voice, The necessity of

In our beginning two-voice studies we shall limit our writing to the

expanding our study to include instrumental combinations. performing all musical exercises and illustrations cannot be overstressed. Consistent with most vocal compositions, we shall employ the following later

tical voice

as prac-

ranges:

Soprano

Alt

$

°

Tenor

/'

^=^

Bass

Each

voice

is

ti"

granted a potential range of a twelfth. Needless

to say, consider-

able care should be taken in approaching the extremities of any voice range.

The

low areas of any voice is lost when overused, and average singers are not "at home" with melodies that remain in extreme lows or highs for effectiveness of the high or

long periods.

The

highest note {g') for the tenor in the

Machaut composition,

Ex. 9-21, occurs only once during forty-four measures of melody, while the lowest note of our given tenor range

(c)

is

notes in the soprano, are often thin

never used.

and lack

Low

tones in the bass, like high

definition.

Great care should be given

to their use.

The

two parts will depend partially on the particular voices used. For example, the widest gap that might occur between alto and soprano (in two-voice writing) would be a perfect fifteenth, considering the given ranges of distances between

—

rWO-VO/CE COMBINATIONS

131

both voices. Although possibly effective in isolated cases, such a wide space between two adjacent, unsupported voices would be rare indeed. On the other hand, unisons represent the smallest distance (or relationship) and are quite common cadentially.

The

usual limit for two adjacent voices

is

the octave with tenths ,

and even

twelfths as rare possibilities.

common two-voice combinations such may exploit wider spacings because of the

Less bass,

registers.

Palestrina

te

Alto

^

:

Josquin des Pres

')'

Bass

(i

Common

two-voice spacings are

Motet: Sicut cervus.

^

^

:

Motet

('

i

m

i cat

:

Tu

^

zz:

?S

txj

22

^-*

pauperum refugium.

^^

Tenor

and

In these cases the interval of a twelfth should be regarded as normal,

Soprano

Ex. 9-23.

alto

natural separation of the individual

with two octaves as a usual limit of separation. shown in Ex. 9-22, Ex. 9-23, and Ex. 9-24.

Ex. 9-22.

and soprano, or

as tenor

— w 1

$

m

p

^

J

W

'

L

U ^

zz:

Ex. 9-24.

The

principles for two-voice spacing that have been outlined here can be

marized

seldom exceed the octave, while non-adjacent soprano and tenor, or alto and bass) may move as far apart as two

as follows: adjacent voices

pairs (such as octaves.

sum-

These principles

will generally

apply even

when more than two

parts are

.

132

TWO-VOICE COMBINATIONS

present. For the time being these principles mental textures as well as vocal. will

occur in Chapter

A

more

may

be used as a reference

for instru-

detailed discussion of instrumental spacings

15.

Exercises

For more detailed assignments 1

see Materials and Structure of Music

I,

Workbook, Chapter 9.

Organize two-voice rhythmic phrases of eight measures, choosing rhythm patterns from Ex. 9-2 or Ex. 9-3 as a basis for unifying repetition.

2.

Make

3.

Locate

all

cadential consonances in Ex. 9-1 3a.

4.

Locate

all

decorative consonances in Ex. 9-15 and Ex. 9-16.

5.

Locate

all

dissonant intervals in Ex. 9-22, Ex. 9-23, and Ex. 9-24 and note the resolu-

6.

Build cadential and decorative consonances above

two-voice reductions of Ex. 9-2 and Ex. 9-7.

tion of each.

7.

Build

five

dissonances above

d',

g and/! labeling each interval and spacing them for alto and c', e',

b,

soprano. 8.

Add

9.

between parts. Try to use a wide variety of cadential or decorative consonances. Analyze each harmonic interval used, and circle its root. Make a two-voice reduction of the preceding exercise, indicating any important step-

a tenor part above the bass-line in Ex. 9-12 a, using only cadential or decorative consonances. Use predominately stepwise motion, writing in the same rhythm (note against note) as the bass. Plan cadences carefully, and avoid using successive fifths or octaves

progressions (as

shown

in this chapter).

Two -Voice Combinotions;

70

Decorative Pitch es

Decorative Pitches Decorative patterns frequently produce harmonic intervals that otherwise are avoided. In this chapter

we

shall study dissonances, or unstable

and describe some of the procedures that composers have developed for manipulating decorative pitches those that connect and embellish basic melody pitches,

—

in the two-voice texture.

We

Chapter 8 how passing tones create conjunct (step) activity, often "filling in" the interval of a third between two basic pitches of a single melodic line. When a second voice is added to the texture, a new dimension is created in the form of harmonic intervals. Thus our perception of basic and decorative pitches in two-voice combinations is affected by both melodic and harmonic elements. Usually the addition of a second part will confirm an appraisal of basic or decorative activity in a single line. This is exemplified by the following pattern in which decorative pitches in the melody (a),

saw

in

j^r icii;

m

are heard as unstable in association with the supporting voice in (b)

i=.==i

analysis of (a)

^mm ^ P.

m

t.

p.

t.

p.

t.

e.

t.

733

;

134

TWO-VOICE COMBINATIONS; DECORATIVE PITCHES

In some examples, however, the greater weight of two voices will result in an

and decorative patterns on the basis of stable intervals (conIn other sonances). words, consonant relations between voices may well effect a stability not apparent in the single melodic line. In the pattern which follows, interpretation of basic

basic pitches (apparently) occur

pattern:

(c)

analysis of (c)

f

'i

(jki>

o

on the beat,

as

in the analysis following the

^n U J

J

^

J

J

However, with the addition of a lower voice unstable, creating

shown

momentary

1

"-^-"

(d), the

J

on-the-beat pitches become

and the after-beat pitches represent and are therefore regarded as basic pitches

dissonances,

brief points of relaxation or stability,

.fly^^|J|,^-pl^^

(d)

analysis of (d)

^^

^^

r

Jl Jo

J ffi

Passing tones frequently result in fleeting dissonances, as on the second half of

beat three of measure

1

in Ex. 10-1.

Kpn

a Ex.

10-1. Bach: Invention in E Minor.

.fiM^^^ 'y-u^^i

CJjpr

vQ'c^

^s o-^r..fl'

^

:

1=^^

^

g

m

^ i^

i

A passing tone a^ is also found in the top voice on the first beat of the first measure. It is

perceived as an unstable pitch,

filling in

the gap between two structural

TWO-VOICE COMBINATIONS; DECORATIVE PITCHES pitches, b^

and

g^.

perfect fourth. It

But

a^

is

135

not a dissonance;

perceived as unstable in

is

cadential consonances, b^ and

g^. (g^

it

creates a decorative consonance, a

this

context because

it

connects two

actually sounds alone, but will be associated

with the previous bass note E.) As is more often the case, both of the passing tones in Ex. 10-1 are unaccented, and their effect as dissonances is negligible, since they

have so

little

duration. Their effect

is

best described as melodic decoration.

Some of the most characteristic uses of passing tones are shown in Ex. 10-2. They may occur in either voice, and in some instances occur simultaneously in both parts, as in Example 10-2. Both diatonic and chromatic forms occur, filling in distances as small as the major second and as wide as the perfect fourth.

10-2. Illustration of passing tones.

^ ^

Ex.

^m ^ ^ffi^M m A

s

B

JCOEM

^

^

Play Ex. 10-3, and notice

10-3. Frescobaldi

a

^

^

^m

Ex.

?

:

all

%

^

passing tones. Consider both voices.

Canzona dopo

m^^^ ^ m

^

I'Epistola.

'-

S J »

i

J-

r

t O"

:

736

The

TWO-VOICE COMBINATIONS e'

after the first beat of

measure

3,

top voice,

however, consonant with the lower voice

The

connects two basic pitches,/' and

a,

is

since

it

;

DECORATIVE PITCHES

obviously a passing tone. It

is,

creates a perfect fifth with

it.

on the third beat of the same measure. The/' is a basic pitch both because of its metric position and because it forms a strong step progression with the preceding g' and the e' of the next e'

measure.

The importance

d',

as does the

e'

of relating decorative pitches to basic pitches, rather than

simply singHng out dissonances,

is

illustrated in Ex. 10-3.

Neighbor Tones. Neighbor tones, together with passing tones, comprise another common type of melodic decoration. Like the passing tone, the neighbor represents the intermediary step of a three note figure. Thus, in the figure

^=i

(a)

(b)

$T

tone.

may

£

,

G

a dissonant lower neighbor to F, while in

is

embellishes the

F

which

to

Although neighbors appear most often be in an accented position

as

it

returns, as

an upper neighbor

unaccented embellishments, they

$fm r

In

melodic decoration, the upper or lower neighbor,

fulfilling its role of

^

passing tone,

may

occur without actually creating dissonance. For example

ir

;

here c"

is

obviously a melodic neighbor tone to

does not form a dissonance with the lower It is essential to

like the

b',

but

it

e'.

understand, then, that passing tones and neighbors are both

embellishments that are present in melody and controlled by the activity of the

which comprise horizontal are often aware of these decorative

single line. In other words, these are figurative elements

aspects

first,

vertical relationships second.

pitch relationships even

The neighbor is

when hearing

a most useful figure for

chromatic or diatonic embellishment, developing activity while focusing attention on one pitch.

In two-part writing the neighbor,

by

a single strand of melody.

which may occur

tone,

We

as a

like the

passing tone,

relative inactivity in the opposite voice. Just as

textures

is

is

most

eflfectively

melodic activity in two-part

generally divided between voices, so decorative activity

tributed between parts, rather than centered in one.

balanced

Some

is

often dis-

typical illustrations of

neighbor tones are shown in Ex. 10-4. The figure formed by successive occurrences of both upper and lower neighbors

two measures of Ex.

1

0-4.

is

called a neighbor group. It

is

shown

in the last

_

137

TWO-VOICE COMBINATIONS ; DECORATIVE PITCHES Ex.

10-4. Illustration of neighbor tones.

%^^ ^S ^m (b)

(a)

^^

(dl

(c)

^

2

Both neighbor and passing tones occur in Ex.

10-5.

^^m Contrapuntal Motion Between Parts and Approaches to Structural Intervals

An important consideration in counterpoint is the directional relationship formed by the moving voices. When the parts proceed in opposite directions they produce and thus they assume an independence that is denied when they move in tandem, up or down. Contrary motion is an important feature of the cadence in two-voice textures, and it is often found in the interior areas of a phrase contrary motion,

as well.

Contrary motion

and

oblique

motion.

is

generally balanced by other types of relations similar, parallel,

Any

:

two-voice work will reveal a variety of motion types. Those

obtainable are illustrated in Ex. 10-6a, Ex. 10-6b, Ex. 10-6c and Ex. 10-6d.

Ex. (a)

10-6a. Illustration of contrary motion.

^

:

t

ir)-

-s>

A f

TWO-VOICE COMBINATIONS

738

when both

Parallel motion occurs

voices

move

in the

same

;

DECORATIVE PITCHES

direction while maintain-

ing the same intervallic distance.

10-6b. Illustration of parallel motion.

Ex.

^Ori

rr^.

"

IrX^A-)

(b)

i ^^tttf f

^^ i«=^

3

from movements

Similar motion resuks

in the

w same

^»

direction but

which involve

changing interval combinations.

Ex.

10-6c.

Illustration

of similar

motion.

(C)

i^' S • */• ^7^

* — "

« • m— •*

Oblique motion

second voice.

1

u '

— » ~

1

m •

1

1 1

»

V

/L

VU f(r>

m

< -

m

m

m

%

m m

•J

m

_ ^«

1

II

m-

produced by movement in one voice combined with a stationary (Repetition of the same tone is considered to be stationary movement is

as well as uninterrupted sound.)

10-6d. Illustration of oblique motion.

Ex.

(d)

TT'

E it

I r

r

Study the counterpoint

M^ i f-DT TT

CJT

i

r

in Ex. 10-7,

r

^

having

first

performed the music. Locate

the various types of motion that are employed.

Ex.

10-7.

Johann Christoph Bach: Chorale Prelude:

i&

i

—^-^

i

feS

(

mi Cp

>

s :£:

^

,/?
#^^

i

hab

In dieh

ieh gehoffef, Herr.

^m ^ ^m ^

^ #

r r f

p

10

J: 3:

g

rWO-VO/C£ COMBINATIONS

A or

i

DECORATIVE PITCHES

139

further consideration regarding contrapuntal motion concerns the approach

movement

to cadential consonances, particularly the octave, fifth,

and unison.

Since these intervals produce a feeling of stability and relative repose,

gether logical that they have been

much used as the basis for

it

is

alto-

achieving tonal stability.

Howeverj when these intervals are used in uninterrupted succession, they produce an effect of mutual dependence and inactivity that opposes the very nature of counterpoint, melodic independence. For these reasons (coupled with the desire to avoid monotonous repetition) composers have generally avoided consecutive fifths, octaves, and unisons in contrapuntal writing. Furthermore, the movement

to these intervals

one voice (or both) moving by

at least

step.

is

usually by contrary motion, with

This principle

is

evident in measures

and 10 of Ex. 10-7. Movement in contrary motion to basic intervals (such as octaves, fifths and unisons) is more often found where these intervals fall on strong 4, 5

beats, or strong parts of the beat, as in Ex. 10-8.

Ex.

Zachau

10-8.

:

Chorale Prelude: Vom Himmel hoch, da

komm

ich her.

cadence

^^

It

is

f#^

vtrrr

y-h>'.

composer has used a wide variety of consonances and that unstable intervals, which further contribute to a variety

clear in Ex. 10-8 that the

as basic intervals,

of sonority, are the result of decorative patterns. to a large degree, the

way

in

which they are

styles.

possible in two-voice writing.

choice of intervals used and,

treated, differ

However, the proportion of fifths, octaves, unisons, and fourths. A comparison of Ex. 10-9 with Ex. 10-10 musical

The

thirds

and

somewhat

in individual

sixths usually outweighs_

will illustrate the intervallic variety

740

TWO-VOICE COMBINATIONS; DECORATIVE PITCHES

Ex.

10-9. Bach: Invention

Ex.

10-10. Hindemith: Morienleben. (C) 1924 by

in

D Minor.

B.

Schott's Soehne, Mainz.

Renewed

1951,

Reprinted by permission.

Consecutive

r^

fifths in contrary

^

motion

^

1

m £

J

m J -S>-

Oblique fifth

In Ex. 10-9 Bach has relied upon thirds and sonorities.

Not

until the

cadence to

.4 is

sixths, primarily, as

a prominent octave heard.

It is

on-the-beat

approached

by contrary motion. The excerpt by Hindemith, Ex. 10-10, reveals considerably more intervallic variety, but it shows a kinship in the way fifths and octaves are approached by contrary motion. Rhythm also determines vertical relationships. Fifths and octaves that fall on strong beats naturally attract more attention than those occurring on weak beats, and so the approach to these cadential intervals should be viewed in relation to metric position. Again, contrary and oblique motion are usually found in the approach to fifths, octaves, or unisons on strong beats. Similar motion, on the other hand, is not uncommon at cadences to the octave. In such cases the upper voice most often moves by step, while the lower voice skips up or down. As in Ex. 10-1 la, and Ex. 10-1 lb cadential finality can be emphasized by directional agreement. Final cadences to the perfect

ed by similar motion (direct

fifth

(which are quite rare) are almost never approach-

fifth).

*

TWO-VOICE COMBINATIONS; DECORATIVE PITCHES Ex.

10-1 la.

Bach: Invention

^

f*rt

Ex.

I

10-1 lb.

G

Major.

^

^t±

^^^"[ur *'

in

141

m — jjj 0^

Bach: Invention

in

D Minor.

^^

s

p^

^i

Contrapuntal Treatments of Other Consonances.

The

we know, a uncommon, nor is the

perfect fourth

to the fourth are

is,

as

non-cadential interval. Two-voice cadences fourth often formed by the two basic pitches

which approach a cadence. Its use is confined primarily to the interior areas of the phrase. A typical appearance of the fourth in two-voice writing occurs in measure 2 of Ex. 10-12.

Ex.

10-12. Bach: Suite

^ m ^

in

6 Minor, Allemande.

m

^^m ?

^

wm m Jtv

^

#itv#

^ ^^t^m-

^

\n ^

TWO-VOICE COMBINATIONS; DECORATIVE PITCHES

742

The

example involve either a step approach, step resolution, or both. Like fifths, most accented fourths are reached by contrary motion, seldom by parallel or similar motion in two-voice textures and examples of both voices moving in similar motion by skips to a fourth are extremely rare. As we shall fourths found in this

;

see, fourths, especially

When

when

accented, usually resolve to thirds.

do occur, they generally involve durations of less than An example of movement in parallel fourths occurs in measure 1 of the excerpt in d minor by Bach (Ex. 10- lib.) Here the parallel motion in consecutive fourths is the result of movement around the basic pitch A. D", the upper member of the first fourth moves to a lower neighbor, c"-sharp, while a passing tone g connects the lower a with f. The prominence of these fourths is negligible, since they fall on a weak beat. Thirds and sixths are used more freely in two-voice writing. Thirds, of course, occur cadentially, while sixths are seldom found as cadential intervals, never in final cadences in two voices. Like other intervals, thirds and sixths represent only parallel fourths

the prevailing basic duration.

a part of a well-balanced contrapuntal formula. In contrast with other consonances,

approached by similar and parallel, as well as by contrary and oblique motion. As a rule, composers avoid more than three parallel thirds or sixths moving consecutively. When these do occur, they are generally a mixture of major and minor thirds, rather than three major or three minor thirds. Parallel motion in any identical intervals destroys melodic independence and undermines tonality. The degree to which intervallic variety and treatment contribute to interesting counterpoint is apparent in the Mozart illustration of Ex. 10-13.

these intervals are often

10-13. Mozart: Quartet

Ex.

Viola

Cello

m^

im

[b'»«)

m

D Major.

^

jr

W^

^

fE

^

in

'

^ 1^ 1

^

^

i

P

w—w

While subject

to exceptions, the following principles of intervallic succession

and

melodic movement are upheld in most two-voice writing. Their application to our study of two-voice counterpoint should be adopted, and these concepts applied in all

written assignments.

—

TWO-VOICE COMBINATIONS

Summation of

143

DECORATIVE PITCHES

;

Principles of Melodic

Metrically strong (stressed)

Movement and

Intervallic Succession

open consonances

(octaves,

fifths,

fourths

and

unisons) are usually approached in contrary motion.

Successive

fifths,

octaves and unisons are generally avoided.

Any succession of parallel thirds or sixths

should include a mixture of both major

and minor thirds or sixths. For example, a major third will most often be followed by a minor third, or a minor sixth will generally follow a major sixth. Skips in either voice are generally balanced by steps in the other. Simultaneous leaps in both voices are rare, and when they occur, they will generally be in contrary motion.

Leaps are usually followed by step motion or opposite leaps. Melodic or harmonic tritones, like most augmented or diminished generally resolved by step.

Perform and analyze the

Ex.

10-14a. Approaching

illustrations

J ¥

10-14b. Parallel Fifths (avoid).

^^

^U^r

Ex.

10-14c.

Parallel

'.;

'^'1'.^ H-^^~-

10-14d. Consecutive Fifths (avoid).

-i

J

-r

r

^ r

f

r

^

d

t

Octaves (avoid).

fV^ n ^ Ex.

a^fs

r

.

Ex.

shown below.

Open Consonances.

i Ex.

intervals, are

£££

10-14e. Consecutive Octaves (avoid).

-J

\

i

'

^

r~r

ls

^'

144

TWO-VOICE COMBINATIONS 10-14f.

Ex.

Parallel Thirds or Sixths (common).

## Ex.

.

I

1

iJ

10-14g. Skips balanced by steps.

fe

POJ::

1

Fr.ff.i... t

m Ex.

O

DECORATIVE PITCHES

;

f^

i

V

i

10-14h.

Leaps resolved.

*

r Basic Contrapuntal Treatments of Unstable Intervals

We

and ambiguous quality of the melodic tritone, vocal performances of it. It is this same unstable

are familiar with the unstable

and the problems attendant to characteristic that, on the other hand, gives the tritone its special quality of expressiveness which many composers have exploited, as in Ex. 10-15.

Ex.

10-1 5a.

k''

Ex.

i

>j

Wagner:

r

Tristan und Isolde, Act.

U3 Major

in

— Minor

Scales.

XT. -0=0"cr

3x:

XT.

T.T. 1

.

^U W

pt^

-^'

10-1 5b. Tritones

II.

31

^

T.T.

1^

zee ~o~

331 T.T.

IP

145

TWO-VOICE COMBINATIONS; DECORATIVE PITCHES

The

tritone

is

perhaps most prominent in major

— minor music where

it

occurs

between the subdominant and the leading tone (4-7). This relationship occurs both melodically and harmonically in two-voice counterpoint, and is quite effective in developing melodic or harmonic tension and in building strong "resolution tendencies."

We

shall see in

subsequent study that the tritone figures significantly

in two-voice cadences.

There are predictable treatments of melodic and harmonic tritones which are basic to much music, and which can easily be related to our notational practices. Some of their more common treatments are shown below. 1.

up or down an augnieh''^je«HrduVm are usually followed by stepwise motion same direction as the leap. This is true with a// augmented intervals. Like skips of an augmented fourth, skip/l<^ ^n ascending or descending diSkips

in the 2.

minished

fifth

are normally succeeded by stepwise motion, but generally in the

opposite direction

from the

leap. This

is

true with all diminished intervals.

3.

Tritone leaps occur more often as unaccented leaps, often in the course of repetitive patterns whose main feature is rhythm. Stepwise resolutions are usually

4.

Tritone skips,

found here

too. like

most leaps, are

the opposite direction

from the

most often approached by

step, generally in

leap.

5.

Leaps that follow melodic tritones usually take the opposite direction and frequently resolve to pitches that form step progressions with members of the

6.

Harmonic tritones formed by the movement of two contrapuntal voices usually resolve by the same kinds of stepwise movement associated with melodic tritones. Augmented fourths will "expand" by step, while diminished fifths will

tritone.

contract.

Locate

all

melodic and harmonic tritones in Ex. 10- 16a and Ex. 10- 16b.

compare the appearance of each with the various

Ex.

10-16a. Bach: Courante.

Ex.

10-16b. Haydn: Sonata

in

E-flat

:

principles described above.

Menuet.

P.T.

Then

(VT)

TWO-VOICE COMBINATIONS

146

10-1 6c.

Ex.

;

DECORATIVE PITCHES

Bach: Minuet.

Most of the

tri tones

in Ex. 10-16 are the result of decorative patterns. Both

mem-

bers of a harmonic tritone are seldom basic pitches. Furthermore, the tritones illustrated in Ex. 10- 16a

and Ex.

10- 16b involve the

4-7 scale degree relationship,

—

major minor music, while the tritones in Ex. 10- 16c occur in a modulator^' passage which closes with a progressive cadence in g minor. In later study we shall deal with the treatment of tritones as more structural pitches, particularly as members of fuller harmonic textures. as

is

most often the case

in

Other Unstable Intervals

The treatment

of other unstable intervals, such as seconds, sevenths, and aug-

mented and diminished intervals, is similar to that of the tritone; they are generally decorative, and they move by step. (Important exceptions to this will be dealt with Chapter 12 in connection with other forms of decorative activity.) Unaccented passing tones in the upper voice create a variety of dissonances in Ex. 10-17. They clearly decorate basic pitches which form consonances.

in

Ex.

10-17. Sweelinck

'hi'.i

:

Fantasia (for organ).

r

Considerable tonal Ex. 10-18. \'irtually

r

^

r

movement and much all

r

r

r

m

decorative activity can be found in

of the unstable pitches, producing a great variety of

melodic and harmonic intervals, are treated in stepwise motion. Passing and

neighbor tones prevail.

TWO-VOICE COMBINATIONS; DECORATIVE PITCHES Ex.

10-18. Bach: Well-fempered Clavier,

Book

^

m^4U^

we have

147

2,

Prelude

^

in

A-flat Major.

^^

some of the basic ways of organizing pitch motion involving both consonances and decorative pitches. At this point we have established a framework for continued study of pitch relations in two-voice textures. In the next two chapters we shall see how these same patterns of movement, and others, provide a basis for the structure of the phrase, for the creation of points of movement and relaxation, and for the further elaboration of the two-voice In

this

chapter

outlined

frame.

Exercises

For more detailed assignments see Materials and 1.

2.

Structure of

Music

I,

Workbook, Chapter 10.

Using the lower voice of 10-7, add a new upper part in prevailing quarter notes introducing passing and neighbor tones to create decorative eighths. Write your own versions of the example for aural identification of basic consonances and decorative pitches.

3.

4.

Analyze aurally the different types of motion

in Ex. 10-17. Play the lower part of Ex. 10-16a, Ex. 10-16b and Ex. 10-16c on the piano and sing the

upper 5.

part.

Then

reverse the process.

Use

the pitches in the lower voice of Ex. 10-16b as basic pitches, one to each measure. Then add an upper part that is entirely consonant, demonstrating the principles of con-

trapuntal treatment of consonances discussed in this chapter. Write nine measures in simple triple meter. 6.

Sight-sing Ex. 10-8. Analyze

7.

Play the patterns

in

all

decorative pitches in the excerpt.

Ex. 10-14 for identification of parallel or consecutive intervals.-

Continuation

77

if

Two -Voice Combinations

Cadences

One form,

of the most significant areas of a musical work, regardless of

its

texture or

is here that both tonal and rhythmic elements must be drawn to a convincing and satisfying conclusion. We shall concern ourselves first with final cadences in two-voice music, although it should be understood that a study of cadences which delineate phrases and is

sections

the final cadence, also called the close. It

must

also lie within the scope of

any study of musical construction.

Despite the diflfering cadential characteristics of diverse musical

styles,

three

principles of cadence construction are basic to music in general: (1) a slackening

of motion, usually evidenced by long note values; (2) the confirmation of a tonal center; and (3) consonant intervallic relations between the parts.

The

illustrations of

cadences in Ex. 11-1, Ex.

ucts of musical styles separated

1

1-2

and Ex.

1

1-3,

although prod-

by hundreds of years, clearly adhere

to the princi-

ples described above.

Ex.

11-1. Josquin des Pres

^

:

Chanson.

^ ^^ ^ ^^ ^ »

i

m

%

-niz

148

149

CONTINUATION OF TWO-VOICE COMBINATIONS Ex.

11-2. Bach:

Ex.

11-3.

Two-Part Invention.

Mikrokosmos, Copyright 1940 by Hawkes by permission of Boosey & Hawkes Inc.

Bartok

:

1 '> 'i

>^''^ J J

^

& Son (London)

i

# fcfc=4

r (SJ

Ltd. Reprinted

m ^

In each case (Ex. 11-1, Ex. 11-2, and Ex. 11-3), cadential to nes occ ur on strong

C adences

on weak beats or weak parts of the beat (sometimes called "feminine endings") are exceptions. A_certain prominence is assured caderiliaL t ones because ctf th eir duration (usually more than one beat), by their strong metric^ loc ation, and through their obvious importance as the last tones of a melodic patt ern. Furthermore, this rhythmic-metric prominence is often made more evident by broadening or slowing down the melodic pace with longer note values introduced in the approach to the actual cadence. Such is the case in each of the excerpts of Ex. 11-1, Ex. 11-2 and Ex. 11-3. The importance of these and other rhythmic aspects of the cadence and its approach cannot be overstressed. Composers sometimes prolong activity in one voice after the cadential tone has been clearly arrived at in both parts. Through such an extension, each voice maintains its individuality and independence into the cadence proper. In Ex. 1-4, the lower voice asserts the tonic A, while the upper voice, having touched upon a', continues down by a series of leaps to the octave a. heats.

that

fall

1

Ex.

11-4.

Bach: Invention

in

A

Minor.

'50

CONTINUATION OF TWO-VOICE COMBINATIONS

A

codetta is

an extension of musical

Ex. 11-5. Sweelinck

:

Organ Toccata

cadence area.

(cadence).

^J^*v

* J Jj ^ JJJJi

• J

^

activity that prolongs the

^gr zuz 33:

Cadenfial Intervals Formed

in

Anv_ cadential

Two-Voice Textures.

conso-

nance (unison, octave, fifth, third) may occur asthe final sonority of a tw o-voice work. The same applies generally (but by no means always) to internal cadences, ^gardless of the interval, the tonic pitch is always the lower tone at a final c aden ce. (It may also be in the upper part if the cadential interval is an octave or unison.) Final cadences to intervals other than cadential consonances, though possible and

sometimes found in contemporary music, are tonally ambiguous and must be garded

The ity,

as exceptional.

particular choice of cadential interval

the kind of melodic activity that reaches

composer's choice of sonority. the unison

it

The

octave

is

is

determined by the prevailing tonal-

its

as a closing sonority,

represents the strongest, in terms of stability. It

tonal relationship,

is

or thirds. Both major

and the and with

fulfillment in the cadence,

common

teresting as a sonority than the third or fifth;

The

perfect

is

fifth,

perhaps

less in-

though a strong

not found as often in two-voice cadences as octaves, unisons

and minor

thirds, the choice of which

by the mode of the work, occur frequently. firms the tonality of the piece or

The

re-

cadential interval

is

its

Any

is

determined primarily

cadential consonance that con-

closing section

often called the ultimate

may

be employed.

and the interval that Cadence patterns are formed

interval,

immediately precedes it is called the approach interval. by the movement from an approach to an ultimate (or final) interval. Some of the most common two-voice cadence patterns are shown in Ex. 11-6.

CONTINUATION OF TWO-VOICE COMBINATIONS Ex.

11-6. Basic

(a)

*

*

Cadences

=g=

(c)

^ ^^ -e-

^8

(d)

xir

W

V^

l^

-ee-

-e-

331

o

n

^^^

To^

^^

-ee-

-&-

in

^

n

Contrary motion, one voice moving by step.

XT

tu> -e-

^_

^ ^

=

^

:fe:

"TT-

3X

^

331

^ ^

^

'

xn ^^

te

-o-

-» '

^

"

-e-

^^

-e-

XT

"

321

33:

b

in

HX

motion.

Similar or parallel

Skips

^

^»^

xr

I^ ^

^

~cr

^o-

%==^

=w

-e-e-

1

zaz

^«-

XT

i b^

Intervals).

Stepwise contrary motion.

~cr

(b)

I

Two-Voices (Approach and Ultimate

in

zcn

e=

151

»

ij

s

t^^

»

.g.

^^

s

-e-

Direct

fifths

S

JOZ

-e-

contrary motion.

S

-»

-

^-^

-e-

-o-

331

^r

331

—

-

33: -©-

^^

:

CONTINUATION OF TWO-VOICE COMBINATIONS

152

Various forms of

scales are implicit in the different patterns.

often labelled according to the melodic

movement

These patterns are

of the voices in their relation

For instance, the first pattern in Ex. would be indicated as 2-1 and the first pattern under Ex. 11 -6b would be written as 5-1 The numbers 7-8 indicate step-movement from the leading tone (or subtonic) to tonic, whereas 2-1 indicates a step descent from supertonic to to tonic (the root of the cadential interval). 11 -6a

These patterns represent an intervallic framework that results from melodic movement at the cadence. However, any of these basic pitches could be decorated with a variety of embellishment involving passing tones, neighbors or other elaboratonic.

tive pitches.

Two

voices

moving

This

covered fifth.

Direct octaves,

in similar

effect

motion

to a perfect fifth

produce the

direct fiftho£_

has been generally avoided in two-voice cadential practice.

on the other hand, are quite common,

if

the upper voice

moves by

ascending or descending step.

approach intervals of the basic patterns shown in Ex. 1 comprised of cadential and decorative consonances. Perfect fourths do not occur frequently as approach intervals in two-voice writing, nor do tritones. It

is

significant that the

1-6 are all

Two Voices. We are familiar with some of the charassociated with modal melodies, and the group of scales known as

Modal Cadences acteristics

in

modes

Ex.

11-7. ?^->

JbuxiiiA

m

^

.^4<^

Dorian

Phrygi ti

o

331

zcn

m:

O

(

*

«»

O

3x:

JcnjocuA Mixolydian

"

i.

Aeolian 3i: -o-

o

i»

^^

ice:

ac..u)ci i

Lydian

n

o

^'

-^e-

"

Natural minor

^

3r

o

_Q_

'^

)

HSZ

Just as modal melodies exploit certain characteristic interval relationships, so twovoice combinations adhere to a group of basic cadence patterns that incorporate

modal patterns. It is significant also that many of these patterns, some of which are shown in Ex. 1 1-8, are by no means limited in use to modal melodies; they can also be found in compositions oriented around major-minor scales and more chromatic works. All of these patterns, associated with two-voice textures, involve the basic pattern

r,"i

or

its

inversion, fr..

•

153

CONTINUATION OF TWO-VOICE COMBINATIONS 7 8

Ex.

11-8. »",

Two-voice Modal Cadences.

Dorian and

$

_Q_

xn

331 ~&-

^ ^ .DR

>^

Ex.

t»

-e-

nr

TT

-e-

HE

"D"

fl v-v

v.^

IJ

L-S-

tK>

2^

O ^ ^

t» l» 1

l5_po

J.

Mixolydian

o

2^

3a:

o

Lydian

J-

2-

Phrygian

Aeolian

11 11

tl

j'^j'^

n

'^^

II

1

11 -8a. Willaert.

P

^

S?

'Lc£;

r'

i

y

r

pr r

i

^rtrrir'^

|

I

g

3r*^

£

=^

—

^ 7-8 2

Ex.

11 -8b.

fr "^^

^

11 -8c.

^'

J

^^

1

Giovanni da Florentia.

'Y 2

Ex.

-

r

r a

M f

—

1

r

^

P

^

f9

=]

fl

^

A

iLfr

ii

1 1

r 2

1

7

8

Josquin des Pres.

J^^=^

i

^ST^ DCH

-e7 2

-

-

8 1

Dorian and Aeolian mode compositions, as shown in Ex. 11-8, usually employ cadences that approach tonic from the whole step below and the whole step above, while Phrygian cadences approach tonic from the whole step below and the half step above. Cadences in the Lydian mode, as in major and minor, involve a leading-tone to tonic ascent while the other voice (usually the lower) moves by a descending whole step from 2-1. Mixolydian cadences, like Dorian and Aeolian, contain no half step, and tonic is approached from the whole step below and above

154

CONTINUATION OF TWO-VOICE COMBINATIONS

tonic. All of these patterns deal

with cadences to the octave or unison, reached by contrary motion. Other patterns can be found in two-voice textures employing

modal melodies. However, those which employ interval are most common. Two-Voice Cadences

^^ ^

i$ P-

"

ijjjJ.' r

)^

r

m

m

i9-

s

^

Major and Minor Keys

in

Obrecht: Missa Sine Nomine, Agnus Dei.

11-9.

Ex.

the octave or unison as an ultimate

r f

gf^

J

SI

^

I

-#

^

-&^

iii^ #

r

m^

zsn

In Ex. 11-9, a cadential/'j-Aar/) has been introduced to create a leading tone to tonic, thereby emphasizing G as a point of focus. The resulting scale structure of the whole example

is

a mixture of

incorporation of leading tones, the major-minor scales

first

became

embody

features of

usually, of the following features

perfect fourth or

sonant intervals whose

F

A

major. With the gradual

cadentially only, then into

melody

as a whole,

and a group of cadences reflecting the we shall see, some of these cadential patterns

The most common

written during the past 500 years

up a

G

modal cadences.

Terminal Cadences.

per) part

Mixolydian and

established,

use of leading tones developed. As still

G

roots

cadential pattern of music

final

described as the V-I cadence. It is comprised, melodic movement in the lower (less often up-

is :

down

a perfect

fifth;

and a succession of two con-

are a perfect fourth or perfect

fifth

apart; that

is,

G

to

D, or D-Jiat to G-flat. The roots of the intervals that form the V-I pattern correspond to the dominant and tonic degrees of the prevailing tonality. Several illustrations of the V-I pattern are shown in Ex. 11-10. C,

Ex.

to B-flat,

to

ll-10a. Bach.

Roots

Roots

^m

V

I

Dominant

Tonic

:

155

CONTINUATION OF TWO-VOICE COMBINATIONS 11-lOb. Handel.

Ex.

Pi wt

S

^

i

Roots

V

I

Dominant

Tonic

In contrast with the ascending leap of a fourth (or descending

fifth)

that

is

found most often in the lower part, the upper voice usually moves by step from 7-8 (leading tone to tonic), or from 2-1 (supertonic to tonic).

fc:

*

znz ini

3E

"O"

-

1

-1

As shown

in Ex.

1

1-lOa and Ex.

1 1

movement of both voices can horizontal movement of the voices.

-10b, the melodic

be indicated by numbers which represent the Several basic V-I patterns are shown in Ex. 11-11.

11-11. V-I Cadences.

Ex.

-p

i>

/r i&i ysu

^-\

~ o

J

-e-

^

r\•/•

'-'

'/

The

It

7t>

*'

/-»

2

5

-

1 1

*»>

*-»

*'

1

hnt

t>

n

-

1

C)

e-

o

5-3 7-8

-e-

-e-

^-k

7-8 5

It

^^

^-k

i~\

LI

5-3

2

-

5

5

1

-

3

2-3

1

5

-

1

7-8 5

-

1

following principles apply to the handling of V-I cadences in two-voice

textures 1

.

The lower voice fifth,

moves by ascending perfect fourth or descending perfect while the upper part moves from 2-1 or 7-8, generally in contrary motion

with the lower.

usually

CONTINUATION OF TWO-VOICE COMBINATIONS

156

Ex.

11-12.

m

i r

'j-^i

2.

The

r

r

5?z:

inversion of the above, with 7-8

up a fourth or down a

fifth,

two-voice cadences. 2-1

when

Ex.

the upper part

movement

is

in the lower voice

and a leap

an unusual exception

in the lower part

is

in final

virtually never

found

leap.

11-13.

^

^^

f

d

• ^

P

Contrary motion

prevails,

upper voice moves by

Ex.

although possible,

moves by a

i

3.

movement

although direct octaves

may

be found when the

step.

11-14.

s Tnr^^ m

uT4.

7-8

movement most

often involves the leading tone to tonic, but 7-8 motion

a whole step (subtonic to tonic)

must be indicated by

Ex.

i

'fjfsm:

I

J

J

be found. (Leading tones in minor keys

accidentals.)

i

^^^

^

^

11-15.

j^'' \l'ii

may

by

^ ^

:nj

-O-izz

157

'CONTINUATION OF TWO-VOICE COMBINATIONS

V-I cadences create root relations up a perfect fourth (or down a perfect fifth). The roots of these two intervals always correspond with dominant and tonic at

5.

final cadences.

11-16.

Ex.

V

The

6.

I

cadential interval usually

falls

in a strong metric position.

11-17.

Ex.

^

LJlI

^=J

V-I cadences are often embellished by decorative pitches. Codettas frequently

7.

occur as extensions of these basic patterns.

11-18.

Ex.

I

Progressive Cadences. to terminate phrases

and

codetta

Composers have employed a great variety of patterns

larger sections of two-voice compositions.

The

types

fall

two principle groups: progressive and transient-terminal cadences. The possibilities for creating progressive cadences are enormous. .Several basic

into

made: (1) tonic will not be the root of the cadential interval, are some progressive cadences which do include tonic) (2) acjive^

observations can be

(although there

;

pitche s, such a s the leading tone or subdominantj usual!) will form part of

tlie

cadential interval; (3) decorative consonances as well as cadential consonances

may

be found, and even dissonances

may

occur as cadential intervals of progressive

758

CONTINUATION OF TWO-VOICE COMBINATIONS

and (4) rhythmic activity may be maintained thus weakening the cadential effect. cadences

In Ex.

Ex. 11-19.

;

1

1-19, a progressive

cadence

in the

in

one or even both voices,

key of ^ minor occurs in measure

6.

^^^ ^m ^ m

Handel: Fughetta.

^m ^

^

IV

The cadential major third is formed by the leading tone A-sharp and F-sharp. The root of this interval, F-sharp, is the dominant of ^ minor; "more to follow" is strongly implied by the absence of tonic,

and by the presence of the leading

tone.

Progressiv e c adences to intervals^ whose roots- are._th£.jiominant-ar£_ traditjo na ly called half cadences. 1

Another form of progressive cadence involves root movement from the dominant to the submediant (V to VI). This pattern, often used to avoid the sense of finality associated with

movement

to

a tonic root,

is

generally introduced by ascending

motion in the lower voice, accompanied in the upper part by parallel or contrary motion to tonic, or contrary motion to the mediant. The resulting effect is

step

called deceptive,

root

Ex.

is

(deceptive cadence), because anticipated

movement

to a tonic

evaded. Bach has employed a deceptive cadence in measure 4 of Ex.

11-20. Bach: Two-Part Invention

in

D Major.

V

1

1-20.

S-

movement to d, in the lower part, is replaced by movement to b, the submediant. The root progression is up a major second. The root of the approach Anticipated

interval in the deceptive cadence

is

usually the

dominant (V), producing the root

progression V-VI. (Deceptive cadences involving other root progressions are a possibility, as

we

shall see in later study.)

CONTINUATION OF TWO-VOICE COMBINATIONS

759

Several other types of progressive cadences are

11-21. Progressive

Ex.

I f

s

3

^

fe

r

Cadence

Patterns.

zaz -e-

s

shown

in Ex. 11-21,

I

331 ~n:

33=

f

r

4 f

33:

e

5

-o-

r

^

Deceptive zaz

^

-e-

T

T

T

3jr.

Although "modal cadences" are not indigenous occur frequently at interior cadences

comparison of Ex. 11-6 and Ex. 11-21

to

—particularly will

show.

major-minor music, they do progressive cadences

The

tritone,

— as

a

although not used

harmonic interval in final cadences, can be found as the approach interval in both progressive and transient-terminal cadences. Cadential uses of tritones are usually the product of decorative activity in one or both voices. A study of the cadences discussed in this chapter will show that most cadences

often as a basic

involve root

movement

in ascending or descending perfect fourths, or ascending or

descending major or minor seconds. Root movement in thirds

Other

Interior

is

infrequent.

Cadence Patterns

Cadences which confirm or imply changes of tonal center are an important means of creating tonal variety, and help to delineate melodic form. These cadences, occurring at phrase or sectional closes, are often of the

and any cadences which are the

root

of the cadential interval

The opening dence

terminal in effect is

V-I group, although

may

be found. As in

7-8 <-,'.

cadences

final cadences,

generally in the lower voice.

eleven measures of Bach's

G Minor

Invention

contain a terminal ca-

and a modulation to d minor. All of the cadences are basic V-I patterns, elaborated by various forms of decorative activity. Each cadence marks the close of a phrase and is signaled by the introduction of longer durations in one of the voices. Melodic activity continues the other to G, a transient-terminal

cadence

voice, however, thus diminishing the

pitches inevitably occur

on strong

to B-Jlat,

rhythmic

beats.

effect of

cadence.

The

cadential

760

Ex.

CONTINUATION OF TWO-VOICE COMBINATIONS 11-22. Bach: Invention

i 2^

G

Minor.

^

^y^

Measures

in

^^jP^m

Szm

S

^

and 6 contain a modulatory sequence, which represents a patterned means of effecting a change of key from g minor, through its relative major, B-flat, to d minor. Two shifts of tonality, each up a third and each punctuated by a ca5

dence, bring about the change.

Dominant is

— tonic cadences to F are heard in bars 3 and 5 of Ex.

1

1-23.

The

first

transient-terminal, since B-flat has been established as tonic in the music preceding

F

momentarily emphasized, by the leading tone e'-natural, which with c" forms a V-I pattern. We anticipate a return to the Bflat tonic. This is denied, however, and F is developed in the subsequent phrase as a continuing point of focus. The cadence in bar 5 confirms Fas a new tonality. As in the example by Bach quoted as Ex. 11-22, the change of key represents a modulation to the dominant key. The interplay of tonic and dominant keys is the most common tonality the cadence.

is

CONTINUATION OF TWO-VOICE COMBINATIONS relationship in Western music.

161

Most transient-terminal cadences occur

as a

means

of effecting this significant relationship.

11-23. Handel:

Ex.

Keyboard

Suite,

Allemande.

Tonal Function Within the Phrase; Root Relations

The melodic and harmonic

in

the Two-Voice Frame.

action of the cadence has been described in terms

of the root relations of cadential patterns such as V-I, V-VI, I-V,

Any

Roman

cadential pattern can be described with

roots of basic intervals. This procedure

is

and

so forth.

numerals representing the

equally applicable to an entire phrase or

composition. In other words, having discovered the basic harmonic intervals and their roots, for

one can represent their relationship

by using a

Roman numeral

mode dealt with. harmonic movement I-VI-II-V-I,

each scale degree, regardless of the type of key or

The

passage of Ex. 11-24 consists o{ basic

an analysis of the accompanying reduction

Ex.

to tonic

as

will show.

11-24.

When

a change of tonality occurs, the same procedure can be adapted to the

ferent degrees of the

new

key, as

shown

in Ex.

1

1-25.

This analytical

dif-

set of symbols

CONTINUATION OF TWO-VOICE COMBINATIONS

762

be discussed extensively in subsequent chapters.

will

It is

a convenient

method

for

both planning and analyzing the harmonic interval roots of two-voice writing.

11-25. Handel: Suite for

Ex.

Keyboard, Allemande.

M^ ^m ^5 m mm

(Articulated Pedal)

*i_*

m

£

^

^

*»•=

F:V

rfJ

ab^

^^

*

fe

nV

^

IV

^^

B^:I

IV

> r •

F./l

I

:^

LllJ

^

^

^

C£[fr

V

mt ^S ^ ^^ ^^ ^^ ^^

^m^ 'Tf

IV

I

p

=t=

V

II

^

^

^^

^

^

~

1*—y^

:zi

^

^

?

^

^ -e-

Organization of Two-Voice Phrases.^

The

contoural relationship of both voices

mere

a two- voice phrase. If one voice

is

simultaneously with the other,

interest

its

a

is

is

a basic consideration in organizing

follower, reaching high

and low peaks

diminished in the same

way that rhyth-

mic duplication minimizes the independence of parts. In Ex. 1 1-26 the lower voice is essentially accompanimental. Its contour, like the upper part, is primarily descending, so its importance as an independent voice is

minimized.

'

A

Basic rhythmic associations of two-voice textures were discussed in the beginning of Chapter 9.

rev

iew of

this

information

is

appropriate at this time.

163

CONTINUATION OF TWO-VOICE COMBINATIONS 11-26.

Ex.

Haydn: Piano Sonata

in

A Major.

n^ ^m

Adagio

^

j

l

-'-Mi!

Two

i^lr

voices of

^

J

m

shown in Ex. 11-27. Again, contours, and the low and high points of both

more equal rhythmic

however, both voices outline similar

ar

i

interest are

occur at about the same points in the phrase, although not simultaneously. The accompanying reduction to basic pitches shows the similarity of contour in a skeletal form.

11-27.

Ex.

^m

P

if^

^ s ^

m

^

p

~&

T21

3=*

t IC

XE

s

s«

JQI -JX-

^

ztn

by their parallel step progressions, is obvious. The lower part retains some rhythmic individuality through the use of decorative sixteenths, but linear independence is greatly minimized because of the

The

similar contours of these lines, as evidenced

duplication of basic contours.

In contrast to Ex. 11-26 and Ex. 11-27, the voices in Ex. 11-28 have more

dependent melodic curves. Here the voices

take turns as

predominant

parts,

in-

but

CONTINUATION OF TWO-VOICE COMBINATIONS

164

even

so,

they outline basic pitches in essentially contrary motion, and the high and

low points of succeeding motives occur one

after the other, rather

than simulta-

neously.

Ex. 11-28. Bach: Invention in

D Major.

Contrapuntal interest can be achieved, as in Ex. 1 1-28, not only through an equal distribution of activity, but also through variety of melodic contours. Two equal voices compete imitatively in Ex. 1 1-29. Although they use identical melodic materials, successively, the two voices are delineated effectively by two simple processes: Each successive basic interval

motion, which

is

continued right up to the

is

approached through contrary

last interval.

The

highest note of the

with the lowest note in the bottom part. Furthermore, each basic pitch, as shown in the reduction, is approached in contrary motion. An organizational pattern such as this can easily become as dull as any other procedure, if overdone. The effectiveness of the example, however, illustrates the degree to

upper

line occurs

which contrasting contours can contribute even when other factors are virtually equal.

to

melodic interest and independence,

)

CONTINUATION OF TWO-VOICE COMBINATIONS Ex.

11-29. C.

P. E.

165

Bach: Keyboard Sonata.

Repetitive Factors

in

Phrase Organization.

In earlier study of melody (Chapters 1-8) several repetitive processes such as

motive repetition and sequence were discussed. These same processes are equally fundamental to phrase and sectional organization in two-voice textures.

Both voices in Ex. 11-30 make acceptable melodies Both use repetitions of a short motive.

Ex.

11-30. Handel: Suite for

j'''^

performed separately.

Keyboard, Allemande.

-^LLLr P

S

if

7

P

^^

f^ m ^

^

^

m

_

m

P

^m ^^ ^

(Art]cu]ated_ Pedal

0^0

m^ The motive

feS

:^

between the two parts, creating continuous eighth-note activity to the cadence. Both voices are punctuated by rests, and the relative inactivity in one voice makes it easy for the listener to shift attention to the other part. This kind of rhythmic exchange, based on repetitions of one basic motive treated in two parts, is a fundamental principle of two-part writing. fluctuates

766

CONTINUATION OF TWO-VOICE COMBINATIONS

A

different kind of repetition organizes Ex. 11-31.

tirely

The upper

line unfolds en-

through successive patterns of three eighths. The less active lower part, which accompanimental, is differentiated from the upper line by quarter

essentially

is

notes.

The

prevailing contrary motion further contrasts the two voices.

Ex. 11-31. Bach: Invention in

G

Major.

4''<^^^UsaJ

^^

PUj'

"Usr

"^'iii

i

w~7^:

^

J)

Although both voices are unified through repeated eighth-note activity, they are at the same time clearly contrasted rhythmically and move independently of each other.

A

example of motive organization is shown in Ex. 11-32, which contains two independent voices, each unfolding through sequential repetition of a motive.

The

final

brackets, indicate that

it is

entirely possible to perceive the beginning of each

repetition at several points. This alike,

Ex.

seem

to overlap,

is

true because the successive melodic units are

and are not separated by

rests or contrasting durations.

11-32. Beethoven: Piano Sonata, Op. 110, Fugue.

Sequence. Sequential activity in one voice in the other.

matched by a corresponding sequence Ex. 11-33 shows three statements of a one measure pattern in the is

usually

CONTINUATION OF TWO-VOICE COMBINATIONS

167

accompanied by a sequential lower part. The lower voice accompanies with a twice-stated pattern which is also repeated a second lower. upper

part,

11-33. Bach: Invention

Ex.

A

in

D Major.

similar sequential organization occurs in exact form three times

modified a fourth time in Ex.

11-34.

Ex.

HIndemith

:

1

and then

1-34.

Ludus Tonalis, Fugue

in

E.

1943 by Schott

(C)

&

Co., Ltd., London.

Reprinted by permission.

-/

^

^

\'j

^ m^ ^ §

i

i,

m^

P

I

i*^

uJ

l

l,J^^t^

P

m

Roots

"^

As one might expect, the step succession of harmonic roots.

relations of the voice

movement

Successive phrases are frequently built out of a pattern that first

second phrase with material which its

35.

is

treated in the

phrase as an exact sequence and then "borrowed," so to speak, as a point of

departure for a contrasting or "answering" phrase. to

create a stepwise

is

derivative

The

from the

listener

first

is

led into the

but not maintained

termination. Such a technique of smooth phrase delineation

is

seen in Ex.

1

1-

'*^®

Ex.

CONTINUATION OF TWO-VOICE COMBINATIONS 11-35. Corelli: Sonata da

S Roots

for Violin,

B^

Vlnl

A A

camera

Sarabanda.

g ^^

i

^M P P P V

ff'

55^1

131

g

P

^

Roots

The second phrase, which begins at measure 5, is not actually part of the sequence. Both the sequential root pattern (up a fourth down a fifth) and the step progres-

—

sion formed

by basic pitches

in both voices

clearly begins with a restatement of the

is

first

broken. However, the second phrase half of the two-measure motive that

has occurred sequentially in the upper part. Turn to Ex. 11-22. Study both parts separately, paying particular attention to the amount of sequencing that occurs in them. Note where Bach has treated both time, and also notice where he has not. A careful study of this work shows that sequential repetition is one of the most continuously applied techniques in the unfolding and development of this Invention. Together with imitation, which will be discussed later in this book, sequence is indigenous to contrapuntal writing, and represents a common technique for unifying a two-phrase

voices sequentially at the

same

organization.

Exercises

For more detailed assignments see Materials and 1.

Illustrate ten basic

Structure of

Music

I,

Workbook, Chapter II.

cadences in two voices to the tonics F, 5-flat and D. Play the lower and sing the upper, then reverse the process. Use some of the same

voice of each pattern

examples 2.

for class dictation

and

recognition.

Use the same patterns as basic pitches and write short two-voice elaborations of them, using passing and neighbor tones to create rhythmic play. Sing or play these patterns and use them for dictation. Vary the meters that you choose for elaborating the patterns, and limit

them

to

two or three measures' duration.

169

CONTINUATION OF TWO-VOICE COMBINATIONS in Ex. 11-26

and Ex.

1-27.

How

do they

3.

Analyze the sequences

4.

Write a four-measure two-voice phrase, based on motivic treatment of measure

1

differ? 1,

Ex.

1

1-

14. 5.

two measures as the basis for 7—8 cadence to G. Use the exa sequence that occurs two more times, followed by a ^ Continue Ex. 11-13

for five

more measures, using

the

first

,

ample

for sight-singing

and two-voice

dictation.

:

Conclusion

72

.f

Two-Voice

Combinations

Suspensions

In Chapter 8

we

described the suspension as a decorative pattern involving a

kind of melodic "delaying action," in which a basic pitch or basic associate

is

sustained through a subsequent strong beat, and resolved by step on the following

weak beat to another basic pitch. Syncopation often results from suspension patterns, and the three elements which comprise the suspension figure weak beat preparation

suspension

basic pitch

decoration

shown

i^

in the following:

and

resolution

basic pitch

W

W are

weak beat

strong

^

Preparation Susp- resolution (

The

basic pitch) (decor) (basic pitch)

addition of a second voice generally involves the treatment of the suspended

tone as an unstable pitch, as shown in the figure that follows s,

w

$ The

suspension pattern in two-voice textures, then, creates a tiny cycle of melodic-

harmonic movement comprised of

stability-instability-stability,

and the addition

170

.

CONCLUSION OF TWO-VOICE COMBINATIONS

171

of a second part simply clarifies and delineates (harmonically) an essentially

me-

lodic configuration.

Although the suspension figure study

first its

7-8 of a n'l cadence to ^ are

Cadence

12-la. Basic

^ ^&

by no means limited

to the cadence,

we

shall

use as a cadential embellishment.

Two versions

Ex.

is

shown

in Ex. 12- la

and Ex.

12- lb.

to g.

^

*i

W

12-1b. Elaborated with Susoension.

Ex.

^

^

iM

^

•)-(.

movement

upper part, from g^ to f^-sharp, has been delayed, or suspended, and g^ forms a dissonance of a minor seventh with the a in the lower voice. Several observations pertinent to the approach and resolution of the suspended g^ should be made: In the second version the step

1.

g'

was

(upper 2. g'

first

in the

heard as a consonant pitch, having been prepared as a consonance of a minor third), on the last beat of measure

member

was sustained

1

into the next strong beat so that

it

created a dissonance (minor

seventh) with the lower voice. 3.

g' resolved

by descending step tof 'sharp

— a consonance (major

sixth)

—on the

subsequent weak beat.

The

suspension,

g', is

actually heard as the middle

parts: preparation, suspension

and

member

of a figure of three

resolution.

Preparation, then, refers to the point at which the suspended pitch

troduced as part of a consonant vertical relationship. Syncopation, a feature of the suspension figure, results beat, or the

when

the preparation occurs

weak part of any beat preceding a

tied suspension.

{g')

is

in-

common

on the weak

I!»

772

CONCLUSION OF TWO-VOICE COMBINATIONS

The preparation

usually as long as the suspension (dissonance)

is

itself.

In Ex.

12-2, the preparations are of differing lengths.

Ex.

12-2. Suspensions.

Syncopation

a.

/\

^&

Pt Prep.

Sus. Res.

m

g

i

S

^^

i

R

19

Syncopation

m

i&^

^

R

S -&

s

(21

^ m

b.

^

Syncopation

^

^^

S

i

^

^

^

R

S

R

P

^

S

R

?

In Ex. 12-2a, the preparations are at least as long as the prevailing beat (a quarter note or more), and they are of no

less

duration than the suspension

itself

These represent the most common preparations. Less typical preparations occur in Ex. 12-2b, where the preparations are less than one beat's duration and, in most instances, of less duration than the suspended tone. Rearticulated suspensions are shown in the first and last examples of Ex. 12-2b. Although the suspended pitch is generally sustained, a rearticulation after the preparation

is

common.

Different Forms of Suspensions. In Ex. 12-2a

tone formed a minor seventh with the lower voice.

and Ex.

Though

12-2b, the suspended it is

common

to refer

CONCLUSION OF TWO-VOICE COMBINATIONS

173

two voices do not form disHowever, they do create relative instability, and the mterval always be a cadential or decorative consonance. Furthermore,

to the suspension as a dissonance, all suspensions in

sonant intervals. of resolution will the resolution

is

usually to a basic pitch.

Suspensions are described by referring to the intervallic distance between the

by the interval of created by suspending/, which

two voices

at the point of instability (or dissonance), followed

resolution.

For instance, in Ex. 12-3, a seventh

when

in turn forms a sixth

*

,.

J

r

i

The

J

^

r

r

resulting pattern

by step

resolves

to

T is

called a "7-6 suspension."

not usually included in the analysis, although sonant.

The

7-6, then, describes

types: 4-3, 6-5, 9-8

tant

and

common feature

:

e.

LH r^ ?

12-3. Suspensions.

Ex.

it

is

it

is

The

interval of preparation

is

taken for granted to be con-

one basic form of suspension. There are four other

2-3. All of these patterns,

the suspension pitch

is

except the 2-3, have one impor-

in the upper voice.

Although occasional

exceptions can be found, the 7-6, 4-3 6-5 and 9-8 are suspensions in the top voice, ,

whose resolutions occur by

Ex.

descending step movement to a

more

basic pitch.

12-4. Suspensions, a.

Mi

J-

^>Mi r

The

r ^'J

^

i

^

m

^p R

:zz

and non-cadential quality of the perfect fourth is best illustrated by its frequent treatment as a suspension, resolving to a major or minor third. We have already noted that fourths are usually surrounded by step motion in two-voice writing. In Ex. 12-4, a V-I cadence has been rewritten to incorporate a 4-3 suspension. The suspended tone, d, was prepared as a consonance on the second (weak) beat of measure 1. It was then sustained through the following strong beat, creating a perfect fourth with the bass, then resolved by descending step to c^sharp. By rewriting the passage in different keys, we see how both augmented and diminished fourths also may be treated as 4-3 suspensions: instability

174

Ex.

CONCLUSION OF TWO-VOICE COMBINATIONS 12-5. Suspensions.

b.

a.

4-3^

^^

tit -#

P 4-3

,

?^

^

tf^

4-3

tts^ most often resolves by a descending-— of a V-I cadence pattern.

cadentially, the 4-3 suspension

in Ex. 12-6.

12-6. 4-3 Suspensions.

^

^ ^ ^^ ^ <->

%f-#^

l^^ P m P

^

P

^

<=

g

^

^

r

•-3-

^pr

^

t-3-i

L3J

p

suspension figure also occurs as 6-5, involving a decorative consonance

resolving to a cadential consonance.

mild,

"

te

^^f?^ ^ The

J

r

i^ e

r

r

5^^P=5

is

tfd

^

minor second to the leading tone (7) Analyze the 4-3 suspensions in the excerpts shown

Ex.

P 4-3

^i^^

^^ ^ WhexL used

^^

and the

The

effect of this pattern in two-voice writing

interval of resolution often sounds

more

prevailing tonality, than to an anticipated point of arrival.

strongly related to the

175

CONCLUSION OF TWO-VOICE COMBINATIONS

^ ^m

Ex.

12-7. 6-5 Suspensions.

f

The

6-5 suspensions o ccur frequently in approaches to V-I cadences, as seen in

movement

Ex, 12-8. Note that the a descending melodic

line,

and

constituting the resolution of the sixth continues

this contributes to

our expectation of descending

resolution (6-5).

Ex.

12-8. 6-5 Suspensions.

^^

#

^^

f

m-m-ft

1

JOO

-e-

6-5

6-5

^

^=^

1

"TV

-&-

-e-

6-5

6-5

TT

S

£

m ^ ^ 7-6 7-6 4-3

^m

W

lef

i ^ 6-5

9-8 Suspensions. 9-8 suspensions are rare in two- voice writing, especially at cadences.

They

are

more common

and four voice music. Although shown below, they represent unusual

to three

they occasionally occur within a phrase, as exceptions in two-voice practice.

^

Ex.

12-9. 9-8 Suspensions.

u>

i!

m

^=pt

r

^

r 7-

6

^

9-8

7-6

m ^^

—

776

CONCLUSION OF TWO-VOICE COMBINATIONS

An

extremely

common

suspension in two-voice music has the suspension figure in the lower part. This suspension, the 2-3 (or 9-10), is used both cadentially and

within interior areas of the phrase like the others. cadences, however, but

more

It

is

not often found in final

often in sectional or phrase endings.

12-10. 2-3 Suspensions.

Ex.

b.

4^

i

^

J

»

^^

rJ

0_

P -^

§

i

^ ^ 2-3

M

Ornamental Resolutions.

X t^'^ When

one or more pitches are interpolated between the suspension and its note of resolution, the resolution is called ornamental. In most instances decorations of the suspension involve step movement. However, movement to basic associates

may

an embellishment of the suspended tone. The suspensions in Ex. 12-1 la, measures 3 and 4, have been rewritten in Ex. 12-1 lb, ornamented. The d^ in measure 3 is reached by step and creates an escape tone, while the a^ in measure 4 is a basic associate.

Ex.

also occur as

12-1 la.

Ornamental Resolutions.

^m

rzi

m Ex.

*

7-6 Ornamental Resolutions.

m^ 1

(^

#

m

7-6

i

i I

f

^ wm ^^ ®

^

^^ . ^jtf

i

12-1 lb.

I54=?i:

—

^ P i

^=^

f^^p

n

7-6

7-6

s

i

177

CONCLUSION OF TWO-VOICE COMBINATIONS Several ornamental resolutions of a 7-6 suspension are

Ex.

12-llc.

r-U'X

J

in

Ex. 12-1

Ic.

Ornamental Resolutions of a 7-6 Suspension.

^

zaz

Pr

< y* 7

m

shown

-o-

7-6

^«

32:

1

-

m

fe^^^

nx

£

As we know, suspensions usually resolve to basic pitches. This applies to ornamental resolutions as well. Furthermore, the note of resolution is usually equal to the duration of the dissonance, although exceptions to this principle showing resolutions of both more or less duration than the dissonance are not uncommon. In measure 7 of Ex. 12-12 the basic pitch movement of the upper voice involves

— —

The

ornamented by the interpolation of two sixteenth notes {b^, which anticipates the note of resolution, and a^, which is a neighbor to b'^), but the resolution occurs with the arrival of the quarter note b^ on the fourth beat of the measure, and so corresponds with movement to a basic pitch. a^

Ex.

i

c^

b^.

suspension resolution

is

12-12. Praetorius: Chorale Prelude, Ein fesfe Burg

r

r

r

ist

unser Goft.

m m^

pp

&

^ ^ m

s

^ m

^m f

f

f -

6

^

778

CONCLUSION OF TWO-VOICE COMBINATIONS

The

note of resolution of a suspension

may

be more pronounced because

it

forms

part of a step progression than because

it is the resolution of a dissonance. In Ex. 12-13 the g^ of measure four forms the resolution of the suspended a^ heard on the first beat of measure three. Five notes of an ascending pattern intervene between

the suspension and

its

two basic

and

pitches, a

anticipated resolution. g, is

The

step progression

formed by the

another factor that causes g to be heard as a natural

point of arrival of a.

12-13. Bach: Invention

Ex.

in

D Major.

i»^^ *l

W J

V

m

^m A

m

=^ ?itF«rf

similar delayed resolution occurs in Ex. 12-14. Locate

it

and analyze the

suspension.

Ex.

12-14. Bach: Invention

in

D Major.

The Change of Bass Resolution

One called

of the most interesting techniques associated with the suspension

"change of bass."

is

the so-

CONCLUSION OF TWO-VOICE COM6INATIONS Ex.

Change of Bass

12-15. The

In

179

Resolution.

type of suspension the lower voice, which normally remains stationary

this

as the suspension in the

upper part

The

is

resolved,

moves by an ascending perfect

formed at the point of resolution of the suspended seventh is a third, and the resulting pattern is described as 7-3. Note that the anticipated stepwise resolution of the suspension to a consonance still takes place. The 7-3 figure is common as an approach to the V-I cadence. It fourth to another pitch.

is

also

common

T he

change of ba_s s

hejnun^

in

within the phrase.

general, the bass

The

figure,

may move

Ho wever,

it

to

any pitch that

usually

m oves

is

in contrary motion with, the top voice^

change of bass patterns found in conof the suspensions that we have studied.

all

12-16. Suspensions with

Changes of Bass

(or Soprano).

With chang£ of.bass

Basic Pattern

I

njz ''

V-.-

j"

^

'

"r

f

^

^? §

consonant with the resolution of

illustrations of Ex. 12-16 illustrate

junction with

Ex.

change of soprano (or upper voice) jm ay although it is most commonly found as 7-3. In

(or lower voice), or

any suspe nsion

the suspension.

interval

^

r

f'r

^7-6

3i:

P^

331

^

^^

r

r

f

"0~

r

^^ ^^ p

^m

nx

-Q"

^ 4-6

^ 2-3

331

7-3

JClL

r

^

^

2-5

ZUl

CONCLUSION OF TWO-VOICE COMBINATIONS

780

Ex.

12-16. continued.

'^

p ^

n

^

^^

ini

r

s

/•-^

iE

p6-3

6-5

^)-lI',

<'

g-tr-^

^^ 9-6

9-8

^^ i ^^

nx:

ij "

^E^^

f

r

^

r

33=

7-6

The name

retardation

is

ini

^

a

r

^

e

P s

^^

i ft=i^

/?

lai

33:

7-5

sometimes given to suspensions which resolve by ascending

These patterns occur most often in association with unstable intervals that normally resolve by "expanding" to a consonance. These include the augmented second, augmented fourth, augmented fifth, augmented sixth, and major seventh (particularly when the leading tone occurs in the upper voice). The "normal step.

when upper member of

resolutions" of these intervals were discussed in Chapter 9. Their treatment,

they are a result of a suspension, does not

differ,

except that the

the interval will have been prepared melodically.

Ex.

12-17. Retardations.

m^ U ^ ^ •r-i
m

^

m

i

m

# 9-10

(2 -

m

3)

?

^ 4-5

^ -p-i

i

:

CONCLUSION OF TWO-VOICE COMBINATIONS

181

^^

^rijim The

7-8

various forms of the suspension clearly constitute an important facet of two-

voice counterpoint. Like other contrapuntal

suspension figure

is

and organizational techniques, the

found in varying degrees in most musical

styles,

representing

another type of patterned movement that establishes an interdependent relationship between basic pitches in two musical lines.

A summary

of the foregoing study of the suspension should recall the following

principles 1.

The

suspension figure in a two-voice texture usually involves a dissonance or

most often in the form of a syncopated pattern, in the upper part, prepared as a consonance on the preceding weak beat or weak part of the beat, and resolved on a weak beat by descending step. The suspension pitch, in contrast with its preparation and resolution, occurs on a strong beat relatively unstable tone,

or strong part of a beat. 2.

The

three steps that comprise the figure are: Preparation, Suspension

and

Resolution, abbreviated P.-S.-R. 3.

Suspensions are usually, but not always of the same duration as the prevailing basic duration.

4.

5.

The preparation is usually equal (or greater) The duration of the resolution may be equal

to or less

suspended tone.

than the suspended note.

Suspensions are described according to the vertical intervals formed at the suspension and

and

*

in duration to the

6-5^

and

its

resoluton; they include the 7-6, 4-3, 9-8 (rare in two parts)

2-3.

Further discussion of the suspension figure and resolutions will be found in Chapter

15.

—

—

782

CONCLUSION OF TWO-VOICE COMBINATIONS 6. 7.

Suspensions occur cadentially and within phrases.

Suspensions which resolve by ascending step motion are sometimes called retardations.

which form a sequence are called

8.

Series of suspensions

9.

Ornamental resolutions result from the interpolation of one or more pitches between the suspension and its resolution. Such interpolated pitches, usually no more than two, are often called changing tones.

10.

The

resolution of the suspension

may

chain suspensions.

coincide with the introduction of a

new

The change of bass generally occurs in contrary motion with the upper voice, and forms a consonance with the tone of resolutone in the bass (or soprano)

.

tion.

Despite the diversity of style reflected in these works, the principles of the sus-

we have

pension that

discussed are incorporated in Ex. 12-18, Ex. 12-19,

and

Ex. 12-20.

12-18.

Ex.

\fiMr J\ ^Tf^K,

')-|

/^

r*i

1

}

J

^

—

—

— 9^

g

J-

^

3

IT,

— -P

m

P*h

«-J-

^

-n ^

M

—

f

m p

*"»

L-e)

vt 12-19.

Ex.

?t I

'hm \

P f

m

J-

^

pp

12-20. Obrecht

j> i

^=^

W ^^

^^ Ex.

r

^ ^^

:

*-H

f

J*

^ ^i3

^'

"m Pr

r

m

?F l-L

p^

f

^^

^

rn^J^

u

Missa Sine Nomine, Agnus Dei.

#

=

,

-*-^

m

^^ f^^^ ^^^ P^ i

183

CONCLUSION OF TWO-VOICE COMBINATIONS

m^ ^m yr^

p

mm

*-*-#

^

jn=

Vc^

i

^

-t»^

»

icn

V4

}(^

Imitation

Imitatio n results from the stat ement of a melodic pattern by one voice,

and the

The

pattern

a nswer of the same pattern

(e xact or

imitated (usually a motive)

often heard

is

modified) by first

another voice.

as a solo statement, thus underlining

an imitated subject. Compositions of two or mor e voices which employ strict mitation are called canons. Other types of compositions which employ imitative sections interspersed with non-imitative (free) sections include fugues, inventions, chorale preludes, ricercares, motets, canzonas, and others. We are concerned here with the principle of imitation, rather than the study of large musical forms in which imitation is found. Shostakovitch has employed imitation at the octave in Ex. 12-21. The time lapse between statements is quite close, one beat. role as

its

'^

i

Ex.

12-21. Shostakovitch:

Symphony No.

Music Corporation,

New

5,

Op. 47,

I.

(C)

Copyright

York, N. Y. Used by Permission.

MCMXLV

by Leeds

rights

reserved.

All

^^ '^'<'

1

1^

m.

Although the imitating voice may enter at any pitch-interval above or below the initial statement of a pattern, im itation at the unison (beginning the imitative) answer on the same pitch as the first statement), octave, fifth or fourth, xepresents, the norm. Furthermore, the imitation of a melodic unit may be strict, the answer duplicating the first statement in rhythm and interval, or it may be modified rhythmically or intervallicly. Three kinds of imitation are shown in Ex. 12-22, Ex. 12-23, and Ex. 12-24. -

The term

in the other.

canon refers to "law," in this case denoting the "laws" of

one voice dictating activity

784

Ex.

CONCLUSION OF TWO-VOICE COMBINATIONS 12-22. Frescobaldi

^ ^ Ex.

:

Organ

^E^ a-

P

^i^

^

p

12-23. Mendelssohn: String Quartet

in

zn

i.

m I

^ p^

pff^f

D major.

Co! era

i^ V

"^^i^

loco

^

^

I ^^-4^

m^^ Ex.

Ricercare.

12-24. Shostakovitch:

rgfS^

^^

Symphony No.

Music Corporation,

New

1,

=^

s as«

m

Op.

10,

^

i

II.

(C)

Copyright

York, N. Y. Used by permission.

^te: ;i^

MCMXLVI by Leeds All

rights reserved.

I

i

Oboe

Clarinet in

A

Fagotto

Violin

Solo

I

Violin n

^^^i

g

rnnn^ ^

^

^

0Pm lE^^

* t

Viola

i

Violoncello

g

-^

J'

^

J'

<

,S> ^ ll

ContraBass

1^

fMi

^M

CONCLUSION OF TWO-VOICt COMBINATIONS

IBS

^

^^ ^=^

/

n Solo

i

fc±

^

r jfli

p

tJg

I

-

'

J)

^r^

i i

i

^#

s

^

J)

7

7

.J)

^

h^

'^

J)

^^

^m

3 Imitation need not be limited to the opening of a composition, but

may

occur

any point in the unfolding of a work. In fact it is often effective in later portions of a piece, where contrast and changes of texture intensify and heighten developat

ment. In other instances, a piece that begins imitatively subsequent imitative

The

may

continue without

entries.

excerpt from a two-voice composition by Lasso, Ex. 12-25, affords an ex-

cellent opportunity to see

how some

we have been

of the structural elements that

studying are integrated into larger sections of pieces.

12-25. Lasso: Sequentur Cantiones

Ex.

o

im

P

-S-

^m

^

|>

(first

part).

-

^=s

^ 2t=^

#

P

P

^P^ p ^

w p

^

p

^^i

t»

fg

m ^

^ 'j^^' fj

p

^

:

786

CONCLUSION OF TWO-VOICE COMBINATIONS 12-25. continued.

Ex.

^

^

» P^

*=iF»

^3E

I The

?

i P

?

texture of this passage, written in the key of

m ^

i G

Dorian,

is

3x:

contrapuntal, and

maintained throughout. The music of both voices is developed, with rhythmic variations, out of the two motives heard first in the lower voice free imitation

is

1

;i2

^

.

o

The second motive

12

repetition of the

first,

transposed a perfect

fifth

is

a modified

above.

These motives are transformed rhythmically, through syncopation, augmentation, and diminution, to produce continuous motion distributed betw'een two equal parts. Despite the similar melodic content of both parts, contrapuntal independence is maintained by staggering the entrances and avoiding the simultaneous use of identical durations. Not until the final cadence of the excerpt do the two voices converge rhythmically.

Even though no strong cadence occurs

measure

14,

the music "breathes,"

Thus the piece takes on shape, and more independent than they would be if they moved continuously

because the voices the parts are

until

rest at

staggered locations.

from opening to close. Sing through the piece, then analyze the structure, paying particular attention to melodic motion and treatment of skips, the occurrence of dissonance, vertical combinations, and imitation. :

Other Forms of Melodic Decoration

:

Anticipation, Leaning Tone and Escape Tone

which occur in two-voice textures sometimes form dissonances with the other voice, sometimes they do not. Several anticipations occur in Ex. 12-26 and Ex. 12-27.

As melodic

patterns, anticipations

12-26. Bach: Chorale, Christ lag in Todesbanden (outer voices).

Ex.

4L

^

^^

g

i^'r

me^Lh

^ ^

—

—

CONCLUSION OF TWO-VOICE COMBINATIONS Book

12-27. Bach: Well-fempered Clavier,

Ex.

In Ex. 12-26, the tonic cadential basic pitch

and

is

When

(e)

1,

Fugue

weak

anticipation of the

anticipation, of course, involves pitch repetition,

where a relaxation of movement

effective

D Minor.

in

occurs as a rhythmically

The

(e).

187

is

desired, as in the cadence.

anticipations occur at the beginning or within the phrase, they generally

form segments of characteristic motives, often treated sequentially, rather than mere pitch repetitions. A sequential treatment of anticipations can be seen in Ex. 12-27. Another example of a patterned use of anticipations is shown in Ex. 12-28.

Ex.

^

12-28. Binchois

:

Rondeau, De plus en

^^

plus.

S^ X

X

W—JZMZ

P

^& ^

¥

^^

ZSl

331

Tied anticipations create syncopations, not unlike those often found sions.

duced

Ex.

In the example by

Edition

2_.

9-

-^^

Copyright 1924 by Edition Russe de Musique

;

-

— ^

jJT3

Hi.

1952. Copyright

, 1^^

intro-

& Renewal assigned to Boosey & Hawkes Inc. Revised Copyright 1952 by Boosey & Hawkes Inc. Reprinted by permission.

Renewed

-^

is

as a tied anticipation.

12-29. Stravinsky: Octet for Winds,

-4)i-9

in suspen-

Stravinsky, (Ex. 12-29) f-sharp in measures 2-3

1

—

-0 *

leaning Tones.

The

J—«

^

iiip

'-\rrf-

N

J

J

II

W^

^

use of the leaning tone in two-voice writing

almost entirely to the upper part, as illustrated in Ex. 12-30.

ff.-.

Y—l

is

limited

788

Ex.

CONCLUSION OF TV/OVOICE COMBINATIONS 12-30. C.

P. E.

Bach: Prussian Sonata

*

m ^5 The

m fcss FS

T*

6

^

£

^

its

appearance

the nineteenth century.

is

a predictable feature of

Most leaning

augmented or diminished

intervals,

it

many

full-textured works of

tones create harmonic interval patterns

similar to those of suspensions: 4-3, 7-6, 6-5, 9-8

and

7-8.

When

the pattern creates

way

consistent with the

usually resolves in a

resolutions of those intervals noted earlier.

12-31. Leaning Tones.

^ fei^

m ^g s

S

leaning tone has been regarded as a particularly expressive melodic ele-

ment, and

Ex.

<^~)

*

^ ^

^

p

d

•

i

'

^

© r

p

^

SS

f^^ ^1^

®

P s

i^

^

CONCLUSION OF TWO-VOICE COMBINATIONS

769

(Two- voice reduction)

t±

I

a

i

t'

p'

^

T

r

Ex.

(

i

Unaccented leaning tones occur

12-32. Bach: Well-fempered Clavier,

m

fc te

^n\

<'

^)

m

P

Like most other decorative patterns, leaning tones cented.

m

^

Book

fe

be accented or unac-

in Ex. 12-32.

(^J

p

may

1,

^

Prelude

in

D Major.

ig'^

J

^

p

^

^ -^

J)

P

Pedal

Escape Tones. Escape-tones, approached by step and

left

by

leap, are usual-

unaccented and occur most often within the phrase, rather than cadentially. Like leaning tones, escape tones are generally found in the upper of two voices,

ly

as seen in Ex. 33

Ex.

12-33. Barret:

and

34.

Keyboard Sonata.

Escape Tones

j¥

-j

'):tiji

'4

Ex.

r

C-fi

rJ

r

^

m

12-34. Bach: Invention in E Minor.

fe fc^ ± m^ =e=^

f^=U

# J *

f-r

^

^

790

CONCLUSION OF TWO-VOICE COMBINATIONS

Structural Aspects of Melodic Dissonance

We

have seen in this and earlier chapters how decorative pitches connect and embelUsh basic pitches of a melodic line. Pitches that form unstable intervals with a second part may be a part of the basic melody, thereby assuming a more structural role. One of the main considerations is metric placement and duration. In Ex. 12-35a dissonance is formed by pitches which are related to a recurrent basic pitch that is established by its repetition and metric placement.

Ex.

12-35a. Haydn: Piano Sonata

^^ 'y-^'..

i

}

I

in

E-flat,

r^?rr;

f

AAinuet.

r? irLT

i

f^jyi^ 3— TTT^

:*=t

T^

I

J

'

J>

The tone e^-JIat occurs throughout the passage, except in measure 7, as the lower member of an accompanimental pattern in the lower part. In the second measure upper line. This conflict continues through measure 3, and is finally resolved in measure 4. There is nothing decorative about the continued presence of the e-JIat throughout the example, so it must be regarded as a pitch of considerable structural importance. Its role is that oi^ a. pedal (or ground), that produces a strong tonal reference for the melodic activity above. it

creates a persistent dissonance with d- in the

Two

voices are implicit in the

accompanimental pattern,

as the reduction to basic

pitches shows (Ex. 12-35b).

A

b^-natural occurs three times in the

Again, although pitch,

that

^

we

upper voice

duration

is

.

compositions as well.

heard as a basic

its

note of resolution,

c"^.

which create similar effects are called homophonic music, pedal points may be found in two-voice

rearticulated, pitches to

c^, it is

5 of Ex. 12-35a.

in the design of the melody. Notice

considerably longer than that of

Whether they are sustained or Although more common

pedal points

measure

anticipate a resolution of this pitch to

and therefore a fundamental element

its

in

CONCLUSION OF TWO-VOICE COMBINATIONS

191

12-35b. Reduction of Ex. 12-35a.

Ex.

t±

m % 4

^"^-V^I1 j

^ ^

^ ^ t

?^

4^-)-

i i r

i

p;

r

(#)

-i*4-

a

lA

^

P.t.

e.t.

P

^

^^ ip.t

i

-J)u.n. (^)

^ i

15>^

f

f The four-measure a

<9-

excerpt from Bach's

A minor

predominance of disjunct motion. This

Invention, Ex. 12-36, contains

with the melodic

activity, associated

oudining (horizontalization) of chords, suggests analysis which takes chordal implications into account. These procedures will be discussed in later chapters dealing with thicker textures.

shown as Ex. 12-36b and Ex. 12-36c. In reduction (I), the melodic lines are shown as the chords which they outline. Reduction (II) eliminates decorative pitches and shows the addition of a third voice in measures 1 and 2, that is suggested by the activity on two levels that forms

Two

reductions of this Bach invention, are

the lower voice.

Ex.

12-36a. Bach: Invention

itJ

\)'

\l H-

(;

in

A Minor.

U^

J

'^

^ ^^

^

^.rrrrr^^r^rrTrr .r ri

TTM

ri

1

fri

i

rr-n ea--a'^

f ri

— '^4i frr:

-^ 1

U,.^^^

^

B M^

J

n

1

1

,

—

)

'^

"

r

192

Ex.

CONCLUSION OF TWO-VOICE COMBINATIONS 12-36b. Reduction

j j

j

4^?

t •eM

3

g=

^te

f^,)

')

p.t.

Ex.

(I).

12-36c.

i= '

Reduction

—

n

r

^

'

J

in this

^^ *w^ i

is

S

m Even

z;

(II).

I

$ ^

^^

ii

J

J

^^

more complex and chord oriented counterpoint,

sonances associated with melodic embellishment are

still

lower voice, measure

e

1,

acts as a passing tone

between

resolutions of dis-

applied.

and

c.

Its

The

D

progress

in the

is

inter-

and a reiteration of d. Then d'^, e'^, f^ and g^ are heard as a step progression in the upper voice, beginning with the third beat of measure 1 and continuing to the third beat of measure 2. As members of a sequence, based on an ascending chord pattern, each of these pitches may be regarded as an unaccented leaning tone with the "middle voice," (see reduction II). rupted by leaps to

b

and

g-sharp,

,

Cross Relation Gross relation (sometimes cdAXtd false

note occur on 12-37 a.,

relation) results

successive beats (or beat divisions)

/-natural in the lower part

is

when

between

variants of the

different voices.

followed by anf-sharp in the upper.

relation results, although the melodic effect of

each voice

is

same

In Ex.

A

cross

perfectly satisfactory.

In the approach to the cadence of the same passage, b-natural and b-fiat are cross related, producing the effect of a change of mode. Ex. 12-37b contains three cross

and creates an inconsistency of mode, (modal conflict), by pitting A major in the upper voice against a minor in the lower. Simultaneous cross relation occurs when different note variants occur at the same time, rather than successively, relations,

as in Ex. 12-37c.

^sssssti.

CONCLUSION OF TWO-VOICE COMBINATIONS Ex.

12-37. Cross Relations.

^m a

,

-^"^

h

^m

^^ An

i

beat of measure

measure

^^^m.

7

m

m:

3,

can be found

supertonic in the bottom part.

effective.

The lowered

The

b-mtural,

on

is

created by the use of the lowered

supertonic often occurs before ca-

somewhat jarring effect makes the establishment of tonic even more Ex. 12-38 and Ex. 12-39 also illustrate cross relations. its

Ex.

12-38. Bach: Well-fempered Clavier,

Ex.

12-39. Stravinsky:

&

Symphony

in

m W ^ ¥

Book

1,

Fugue

Three Movements,

Co., Ltd., London. Reprinted

m m

3

in Ex. 12-35.

creates a cross relation with the b-fat just heard in

2 in the lower voice. This colorful effect

dences, and

^

^

Ef^

p

interesting use of cross relation

first

^M ^ ^

yTOr

t

1

the

193

I,

E

Minor.

(piano part). (C) 1946 by Schott

by permission.

-^

-3*^

in

^m

^ w. ^ W ^ te

1 t

$ i

^

'

:

194

CONCLUSION OF TWO-VOICE COMBINATIONS

Several generalizations pertinent to the use of cross relations can be

Ascending movement

I.

in

one part

with descending

in contrast

movement

other frequently creates acceptable cross relations, as in Ex. involves the ascending

Ex.

(^

and descending forms of a melodic minor

12-40. Treatments of Cross Relation

<'

^-^J^' J^r

in

r

Cf

^^TTT-fT^

Two

made

12-40,

in the

which

scale.

Voices.

jgr

J

LLLT^J

Cross relations occur naturally from combinations of essentially diatonic move-

2.

ment

in

one part with chromatic alterations

such as those

in

measure

1

in another.

Chromatic

alterations,

of Ex. 12-38, and those in Ex. 12-41 are essentially

decorative, rather than basic pitches. Basic pitches seldom create cross relations.

Ex.

12-41. Cross Relation.

^

^ -

ijUi^J^

^1''' f

^

1

'

^£Q'»^^^

^^ ^^

Mutation (a change of mode) as found in Ex. 12-42, with a clear change of mode from minor to major, frequently results in cross relation.

3.

Ex.

j fTf

12-42. Cross Relation.

b^

t± *'

i -

k

m-

m

m

^P

d ' S C Minor

—

—^i

\^

'^^'^^^

^

:

fct

j

C

m

te

i :

Major

(Mutation)

f^i^^SHh

^*

Wj

^

^ :

i

m \^^^

^

CONCLUSION OF TWO-VOICE COMBINATIONS

195

Cross relation has had a variety of treatments in the course of Western music.

seldom arbitrarily used, and in most works it is either a logical outgrowth of independent melodic movement, or, as we shall see in later study, an inseparable element of certain established harmonic patterns. The treatments illustrated in Ex. 12-40, Ex. 12-41, and Ex. 12-42 show what occurrences of cross relation might be encountered in written exercises or analysis of two -voice counterpoint. It

is

Exercises.

For more detailed assignments 1.

Use

see Materials

and Structure of Music

I,

Workbook, Chapter 12.

the examples in the section dealing with suspension for sight reading

and aural

recognition of suspension figures. 2.

Using the two motives from Ex. 12-25 which appear in the text (p. 194) follow the example as a lower voice and add a new upper part which incorporates suspensions. Extend the second motive so that it ends with a cadence on G.

3.

Analyze

4.

framework of four measures in C time. Write two basic pitches per with a V-I cadence in the key of E-flat major. Elaborate both voices measure and close with all forms of decorative activity studied in this chapter. Label each decorative

all

Make up

forms of decorative activity in Ex. 12-13 and Ex. 12-14.

a two-voice

pitch. 5. 6.

Add a new lower part for Ex. 12-14. Use an imitative entry for the added part. Make up short two-voice examples (no more than two measures long) illustrating

a

dif-

change of bass in each. Label each step (P.S.R.). Rewrite Ex. 12-19, keeping the upper line as it appears, but using a different accompaniment and transposing the example to E-flat. ferent type of suspension with a

7.

8.

Work

out a keyboard setting of the upper voice in Ex. 12-12 that begins with an imitative 2. Accompany the upper voice so that suspensions occur in measures 5 and 6. Close with a cadential 4-3 suspension. entry in measure

9.

Make up the book.

short illustrations of

Use

all

forms of decorative pitches that have been dealt with in

basic cadences as a

framework

for the illustrations.

Three-Voice

13

Combinotions

Our

study of two-voice textures dealt with principles of organization

any number of parts. Adding more voices creates new problems of spacing, part-clarity, and harmonic logic, but the linear basis for that can be

expanded

effective three-part

new

combinations

— articulate

melodic structure

—

is

not different

Except for the introduction of the chord as a potential new the vertical alignment of three voices likewise poses no drastically

from that of two structural unit,

to

parts.

problems.

Rhythmic Association

The degree

of individuality displayed by the separate parts of a three-voice tex-

dependence to total independence. The term ho mophone combinations in which a single part can be regarde d as a^

ture can vary from total is

usually reserved for

Whereas the slow-moving lines in Ex. 13-1 represent the most unobtrusive kind of homophonic association, the active parts of Ex. 13-2 are so thoroughly enmeshed with the motion of the top line that they, too, represent a form of homophonic texture. principal melody, the remaining parts accompanimental.

Ex.

13-1. Schubert: Morgengruss,

^5

f

^m^

"Die schone

M^ ^1

Miillerin."

s

? 1S2

196

THREE-VOICE COMBINATIONS

Ex.

Mendelssohn: Op.

13-2.

197

19.

^ m^ s P fr

^

r

r r tF i

The Mendelssohn

<

^

m ^

s

i ^

^

tj)

.

J

^

^^

i

ip

j)

excerpt of Ex. 13-2 contains brief suggestions of part in-

dividuality, the rhythmic separation of the middle voice in measures

and the independent contour of the bass

at several points.

two and

To

:

present. " justify the description contrapuntal." a three-voir.p r.om V»ma|jr>n

tain_parts that

have

three,

But on the whole,

three voices are relatively unified in pitch contour and rhythmic play

kind of counterpoint

^

all

a minimum

is

Qme

s.

degree of individuality

;

and

yet, all three

piii<;t

rr>n-

must coalesce

into a u nified as sociation. In fulfilling these basic requirements the parts can he

combined Type

1:

into one of the three following dispositions:

One voice dominating; remaining voices

aligned as accompanying parts,

varying one from the other only to an extent that preserves their separate identities.

Ex.

Bach: 3-Part Invention

13-3.

ph^

in

E

Major.

'^-

r

* dominating voice

Ex.

Hindemith, Ludus Tonalis, Fugue

13-4.

in

E,

No.

4.

(C)

1943 by Schott &

Co.,

Ltd.,

London. Reprinted by permission.

i

J

s

.

m ^^

"h^

# *

Even

dominating

voice

u

1

^

i f

f

two examples of the one basic type, a latitude of linear interest is displayed by the separate "subordinate" parts. The upper parts of the Bach exin these

THREE-VOICE COMBINATIONS

798

cerpt form a simple

foil for

the greater melodic interest of the bass through the

and bottom voices are switched in measure four). The upper parts of the Hindemith excerpt are less subordinate in character, for they move in faster relative note values and cut more interesting lines in contrary motion to the bass. first

three measures (the roles of the middle

Type 2:

Two voices

Symphony

13-5. Franck,

Ex.

$ ^m

of about equal interest; a third voice decidedly subordinate.

J

,j

in

D Minor,

I.

i^i ;J J

r ^r=r r i

P^i

^frffi^

#

i

r

right

Schuman, Symphony No. owner, G. Schirmer, Inc.

^^^m

^

|)iJ.

E^

13-6. William

Ex.

w

3,

J)

^ 1^

Fugue. Reprinted by permission of Copy-

r=""*=f

s^^ • S i» \?

mi *^

i

g¥

^

Iffl

In the Franck excerpt of Ex. 13-5, the two outer parts dominate because of greater rhythmic interest and imitation of patterns (the bass of measure two and three imitate the soprano of measures one similar, for the disposition of

and two). The Schuman example

melodic interest again

is

in the outer voices.

the lower part does not contain imitative statements, nor

is

it

is

But here

quite as active as

the top part.

Type 3: Three voices of approximately equal interest, each sharing the er's attention in

listen-

a "give-and-take" succession; frequently an imitative relation-

ship.

Ex.

13-7.

Handel: Clavier Suite No.

3,

Fugue

^-^ n /l,^ ^m^M^S^ ^ P^ r m ^^ a n^ i

!

f

^ffi

j

r

199

THREE-VOICE COMBINATIONS

Ex.

13-8. Lasso

j'^'UJ

:

Penitential Psalm

No.

^^ ^ yr^ f rr

ss

^

Wf^

i

^^ fT^

i

^ f=r=^ rrrf

f

^^ ^

3 "N

—i

rt

frr i

Both the Handel and the Lasso textures use imitation. In Ex. 13-7 the bass line imitates the top (beginning in the last half of measure two), and the top imitates the bass (beginning in measure three). During this exchange the middle voice winds through its own separate and quite individual motion. Ex. 13-8 contains imitative statements

among

all

three voices at various points.

Almost any contrapuntal texture of three parts can be fitted into one of these three categories, but music does not normally remain set in a single disposition for long. The composer is free to shift or vary textural relationships. Consequently, it is often futile to describe an entire composition or large section by any one of these types.

Within a three-voice comVjination one line can dominate the other two by virtue of its more interesting rhythmic pattern. But faster motion alone does not ensure melodic domination over slower moving lines, unless this faster motion is couched in rhythmic patterns that are diversified enough to be interesting. The comparatively rapid motion of the "continuous basses" in many compositions of the Baroque era recedes into a subordinate "background" role because it also

happens

Ex.

13-9.

to

move

in rigidly

uniform patterns.

Handel: Trio Sonata, Op.

^^ 'y-Hi)

f

P f

5.

No.

4,

Passocaiile.

^^^ f^ r f ^

ii

rJ

J. r-

^^ r p

r

^

—

^

200

THREE-VOICE COMBINATIONS

Both of the upper voices in Ex. 1 3-9 are marked by rhythmic diversity. This sets them off as conspicuous in comparison with the continuous eighths of the bass hne. When rhythmic diversity is present in all three parts, the pattern of faster articulation usually dominates the texture.^ An exception to these rhythmic "rules of thumb" can occur when a melody that has been firmly established in the listener's mind is sounded in slower motion than its accompanying parts. For instance, the tune that serves as the melodic basis for forms in which variations occur simultaneously with the known melody since it has the advantage of familiarity may be accorded more attention than voices of considerably greater rhythmic interest. The chorale prelude uses a pre-existent melody which, in many settings by composers, employs this contrasting relationship of slow voice accompanied by busy rhythms in remaining voices. In spite of its less interesting motion, its familiarity, coupled with emphasis of registration or instrumention in performance, may still focus our attention on it as the dominating voice.

—

Ex.

13-10. Schiedt: Chorale Prelude on Gefobef se/sf du, Jesu Christ, Verse 4.

^

^ rr ^^M r

^r

4

n f fm

p

9^^ Chorale melody-

Rhythmic Unity

The rhythms of the separate voices normally are

related so that they

complement

one another, avoiding extremes of pattern contrasts that could thwart the association of the three as compatable parts. For this reason, voices normally share the same set of rhythmic divisions, though these divisions are not always articulated simultaneously. In many three-voice textures the separate patterns, though different, tion.

when added

In

this

way

together produce a periodic splitting of the meter's basic dura-

the

combined rhythms of Ex.

13-11 divide the basic duration

(

d

)

into a continuous stream of quarters, while Ex. 13-12 contains divisions into sixteenths.

The

result of these

combinations

is

a continuity of flow for the whole tex-

ture.

^All other factors being equal,

—

we

are prone to regard the highest voice of a combination as the

most important as the "melody". 2 In organ chorale preludes the "melody" en its prominence.

is

frequently reinforced by octave couplings to strength-

.

201

THREE-VOICE COMBINATIONS

Ex.

13-11. Beethoven: String Quartet,

I

J

Combined motion: f

Ex.

J^j

h

i

Op. 131,

J

f f f T

T f f

13-12. Bach: Well-tempered Clavier,

J'"'''l\'g

^,2 P

f Book

ii

f

nh

a) r

Although a

all

^

C

I.

f f f II,

Prelude No.

^^W :

r

f f

f

f f T

f

9.

f

?^^^

i

-^^ !^

part combinations do not consistently divide the metric basis into separate voices often use the same (or closely related) patterns.

set division, the

The

a some-

Ex. 13-13 shows a

less

what

rhythmic propulsion than the passages of Ex. 13-11 and Ex.

less-driving

constant division of the basic duration.

result

is

13-12.

Ex.

13-13. Handel: Clavier Suite No. 4, Sarabande.

Allegretto

^ PP? ^^ ^^ m ^ tr

.

n

{.'ip}

:

M f=^

^^---^ J :

1

^^^ %^

^

Combined

motions:

c/

r

[_&•

f

p r

Infrequently, the several parts lines

is

r

move

r

c/

in identical

r

l;

r

r

r

p

rhythms, and separation of

achieved solely by individual pitch contours. This unusual

way

of main-

taining line identity does not occur often in contrapuntal music. It will be discussed later as a possible

means of pitch organization.

Voice individuality is most commonly achieved by contrasted note durations. Three parts composed of mixed long and short values offer the simplest and surest

202

THREE-VOICE COMBINATIONS

way of creating part separation. Combinations

of three equally active voices usually incorporate a broad diversity of motion, in this way accentuating further the individuahty of each part. The section shown in Ex. 13-14 contains parts whose

rhythms typify

Ex.

h

.

kind of individuality.

13-14. Frescobaldi

f '

this

ici^

J-

4

Jt^

i

«?' i

"s

Here each voice moves acting as a

in

W^ ^^

its

^

own

-o-

i

individual rhythm, the occasional sixteenths

minimum rhythmic bond between

the two upper parts, but with no

closer hint of kinship in evidence. Passages of this kind are infrequent in

music of

three parts, for most textures rely on a closer rhythmic union between at least two

of the

lines.

Stretches of a three-voice combination are comprised often of parts, each of

which represents a duration

itself

(bass voice)

different division of the basic duration or the value of the basic

The Bach

and

excerpt of Ex. 13-15 divides the quarter note into eighths

sixteenths (middle voice) in a continuous relationship, while the

top voice provides articulations of the basic duration.

Ex.

13-15. Bach: We//-fempered Clavier,

The

I,

Fugue

in

E.

uniformity of each pattern adds up to a rhythmic thrust that

music whose is

Book

lines are

(

J

"

J

J

absent in

formed by a greater variety of note durations (but each

also less interesting rhythmically as a result). It

articulations

is

•

J J J J

)

is

this

simple

1

to 2 to

line

4 ratio of

that blends the three different parts together into

such tightly unified association. Aside from diversity of patterns created by fluctuating note values, individuality of parts also can be obtained by contradictory divisions of the basic duration.

Duplet patterns in one voice combined with

triplet patterns in

another creates

203

THREE-VOICE COMBINATIONS

a more severe separation of parts than two versions of a single metric division.

When

the contrast

is

prolonged

it is

difficult for the listener to

determine the funda-

mental metric division unless a third part reinforces one of the patterns. In addition to contrasting or contradictory beat divisions, the displacement of accents in one part, by syncopation, forcibly differentiates that line from sociates.

The

ties

its

as-

across bars in Ex. 13-16 contribute to the clear rhythmic defini-

tion of each of the parts, as well as to the harmonic interest.

13-16. Bach: Art of the Fugue, Contrapunctus

Ex.

m

^

i

5=^=?^

^

^

p

The degree

J

^

i

*„

^ r

IX.

I

I

^

J

r- r^^

i

r

ni^f,.

'itf^[(j I

of unity of voices in a three-voice texture

is

also

coincidence or non-coincidence of cadences in the separate

predominating voice establishes the pattern of cadence

Thus

i^ 1

^

determined by the

lines.

In general, a

for all associated voices.

a chordal texture in which one voice dominates will display a uniformity of

phrase length

among

the constituent parts, these lengths governed by the "mel-

ody's" cadences, as in the next example.

Ex.

13-17. Bach: Chorale harmonization, Vafer unser

m ^ rmf # 1 ij

/7\

i

J

j/i

#

.3^ =Qff

^hJflUj

w

g

i

On

Himmelreich.

f^

^^ ^ mr^ W^ 1

in

?

the other hand, textures of greater contrapuntal interest do not always dis-

play this singularity of cadential form; individual parts sometimes create their phrase lengths and cadences separately. This condition avoids rhythmic

own

stagnation by allowing continued motion in at least one voice while another pauses at

its

own

formal junction. Ex. 13-19

is

bracketed to show the phrase structure of

each part, thereby revealing the variety of cadence locations that create a constantly mobile texture. Only in the sixth measure do all of the voices combine in a halt that creates a strong cadential effect.

The

further enhances this high degree of motion.

imitation between the three voices

—

Z

204

THREE-VOICE COMBINATIONS

13-18. Lasso: Penitential Psalm

Ex.

III.

^

/

a^^^

rT=^ rfff

Voices

S

£f^

li^ f ^

f

ffT

rrrr

i

rfff

^^ TTf ff rW

m

by continued articulation

^f

ZZI

in only

momentum

is

^m r

m

m

imitative combinations,

less

^r-

f

f^

m

>

In

^

:a

sustained at

m^ i some phrase endings

one part. This singular movement reduces the

conspicuous pause of the cadence, and

it

throws the active voice into stark

relief

against the inactive.

13-19. Mozart: Sonata for Violin and Piano, K 376,

Ex.

II.

Andante

^^

Violin

jjjjJi^J -? -9

'

f mf

i 1

>

-^^

>!^

J

fi

i -^

WB

Piano

^m '

j''

U^jU^U^^. w^

m —

^jlm

a

J,nm lm^ycf^ If_^_

f*4-

Cadence ±?±:

VBfi^^

205

THREE-VOICE COMBINATIONS Pitch Association of Three Ports

a

The introduction of a third voice to the musical fabric creates the possibility of new reference unit of harmonic structure, the chord. Up until this time we have

gauged pitch associations by

their intervallic content without relating

them

to

chord structure.

We

chord until Chapter

shall defer discussion of the

14, for the present

dealing

only with the melodic principles that are pertinent to combinations of three rela-

independent parts.

tively

It is helpful to

view a three-voice texture as a two-voice basis to which a third

complementary part has been added. This added part forms a two-voice counterpoint with each of the original voices, and these two new associations follow closely the principles discussed for two-voice textures in Chapters 9, 10, 11, and 12. These contrapuntal relations of three voices are represented in Ex. 1 3-2 by brackets where in a two-voice combination there is only one set of vertical relations, there are three ;

sets in

a three-voice texture.

Three contrapuntal relations.

13-20.

Ex.

Top voice Middle voice

Bottom voice

Since the two outer voices of a three-part texture form the structural pitch limits

—

— the

"top" and the "bottom" they constitute the vertical framework for the combination. For this reason, the success of a three-part union depends strongly

upon the compatability of the outer voices. The middle part in some combinations serves as a rhythmic and harmonic "cushion," filling in where outer parts take momentary pause or where they, alone, do not complete the desired sonority.

Ex.

13-21. Handel: Clavier Suite, No. IV, Courante

Pt

m .

g^^

I

J

.

f

S

5^

i

m m r

I

206

THREE-VOICE COMBINATIONS

In addition to rhythmic diversity (discussed on page 199), pitch contour is another melodic factor capable of arresting the attention of the listener. A contour of greater breadth will dominate another Hne that moves within a limited pitch range, unless the narrower voice has a

more engaging rhythm. A voice of limited contour, however, usually moves in slower, less diversified patterns, thus ensuring its less important, more accompanimental role. Ex. 13-22 and Ex. 13-23 show two passages, each having one subordinate voice. It is true that the less obtrusive Hne in Ex. 13-22 is articulated in relatively brief values, but its durational patterns are the sums of the time between articulations, as well as the actual note values alone, thereby producing a slower motion in relation to the other voices.

Ex.

Ex.

13-22. Bach: Well-tempered Clavier,

13-23. Shostakovitch

MCA

of

New

Inc.,

:

Book

Quartet, Op. 49,

II.

Used by permission of

m^ I

'^

tfe

^ jmji jmji nu

m

s

MCA

Music, a division

^

w

n Jjgji juoj juajg

f^f^ ^ ^> Ff Wf '-^p^

'P-

Fugue No.

York, N.Y. All rights reserved.

g.

^

I.

I,

T-

W^

r-

p^ P^

»»?-

r-

The Shostakovitch passage in Ex. 13-23 is noteworthy because it represents a kind of "bare minimum" counterpoint; its two lower lines lack interesting melodic contour and rhythmic diversity. The middle voice is, of course, pedal figure, and represents the ultimate thus in static pitch contour. The bass is itself relatively static, a.

for

it

consists of

an

ostinato

pattern of the most rudimentary shape.

Individuality of pitch contour determines to a certain extent, then, the equality or inequality of linear interest discussed earlier. Three voices that form quite different pitch outlines, their rises

and

falls

occurring at separate locations, create the

Most

do not incorporate parts so individually contoured, but a texture of three interesting parts will have lines

greatest degree of contour separation.

w^hose highs

Ex.

1

and lows occur separately

textures

as often as together.

3-24 shows a three-part texture in which each line

separated from

its

associates

is

rhythmically unique,

by virtue of individual contour.

THREE-VOICE COMBINATIONS

13-24. Bach:

Ex.

The two follows the

207

Well-tempered Clavier, Book

I,

Fugue No.

15.

outer parts of a three-voice texture can be regarded as a framework that

same organizing principles developed

The

voice textures.

in earlier sections devoted to two-

potential cadence formulae remain identical,

and the

inter-

between the two lines retain cadential consonances except when decorative patterns form dissonances. The middle voice forms a two-part union with each of the outer voices, as we illustrated with Ex. 13-20. Its relations with each of these parts is also that of a vallic relations

two-part texture, but a few extenuating circumstances create some notable ferences

when

dif-

the three parts sound together.

For instance, the perfect fourth, which does not appear frequently as a basic interval in two-voice textures, appears commonly between the upper voices of

The

three-voice combinations.

tonal instability of this interval precludes

currence between the lower two parts as a cadential consonance

when

its

oc-

formed between the two upper parts it is normally accompanied by a major or minor third or a perfect fifth between the lower two parts. ;

it is

13-25.

Ex.

®

*

=P4=&

and fe

lJm3I

H«

and

»** ^^"^^f

3=E

V^

V^T^

A style of writing that makes extensive successive use of the interval combination shown

in Ex. 13-25

can be found in the works of composers from

periods of music history. Its effect

contrapuntal texture that bass"). chord

Ex.

As we

style,

it

is

so striking

when

it

many

different

occurs within a generally

mime faux bourdon ("false more apt name might be sixth-

has been assigned the special

shall see in the following chapter, a

because of the sixth formed between the outer parts.

13-26. Angelus

ad V/rg/nem (Anon). fauxbourdon

^1

m

t

T$ zpz

iw

^

r

208

THREE-VOICE COMBINATIONS

The

and

dominate the structural points of vertical alliance between three voices, with the fourth as a possibility between the two upper parts. Ex, 13-27 and Ex. 13-28 show two three-part combinations which, when reduced to their basic outlines, reveal this use of basic intervals and decorative octave,

fifth,

thirds,

sixths

patterns.

Ex.

^^

13-27. Handel: Clavier Suite, No. 4, Gigue.

r

pp jl^

'^pr

'y-Hmr pr

n^r^r parr

r

py

p

? ^f=^ r 5

Reduction

^,p} ^

gf

P l

1.

2. 3.

^

8-63-53-53-3 6 3

--6 --5

J

r

--6 --5 3

jJ

3

P 1

8

2

4

3

5

F-

4^

6

8

4

6

3

3

^^

P f r

536 685 3

3

3

^

^

^^ ^^ J^ P

.-,

»r

13-28. Landini: Ballata.

»^

hm

J

J

^ r

M^'l

Intervals

Ex.

rP

fe

i

J fM-^ d=bi^ P 5-5 -33 -34 ?^

-

3

5

6

8

1

3

5

most common as the pitch framework around which a three-voice union might be formed. The intervals are all reduced to a single octave compass for ease of reference compound versions of each relation are just as possible.

The

interval combinations in Ex. 13-29 are

;

THREE-VOICE COMBINATIONS

209

13-29.

Ex.

Unis citi

*

(i)

t s

(1) tl

.

i^tKi

33=

(D

(i)

(I)

nr

It

H

^

f ti

Cadential

(I) o-

Decorative

^=s

Consonances

Consonances

which include seconds or sevenths, or which have fourths or tritones between the lowest and either of the other parts, usually arise from a decorative pattern of some kind. We shall deal with some of these matters in greater detail in Chapter 14, where we will discuss chord structure for All other interval combinations

the

first

time.

Sparial Distribution of Parts

The

and the overall pitch range enclosed by these combinations, are both determined by the particular sound desired by the composer and the relative contours of the individual lines. Two outer parts that move in predominantly contrary motion inevitably will lead to a fluctuating texture that varies from "narrower" to "wider." distances maintained by the voice pairs of a three-voice texture,

Similarly, lines of highly individual melodic contours render a tight uniformity of

spacing impossible.

The

very nature of counterpoint dictates that any three-voice

texture will normally encompass at

least

a

full

octave range, thus making individual

part motion possible without constant impingement on the pitch territory of another voice. Three-voice combinations with very active lines usually cover this

more than

bare minimum.

In general, a particular section will maintain a relatively uniform spacing that further unifies texture. As basic types, two distributions of pitch levels to the various parts are

Type

1:

common: Generally equidistant parts, no consistent couplings of any two of the

three in evidence.

Such a

disposition will usually reveal considerable individuality

of lines as far as pitch contour and rhythm are concerned.

Ex.

^

13-30. Bach: Three-part Invention No. 12.

»#-^ti)-p-

^

t

^^

270

THREE-VOICE COMBINATIONS

In Ex. 13-30, each of the three parts remains within a clearly delineated range its unique patterns within its assigned region. An abstrac-

of activity, maintaining

tion of the spacing characteristics in this passage shows tion of pitch activity within the three lines, all of

octaves

and a

'

Q

(.

clearly the distribu-

which cover a

total

span of two

fifth.

13-31. Spacing of parts

Ex.

more

in

Ex.

13-30.

Top voic e plac e men t

^1 Mi ddl e

vo ice placement

Bott om voice placement

m N Textures of

this

type cannot remain for long in a single relationship of parts

unless similar motion prevails, the individual part contours assuming approximately the

same shapes.

Type 2:

Two

parts coupled in close range, the third part separated

by approx-

imately an octave (or more). (The coupling can obtain between the two upper or the two lower voices.)

Schumann: Op.

60, No.

Ex.

13-32.

Ex.

13-33. Bach: V/ el I -tempered Clavier,

1.

Book

I,

Fugue No.

ju-irf^^jffi\jn^im

MiK^I '

^

fl

i

6.

\

m^^4

\;'^l

I

These two excerpts show the coupling possibilities in three parts, in terms of register. In the Schumann sample the upper parts are combined within close

THREE-VOICE COMBINATIONS

211

proximity, while the bottom part winds through a range approximately two octaves

below the middle voice. The Bach excerpt is a reversal of the Schumann, for here the upper part is separated from the coupled pair of lower parts. In both instances, the separate part is more conspicuous by virtue of its highly contrasted octave position in the combination.

Features other than spacing can serve to emphasize a particular voice. Although the two upper parts in Ex.

1

3-34 are coupled in range as distinct from the bottom

upper

part, the longer durations of the

line

make

other two. Here rhythm, not spatial coupling,

13-34. Telemann

Ex.

:

i

[J

a distinct pattern from the

the distinguishing factor.

Chorale prelude, Chrisfus, der uns selig macht.

^^ ^^ ^ wt D^ 'h^W)

is

it

^^ f mr

^^^ erf

^

^

**

mw -e-

In addition to the specific musical effect desired by the composer, voice distribu-

depends upon the instrument or instruments that play them. A distribution such as that in Ex. 13-35 is impractical for a piano because some of the spacings would be clumsy for the right hand. Ex. 13-36 would be ineffectual for tion in a texture

the piano, but for different reasons; here the problem

would be clear articulation and separation of individual melodic strands. The constant voice crossings can be clear when played by flute and two violins (or by any combination of single-line instruments), but the articulation difficulties for the pianist would be ticklish. Added to this purely physical problem would be the lack of tonal contrast between the three separate voices, and the combination of objections make such a spacing most improbable for piano.

Ex.

13-35.

1945 by Hawkes & Son Copyright assigned to Aaron Copland, Copyright Owner, and

Copland: Appalachian Spring, (London)

Ltd.,

Boosey & Hawkes

1^p-m

trnttCT

Inc.,

Bride's Dance. Copyright

Sole Licensees.

^ ^

m»0»m»mm pp mp mpmm -m-^^mmppp

^^m

p'mm pdm^ i^P

^^

.

272

Ex,

THREE-VOICE COMBINATIONS 13-36. Bach: Suite No. 2, Rondeau.

s ^^ ^

Flute

Violins

ffhM4

n

\

'fil

r^i

¥

^

^^^ f

i# P

P^

r=T

gapped spacings that contain no couplings of any kind are associated with highly contrapuntal textures in which individuality of parts is paramount. In more homophonic {homogeneous) combinations a closer spatial alliance of parts becomes essential. The effect of harmony is most readily achieved when parts are close enough to make them fuse into a block of sound. A simple experiment will demonstrate the differences of spacings. If the combinations of Ex. 13-37 are played by separate instruments, the more unified, compact effect of (a) contrasts discernably with the more disparate sound of combinaIn general,

heterogeneous, or

tion (b).

Ex. 13-37. a.

i

Flute or Clar.

4''i

i

Clar. or Trpt.

^

r-f DI

i

Clar. or Trb.

^^

Flute or Clar. Clar. or Trpt.

Bassoon or

Trombone

P ^=T ^

rT

1

xc

L^ ^^

P

"n

Aside from the differences of tone quality produced by the register changes for the top and bottom parts in (b), the wider separation alone reduces the effect of tonal fusion that

is

more apparent

in the closer-knit alliance of (a)

7HRff-VO/C£ COMBINATIONS

213

Exercises

For more detailed assignments see Materials and 1.

Structure of

Music

I,

Workbook, Chapter

Plan a three-part rhythmic texture for percussion (clapped hands will ance if necessary) that consists of three complementary patterns.

suffice for

1

3.

perform-

Model ire-3-e-

m.jr I

2.

3.

I

;)j

J

f

r

^ci/

r

I

r

I

j>,j

Ji

f

r

^ai

r

i

r

r

^

r r

J

J

pr irr

J

^;)

,j-

pt

r

p

n :mp

Look through piano, choral, orchestral, and chamber music to find passages of rhythmic association which correspond to one of the types discussed early in this chapter. Find two parts (or extract them from a composition) which will serve as an outer framework for a three-part texture. Add a third part in complementary pitch and rhythm patterns.

4.

Write an eight to ten measure passage in which the top voice dominates, the two lower voices are relatively subordinate and are coupled together in register. Write another passage in which the bass dominates and the two upper voices are coupled.

5.

Analyze a number of contrapuntal textures (Bach, Handel, Mozart) for basic pitches in three separate voices. Construct a three-voice basic framework as an abstraction of the texture. Then decorate the resultant framework to create a different composition.

Chord

14

Structure

\Vith the addition of another part to a two-voice texture

recognize a

new

unit, the chord, as a basis of pitch organization.

we can

This will not

represent a major change in method, for chords are collections of intervals, and

they are classified by the kinds of intervals they contain, by

chord

relative stability of a

by

the relation

it

is

determined by the intervals which comprise

bears to other chords surrounding

In Chapter 2 we discussed the relative sonance

and

dissonance of intervals.

one that contains only consonant

more dissonant

or

sonority types.

stability

As a general intervals,

it

The and

it.

and

instability,

the relative con-

chord is while a dissonant chord contains one rule, a

consonant,

stable

intervals.

Ex. 14-1 shows four different chords, the

more dissonant than

the

first.

last

three of

Note that each of these

which are considerably

last

three contains at least

one unstable interval.

Ex.

14-1. Chords.

-mS-

i aita:

n

Consonant

i^?3= 3:^5=

^

*Ll M2 -M3-

dissonant

-m^

^^ «5-i-]p4

m^

[¥¥f-

V

fi-

dissonant

dissonant

The more complicated the total interval structure within a chord, the greater the chord's dissonance. Thus we could make a scaling of harmonic sonority that would extend from the most consonant sound combination, the octave, to the most dissonant, in which all twelve pitches of the chromatic scale might sound together in a biting combination.

214

CHORD STRUCTURE Ex.

275

14-2. Chords,

b

a

pt

m Not only (and thus

is

^ ^m

chord

many

(b)

more dissonant than chord

different intervals as well) also

(in this particular spacing) that a

(a), its

impart

to

it

many

different pitches

a high degree of density

few-toned chord would not have.

Between these two sonorities of Ex. 14-2 lies the gamut of chord types that are found in most music. The bulk of our musical heritage has used a restricted harmonic palette that lies closer to the I sonority of Ex. 14-2a than to Ex. 14-2b, but composers since the beginning of our century have considerably broadened the possibilities toward the dissonant side of the scale. One of the recognizable trademarks for any composer is the chord combinations to be found in his music and the way these sonorities are linked together into harmonic successions. Many of our subsequent discussions in this book will be concerned with the recognition and classification of chord types. Any chord that can be reduced to no more nor less than three different notes is called a triad. That is, even a chord made up of five different tones might still be reduceable to a triadic basis if two of the five pitches are octave replicas of two others.

t^oitttLcAid^ Ex.

- tmWiwtXui

MuAjJxMj^

tl

14-3. Triads.

1 chord

triadic

$ chord

reduction

triadic

reduction

w

m ~tT"

ZC^ chord *Q_ 321 33=

triadic reduction

^

W3

chord

triadic

reduction

X

J

276

CHORD STRUCTURE

—

Western music is unique in its development of a concept of chords the "vertical" plane of sound in music in addition to the purely melodic or "horizontal" plane. In non-Western cultures the simultaneous soundings of different tones are regarded (if at all) only as the result of coincidences between the several strands of melody. Some of the "chords" of the Siamese music show^n in Ex. 14-4 "just happen," for they are not derived from any manner of predetermined chord progression, and the musicians who perform such music make no effort to plan their

—

improvisations so that particular tones coincide at

all vertical

combinations.

A

web of lines created by own melodic strand to the

similar result sometimes can be heard in the improvised

jazz musicians as each instrumentalist contributes his total result.

Ex.

14-4.

Siamese Orchestral Piece: Kham Horn (Sweet Words), Hisforical Anthology of 1; Copyright by Harvard University Press. Reprinted by per-

Music, Volume mission.

But

in

our composed music, harmonic motion pervades musical structure,

The simplest units of harmonic structure are triads of relatively consonant quality. They are the only chords which consist of intervals no less stable than major and minor thirds, so they are among adding another dimension

to tonal organization.

the most stable chords. These are the major of a perfect

Ex.

fifth

divided by a third.

14-5. Triads.

±5z

2

L

i» 3

m3

M3

major triad

4^

n

1=W5= ]

m3

minor triad

and minor

triads,

each of which consists

;

;

217

CHORD STRUCTURE It

the location of the constituent thirds that determines major or minor

is

quahty

when

when

in triads:

the

Two

the

first

third

third above the root

first

is

above the root minor, a minor

is

known

other of the simpler triad types are

major, a major

triad results;

triad results.

as diminished

and

These designations are derived from the interval that encompasses tones, the diminished and the augmented fifths respectively.

Ex.

augmented.

their outer

14-6. Triads.

5 m ^f^ 3

-M-8-

'

6

§

ITl3

^'^ll^Wi

diminished

augmented

triad (°5)

triad (+5)

Both of these

triads are relatively unstable, for they lack the intervallic simplicity

that creates a clear root effect. Neither contains a perfect fifth or fourth,

and the

diminished triad contains the relatively unstable tritone. Since both the aug-

mented and diminished diminished

triad,

triads involve equal-sized intervals

major thirds

lack the clarity of tonal focus that

Major and minor

triads are

augmented), they are

in the is

more

(minor thirds in the

slightly

ambiguous and

required of a cadential consonance.

stable,

and

so they are

more important

to

our

present study. Furthermore, they will form the basis of many other chords that will

Note that major and minor than diminished and augmented.

be discussed triads

later.

scales yield

more major and minor

') Ex.

-k^MUT

14-7.

M Major

W

scale

^

m

o

II,

M M

,m

III

H

I

M

m

Nat

m inor

scale

^

t'|

j

;

I

>»

' o

o

+

m

M M

^1

»i

^1

»i ^i

m

+

Hai mir'„"Tai:

m

M M

Melodi

1,, minor seal

Each of is

I",!,

iij t

i

Hi

the chords of Ex. 14-7

built within.

Thus

i

M

t^f

m

i i

m

j

|

o

is

the triad g-b-d

^

3

major

1

diminished

3

;

minor

^^

lit

^^'

3

major

1

diminished

2

major

2

o

°

\i

ii»

'^

2 2

;

3

minor

;

2 minor diminished; 1 augmented ;

;

2 minor major diminished 1 augmented ;

a "diatonic" chord for the particular scale is

diatonic to

D

major, but

it is

it

non-diatonic

278

CHORD STRUCTURE

for (^-natural

diatonic for

minor; and the triad B-flat-D-F

C

is

a diatonic chord of

F major,

non-

major.

Although the major, minor (and less so the diminished and augmented) triads are the harmonic staples of music of the past eleven hundred years, any three different pitches must be regarded as potential triad material. The chord succession in Ex. 14-8 shows six three-note chords, or triads, only the last of which is similar to one of the four types we have been discussing. The remaining five triads are relatively dissonant combinations which are essentially products of the linear motion of the three lines.

Ex.

14-8. Hindemith

ludui Tonalis, Fugue No. 4 London. Reprinted by permission. :

^ f

m

^ ^

^ T^r-

i^

In addition to sonority type classified

forms

— another

tion to other chords in

"behave" or

reflect their

— major,

vital bit of

its

E.

1943 by

(C)

Schott

&

Co.,

^^

i

r

f^

Ltd.,

/?\

m

minor, diminished, or augmented, of the

information about a chord concerns

proximity. That

own

in

is,

its

rela-

chords are like people in that they

identities only in relation to other chords,

and these

familial relationships within a tonality are a necessary aspect of chordal description.

The

individual chord's relation to the tonic pitch

is

denoted by the

Roman

numeral that represents the scale position of the chord's root. If we build a triad on each degree of the major or minor scale, we can number the resultant chords according to their relationships to tonic within

Ex.

f A

14-9.

Chord Nomenclature

Relation to Tonic.

a

Major:

U i

tonic

A

in

Minor:

li

supertonic

U ;

t iil

that scale.

1) I\'

^^ V

VI

ffi ,

\1l°

(I)

leadingdominant submediant submediant tone dominant

^

"

^^

m

IV

VI

ffi vn

(i)

'

CHORD STRUCTURE

The two

219

be known about a particular triad within a tonality are

essential facts to

and here between its sonority

its

tonal function.

Therefore,

it is

important that a distinction be

made

and lower case Roman numerals, for these, in conjunction sign for diminished and the + sign for augmented, are concise ways with the to indicate the two basic facts about any diatonic triad: capital

°

Jejvbodj

Numeral Type (capital or lower case, plus

°

or

+

when

applicable) shows basic

sonority.

Thus

V or

IV

vi or

ii

ii°

denotes major triad

denotes minor triad

or iv° denotes diminished triad

III 4- or

11+

denotes augmented triad

Numeral Value shows scalar degree relationship to tonic pitch. Thus V (or v) denotes a root tone that is a perfect fifth above (or perfect fourth below) tonic. I

(or

i)

indicates the triad built

on

the tonic pitch.

Chord Succession. Within a tonality, the most important chord is the tonic (I or i, depending upon major or minor sonority), for it is the only chord that can render total stability within a progression. Just as almost all melodies end with their tonic pitch, so almost all multi-part music ends with a tonic chord; it is the sonority that can best produce the relaxation of tension normally associated with musical termination. Aside from the tonic, any other stable triad (of major or minor sonority) is a potential tonic, for if emphasized enough, another chord can gain the ascendency and supersede a former tonic as the center of pitch focus: modulation takes place. The next most important chord within a tonality is the dominant (V), because in the traditional key schemes of major and minor and in some modes this triad coembodies the important dominant and leading tone melodic relationships. The combination of these two pitches in the same sonority creates the simplest chord relationship in a key scheme; it is this chord in conjunction with a tonic chord that most clearly delineates an intended tonality. When the two are combined in a weak-strong metric relation there can be little doubt about intended tonal focus.

Ex.

/L

'1:

14-10.

I*

m

V

to

Chord Progressions.

I

^' •

C

m

r.

U--

i

i'

1

d

m

•

9

(.

C

V

I

—

•

c

•

•

220

CHORD STRUCTURE

This simplicity of tonality pattern formed by the tonic-dominant relationship (or its reverse, V-I) causes it to serve as the basis for a great portion of the harmony in the music of our Western tradition. This basic two-chord association has been

used to accompany every conceivable kind of melody, from the modest child's song

works of considerable complexity.

to art

^ ^ u u ^m

Ex.

Ex.

14-1 la. Childrens

Song: Hove you Ever Seen a

ma

Lassie.

^ u u

^

u

F

F

14-1 lb. Beethoven: Donee.

P^m

# m

'

1 f

)--h

_

m

r

J-'

r r #

"^ —f

p

V •

— — — — in r^-rf

I

Any

I

r

1

is,

in a restricted sense, a

tonic,

r

T 1

a

weakening of

However, the root of the dominant chord does not contradict the

the tonic pitch as

ttII

I

digression from the tonic chord

tonality.

w

r- —0 f~irf F

for the root of their

the tonic pitch. This can be illustrated

if

role of

melodic relationship lends emphasis to

we

note in Ex. 14-12 that the interval

formed between the two roots is a fifth or fourth, and the root of both of these intervals is the same pitch, the root of the tonic chord.

Ex.

14-12.

V

to

I

Chord Progressions.

P5

It

ffi^

«m V^

P4

T

root

root

CHORD STRUCTURE

221

when one chord gives way to another is called harmonic succession or harmonic progression. The motion of chordal change imparts another element of psychological movement to musical tones; the change away from the

The change

that occurs

and tension; the eventual return to tonic promises fulfillment and relaxation of movement. If the harmonic structure of a composition remained solidly imbedded in only the tonic chord, no effect of harmonic tension could result, and the important feeling of completion that results from departure and eventual return to a tonic would be missing. The total effect would be dull and static if significant rhythmic or melodic or textural contrasts did not compensate for this harmonic sameness. Viewed as melodies, bugle calls suffer from this severe harmonic limitation, for they are the mere spinning-out of a single chord pattern that is based on the instrument's harmonic series. tonic chord establishes a certain degree of expectation

14-13. Bugle Call: Reveille.

Ex.

^Pii f^TH^W^ £_---

A major:

A

similar negation of

hinp npinn rt^ i

_.---.

harmonic motion might be desired

for particular kinds of

music that serve distinctive functions within a musical or social setting. One way of emphasizing the implied motion of one musical section is to precede it by a sec-

harmonic changes. The excerpt of Ex. 14-14, from a Toccata by Monteverdi, illustrates the avoidance of forward propulsion that can result from such a solidly grounded texture. tion that lacks

Ex.

14-14. Monteverdi: Toccata.

Clarino quinto

Aire e basso vulgano habso

^ ^S

i

m im

•/

]

iTTi]

—

222

CHORD STRUCTURE 14-14. Continued.

Ex.

L^

P^^^r

i

J

J

Sa

ii.

r

rr

xn

J:

J

331

i

XT

Most music incorporates harmonic textures the chord structure

is

successions of one kind or another. In

some

organized in vertical blocks of combined tones, each

of which moves to another, thus achieving direct harmonic change, as in Ex. 14I5a.

But in other textures the chords might appear

in

melodic outlines, the arpeg-

giated patterns adding up to particular chords (as in Ex. 14- 15b).

Ex.

14-1 5a. Bach:

r

J

J

r

r

^

Ex.

Voice

[

rv

14-1 5b. Schubert:

Der

vi

fjDMEJ-P'

^

*

I

iw

T

r

I

I

;:j

fTr?

^^^ D.

f

I7\

h.J^ r

^ ru^ ^

Chorale Setting, AUe Menschen miissen sterben.

j

r

m

j

r r

II

Miiller

*

*^*

i

^piM^-

f

*~^^

II

M^r

m^m

Piano

.&

§53l|^ * Chords

I

m

und der Bach.

na-rrs-d-

£

t

t V

w

V

I

223

CHORD STRUCTURE

In order to understand better the harmonic content of a piece of music, it is customary to analyze the various chords that constitute the harmonic successions

and

to plot this

data in graphic form.

The Roman numerals mentioned

earlier are

indispensable for denoting sonority types and root relations within a tonality. Ex.

14-16 shows a simple analysis of a musical phrase.

Haydn: Piano Sonata No.

14-16.

Ex.

18,

I.

mmm II

I

V

II

VI

(iv)

wi"

In some patterns of music, as in Ex. 14-16,

name with

it is

impossible to assign a chord

absolute assurance, either because the constituent pitches are so brief,

or because there

is

more than one

possibility of analysis.

interpretation because the highly mobile top line of the

a iv or a

i

chord. If

we

Measure

first

five

is

subject to

two beats might imply

return to the guide of basic melody analysis,

e is

revealed

most important pitch, so the iv chord is a most likely interpretation of implied harmony. In ways such as this, basic melody analysis and harmonic analysis are mutually complementary techniques for gaining musical insight. as the

Chord

The

Position.

names for the various parts of triadic chords are derived from the they contain. Thus the three parts are called root,^ third, and fifth. These

structural

intervals

terms are meaningful as designations

when

derived from the simple or fundamental

position of the triad, all notes in their closest relations, as illustrated in Ex. 14-17.

'

With the exception of rootless chords which

will

be discussed on pages 226.

224 Ex.

CHORD STRUCTURE 14-17. Structural

Chord Names.

Chord (D

Chord

m

-p^

Chord

^

fundamental

^ ^m

fundamental position

position

Even when the

t

:^Eti:

fundamental position

position of a chord changes, the individual parts are

still

named

according to their unexpanded relations in the fundamental triadic representation. Each of the chords in Ex. 14-18 consists of the same root [E-flat), the same third (G)

and the same

fifth {B-fiat),

even though vastly different chordal textures are

present.

Ex.

14-18.

^ T

m

^

W.

•>•

''F-i

l

1 T

'?-i

^

Even when more than

three pitches

of triad notes, then the basic structure

make up is still

some are duplications xhc fundamental triad. Thus the chord the chord,

if

type remains the same although voicing and texture change.

Ex.

14-19.

21

^

y

^^

;

9-S-

Chord

The

^

ii=

^

w

w

Inversion.

simpler chord types (major and minor triads and limited derivatives from

can be turned upside down and internally reordered without appreciably changing their basic sonority. This is corroborated by the fact that these topsythese)

225

CHORD STRUCTURE

turvy arrangements do not alter root effects in any appreciable way. We can see that any redistribution of the notes of a major triad not only yields decorative con-

same harmonic root

sonances, but also the

Chord

14-20.

Ex.

retained.

Inversion,

root

basic interval

^

is

root

basic interval

basic interval

a

I

t

root

For the reasons illustrated above, any distribution of tones is known by the name of its fundamental (simplest) reduced form. Thus both chords in Ex. 14-21 are F major triads, even though/is not at the bass position in either arrangement.

14-21. Inverted Chords,

Ex.

b

a

^

1^^ s

s

These denotations refer to the number of note shufflings away from the fundamental root position that are required to achieve the particular chord form. That is, beginning with the simple root position, the first inversion requires one redistribution of notes, the second

Chord

(a)

is

in first inversion, while

chord

(b)

is

in second inversion.

inversion requires two.

14-22. Inverted Chords.

Ex.

*

m root position

first

second

inversion

inversion

Another explanation root as

lowest

inversion;

The

member

for the three possible triad positions

in a root position

and the fifth

as lowest

chord; the

member

would recognize the

third as lowest

member

in a first

in second inversion.

representation of chords in analysis usually indicates the internal distribu-

226

CHORD STRUCTURE

tion of chord

members. This

is

done by appending Arabic numerals

to the

Roman

designation of root tone; these numerals denote interval distances above the bass note.

A

complete representation would be as follows:

? V

IV|

1(1)

6

m)

important to note that these numerical designations are derived from the vals above the bass as if the chord were all contained within a single octave. It

is

$

But

inter-

:

3Q

C:

V(|,

This system of chord symbolization is usually abbreviated. When no Arabic numerals

accompany a chord or

f

in

most

tion

in structure. cases, ^

I is

designation,

And

the designation

can also be taken

assumed that the sonority

it is

® is

mean

to

is

in root position,

normally simplified into just "6", which, "first inversion triad."

The

full

designa-

necessary, of course, for the second inversion triad, in order to distinguish

from the first inversion. Diminished and augmented triads lack the simple perfect fifth (or fourth) and the unequal thirds that create the root effect of major and minor triads, but the theory of inversion is normally extended to these sonorities also.^ The principle that governs chord invertability is derived from the notation of musical tones in stacked third relationshps. In other words, a chord is in root, or prime position when all of

it

members can be stacked one above

its

the other in successive relations of thirds of

any form, major, minor, augmented, or diminished. Therefore, chords la, 2a, and 3a in Ex. 14-23 are not in fundamental (root) position, but their rearrangements in lb, 2b, and 3b reveal their "non-inverted" forms.

Ex.

14-23. Inverted Chords.

la

i a

2a

lb

2b

3a

3b

* (°5)

3

^

This method of symbolization breaks

cussed until Book II, Chapter ^

In subsequent discussions,

which do not possess simple

down with some more complex

chords which are not

dis-

5.

we

roots.

shall

adopt the term prime

for the

fundamental pitch of chords

227

CHORD STRUCTURE

We

chord structure later when our harmonic material includes more than the simple triad. But for the present, the principle of inversion is helpful in that it simplifies the problem of chord classification according shall study other principles of

to structure.

To

determine the structural type of any chord, one must first locate the root of the combined intervals. With major and minor chords this process can be simplified by a search for perfect fifths or fourths or, when these more powerful intervals are missing, thirds or sixths; the root pitch of either of these combinations will be the

root for the whole chord. Lacking

augmented

when two

triads

ble), the principle of is

any of the above evidence

(as in

diminished and

equally plausible choices of thirds or sixths are availa-

superposed thirds produces a workable answer. The process

illustrated below.

Ex.

14-24. Locating Roots of Chords.

1^3^*:

i=:

*

•\

root

S

^i

major or minor third

Jifth

^root

.£>_

S

?&

a three-pitch chord does not contain a

interval, the

m3

root ,^

g^

¥

xn P5

P4

S When

#

root

»T=-

-&f-

^Me^

prime

or fourth, the next simplest

(or sixth) determines the root.

Many three-voice

textures contain these non-triadic structures because individual voice motion rules

out the simultaneous occurrence of three different chord members. Notice that Ex. 14-25 ends with a two-note sonority (or diad) because the composer

demanded

certain resolutions of the melodic tendencies already established.

Ex.

14-25. Lutheran Chorale:

^

Wer

m rn^ rr

=P^^^

r

^

^^f

r

^

^

weiss, wie nohe mir.

i ^P

i rf f rrr T

^ ^m ^^f^

3

Chord analysis

*

'*'

l''' tj

l

l

Tonality: g

i

V

I

tj

V

l"

J

f'll^'

\i

ir

V

ii (V)

V

j'i' m

iv

\

* i

i \i

i^# m * i

V

i

228

CHORD STRUCTURE

Melodic-Harmonic Synthesis

Few compositions of any scope reveal the simplicity of chord structure and voice movement found in Ex. 14-25. In much music our cognizance of chords is so related and affected by melodic elements that melody and chords form an inseparable synthesis of tonal pattern, each reflecting the other, each delineating and clarifying the other. In other words, chords and melodies do not operate in music as to

mutually exclusive properties. Because

examples such as the following which exemplifies a remarkable synthesis of harmonic and melodic elements, cannot be explained in purely harmonic or melodic terms alone.

Ex.

14-26. Beethoven:

mod.

(

{

Opus 18 No.

1,

this

is

I

fast)

V7) prolonged

J

At

first

true,

glance,

and

J

in consideration of the allegro tempo,

J-

one

is

taken by the

apparent complexity of this example. If we attempt to isolate chords by simply noting the sonorities formed by the tones heard simultaneously on each beat, we

acknowledge some chord types (as on the first beats of measures 2, 3 and 4) that have little bearing on the style and idiom of this composition and its composer. Secondly, by trying to reconcile both the b-naturals and b-flals sounded simultaneously in measures 1 3 and 4 to a single chord we produce an

shall

have

to

,

equally inaccurate and misleading appraisal of the tonal organization of the passage.

H>'.'

229

CHORD STRUCTURE Actually the passage consists of a single melodically animated chord:

on the first beat of measure 1 and reiterated in measure 5. But it is through essentially melodic means that the opening chord is projected and prolonged in such a way as to take on meaning in the structure of the piece and importance as a simple point of departure for musical development. The top voice unfolds the upper three notes of the chord {e, g and b-Jlat) while spanning two octaves. Rhythmic interest is created by syncopating the first three articulations of ^, g, and b-JIat. The tenor part (viola) is rhythmically coupled with the top voice and melodically reiterates the three lower notes of the chord in pairs {c, e, and g). The technique used in these two voices is, of course, arpeggiation of stated

basic associates, or the melodic spinning out of a chord.

The technique used quite different, sociation

more

to organize the other voices (second violin,

and both span a C

effect, pass

from one

and

cello)

is

explicitly melodic. Both voices establish a give-and-take as-

C

— C octave,

to another.

groups that embellish Cs,

The

filled in

with a

b-naturals are

and can be regarded

series of pitches

which, in

simply part of the passing

as brief leading tones, which, in,

view of their duration, are hardly heard as conflicting with the basic b-fiat's sounding above. Furthermore, C is the root of the chord prolonged throughout the example, and one can see that it is partly due to the continuing reemphasis of c in the

two voices under consideration that the harmonic function (V7) in F and the structural weight of C is made most clear. Chord in this example can be described as a vertical group of notes that frames and channels the passage; it is through essentially melodic means, however, that the chord

The

is

prolonged.

excerpt shown in Ex. 14-27 appears to involve a change of harmony on each

successive eighth note.

Ex.

14-27. Beethoven; Missa Solemnis.

(fast)

V

IV9

vi4

vii8

:

230

CHORD STRUCTURE

Again, an explanation of such a passage can only be

made by acknowledging

contrapuntal elements as means for prolonging a single harmonic "meaning," in

—

dominant -tonic in E major. Note that the upper voice spans a ninth from leading tone to tonic, while the alto reiterates b^ before passing by step up to tonic, melodically expressing a simple 5-1 relation. The two lower parts are coupled and move by step in parallel thirds, spanning a ninth in contrary motion with the upper voice. Each voice forms a melodically satisfying approach to the closing tonic chord, and each voice (or coupling) displays an essentially melodic character, step movement. The listener is swept up by the movement of parts from the beginning to the close of the passage, its basic pitches the sonorities created by the moving voices, grouped around the repeated b^ in the alto, contribute to the momentum and expectancy of the dominant effect without replacing it in any way. The passage is a contrapuntal elaboration of dominant tonic movement, prolonged by stepwise (passing) movement and a repeated (upper pedal) dominant pitch. The "chords" which occur as each voice carries out a stepwise elaboration of the dominant pattern should be viewed as chords of melodic importance, passing chords, and are neither heard nor generally viewed as a significant part of the basic harmonic structure. The meaninglessness of a detailed description of each of the "chords" that occur in the example, as shown on the music, can be best understood by listening to the passage. Contrapuntal elements are not always as significant or prominent as in the two examples just cited. However, any analysis of chord, or music in general, must acknowledge the coordinate relationship between melody and harmony and the way in which they interact in making musical structure more comprehensible. this case

;

—

Exercises

See Chapter 14 o( Materials and Structure of Music I, Workbook for more detailed exercises. 1. Practice spelling major, minor, diminished, and augmented triads from a given note as root or prime. Think through the component intervals of each chord before spelling with note names. For example: B-Jlat

augmented

Augmented

triad:

triad

= augmented

fifth

major third '

—F-sharp augmented —D major third {D —F sharp major third

B-fiat

major third fifth

B-flat

Spelling: B-flat— 2.

D—F-sharp

Analyze a passage chosen by the instructor, denoting each chord by

Sample

M T

Schumann:

r

^e4

£ G

major:

V

VI

^ I

IV6

3J=

I|

V

its

proper symbol.

:

CHORD STRUCTURE 3.

In class or informally with a friend, listen to major, minor, diminished, and triads played a.

Identify

b. Identify 4.

231

on the piano or organ and identify

augmented

as to sonority.

which member of the major or minor

triad

is

which member of the major or minor triad

is

in the top of the chord.

in the bass of the chord.

Using a three-voice texture, write a passage that is based on the following chord proframework first, add the middle voice, then elaborate each melody to create an effective but simple contrapuntal texture. basic

gression. Write the outer basic

Gmajor: 5.

I /

!«

/V/vi

/

Vg

/I /

V

/ I //

Plot a simple chord progression of about four measures length, one chord per measure.

Using an instrument

(or voice), improvise a simple

chords. Use a simple repeated

rhythm

melody that corresponds

to the selected

for all pitch patterns.

Example

Progression

Rhythm:

J.

J>J

I

''i I

J.

h

V

VI

J.

^i

vi

J'Jij. VI

j,jU ^.

^^

u^

II

:

Conclusion

15

f

Three-Voice

Combinations

Spacing.

In Chapter 13 Let us

now

we

dealt with

some

basic aspects of spacing in three-part writing.

turn our attention to the formulation of more specific guides to the

spatial distribution of three-voice vocal writing.

The overtone

series

is

m The

a useful point of reference for the spacing of three voices

m:

uai

i.

jto

°

between the natural interv^allic arrangement of the the bottom), and the most common arrangement of vocal

similarity

intervals at

distances betvveen lower voices),

is

evidence of

still

series, (widest

parts, (greater

another relationship between

musical practice and the inherent properties of musical sound.

Ex.

15-1. Luca

Marenzio

7" '.

^

'4

'I

^ ^

Madrigal

(3

voices).

j^

^5?

wm

:

J

t

^

f

i t

az

i

4 #

1Z2

CONCLUSION OF THREE-VOICE COMBINATIONS

233

mm ^m ^^ ^^ i

-.a

rr

W

"V

[£[f

lie

i

r " r p

-oe-

r

^-p

i=i

^

we

In the madrigal shown in Ex. 15-1

upper voices

"

find a typical distribution of parts.

The

generally within an octave of each other, while the two lower

two octaves. The upper parts move as close together as a unison, and while not illustrated in this example, the same relationship also occurs between the lower voices, particularly when they are coupled. While subject to individual vocal ranges and melodic contour, the outer voices seldom ^re farthex .a part than two octaves and a fifth, as mentioned earlier in Chapter 13. Two octaves is a much more common limit. An interesting exception to this rule of thumb can be seen in measure 2. Here the soprano and alto move in contrary motion to the interval of a minor tenth. This exception to the rule is the parts are occasionally as far apart as

logical result of a primarily contrapuntal association involving contrary motion.

Most three-voice works reveal considerable variety of spacing procedures. This can be seen by comparing the first and second phrases (measures 1-2 and 5-7) of the Marenzio example. Throughout the first phrase the voices are deployed so that different intervals occur between voices on nearly every beat. The second phrase begins with parallel textural relationship

between

parts,

movement

in all voices, thus establishing a contrasting

between two successive phrases. The rhythmic association

however,

is

basically the

same

in

both phrases, since identical dura-

motion in triads, as in measure 5, is seldom found in three-voice writing. The effect is of melodic duplication of one voice in two accompanying voices, rather than independent contrapuntal movement. The example illustrates a texture in which one voice tions generally

occur

in all parts simultaneously. Parallel

predominates, with the other voices serving as accompanying parts. In spacing three voices, one must take into consideration the ranges of the voices involved, for different combinations

major triad has been spaced

demand

different spacings. In Ex. 15-2, a

for several different three-voice combinations.

C

As can

be seen, some of the spacings are performable by only one or two combinations of three-voice groups, because of range limits.

Ex.

15-2. Three-voice distribution of a

C major

A Soprano

\0

Alto

Tenor

S

M

,

•

triad (Root position

^

and

first

•

#

inversion).

~m~

—

—

234 Ex.

CONCLUSION OF THREE-VOICE COMBINATIONS 15-2. continued.

B *_

_•

Soprano Alto

<

f

W^

Bass

U— — —— — — —

Alto

4)

.

.

:

i

'i

'

•J

Tenor Bass

^.

\

\

i

"

:

:

:

;

',

',

— — •

1

•

'

^

'

\

—.—

-f

1

1

*

!

I

——— '

i

:

:

D

Soprano

'^^ ^^

Tenor Bass

*

*

Exceptional spacings sometimes occur as the result of decorative pitches. These

unusual separations occur most often in weak metric positions, and they do not attract the

same attention or create the sense of imbalance that would

result

their use in accented positions or longer durations. Several examples of

from

more

ex-

ceptional spacings which result from melodic decorative activity are in Ex. 15-3.

Ex.

15-3. Exceptional three-voice distribution.

3C\

S.

A.

Soprano Alto

Tenor

The

^m

principles of spacing three voices should not be taken as absolute rules, but

rather as guides to the intervallic distribution of melodic

These principles are useful in achieving a

clarity

movement between

and balance of pitch

parts.

relationships.

CONCLUSION OF THREE-VOICE COMBINATIONS 1.

2. 3.

235

The upper voices usually lie an octave or less from each other. The lower voices may move as far apart as required by melodic considerations. As in the overtone series, wider intervals are more often found between lower parts; smaller intervals separate the

4.

A

upper

voices.

variety of spacings should be employed; parallel movement,

if

prolonged,

negates melodic independence of parts. 5.

Decorative activity

may

create abnormally wide or narrow spacing momentari-

ly-

6.

Outer voices are seldom separated by more than two octaves.

7.

Systematic coupling of a pair of the voices, particularly at the interval of a third,

may

bring about unusually wide separations from the third voice.

Crossing Voices.

An

interesting contrapuntal effect

is

often achieved in both instrumental

and

by the momentary exchange of the range positions of tv^^o parts. If the alto moves above the soprano or below the tenor, for example, the voices involved in the high-low exchange are said to have crossed. Crossing most often occurs between adjacent parts, and it is usually the result of vocal textures by crossing voices, that

is,

the fulfillment of a particular melodic pattern.

Voice crossing most often occurs within a phrase, although cadences involving crossed parts, or phrase beginnings using this procedure can be found. A typical

example of crossing

seen in Ex. 15-4.

is

^^

Ex.

15-4. William

Byrd

:

Madrigal.

^ $ rr

i

^

m

^

^m

Contrapuntal and Homophonic Textures.

The

possibilities for

organizing three voices, vocal or instrumental, are, as

we

have seen, almost unlimited. No two works are identical, nor do any two derive their musical interest from identically developed compositional techniques, no matter how similar their outer surfaces may appear. Nonetheless, just as the most complex contrapuntal activity will adhere to certain harmonic formations, so even the most simply developed

counterpoint,

if

homophony

on rudimentary principles of the most basic aspects of musical

will rely

only because they are implicit in

organization.

Ex. 15-5a illustrates an unadorned homophonic texture.

236 Ex.

CONCLUSION OF THREE-VOICE COMBINATIONS 15-5a.

Domenico

1 ^EEi

Scarlatti:

Keyboard Sonata

m f^

in

C

i^

t

major.

^ ^Em" fcit*

i

^^ ^ £^ ^ ^ ^ ^ r

r

^ f

^

A

predominant upper part is accompanied by repeated pedal c's in the left hand and a middle voice is developed entirely out of motion from e^ to its upper neighbor /' and back to e'. The harmonic activity, featuring a harmonic rhythm of one chord per measure, consists of three chords: tonic, subdominant and a tritone, all organized above a tonic pedal. The contrapuntal resolution of the tritone occurs in measures 5 and 8, while each voice maintains at least some degree of rhythmic independence. It is, in fact, through the incorporation of decorative activity that the work derives its minimum contrapuntal motion. Stripped of these decorative elements, the piece would appear as in Ex. 15-5b.

Ex.

15-5b. Reduction of Ex.

a^

T

The

point

is

15-5a.

f

f

^ T

i

i

i

i

i

r

P

f

^

#

B

^ f

t

i

homophonic texture may reveal elements of contrapuntal relationships, however mild and unpre-

that even the simplest

organization that reflect possessing.

Contrapuntal writing dominates the texture of Ex. 15-6a.

Ex.

15-6a.

J.

1

^

^

G. Walther 2

:

Chorale Prelude for Organ. 3

4

^ ^ ^

^^ i 5

w i-

f

^ ^

CONCLUSION OF THREE-VOICE COMBINATIONS

237

Not only does each voice maintain rhythmic independence, imitative entries, but each also participates in

by successive an exchange of melodic material set off

that consists of three contrasting elements: dotted or plain quarter notes, syncopa-

and continuous

by conjunct motion. Cadences, occurring at bars 4, 8 and 12, are weakened by continuous motion in one or more voices, so that the effect of the example is of one broad, continuously tion,

sixteenths. All three parts are unified

unfolding contrapuntal section, that reaches a terminal cadence in measure

12.

Despite the continuity and flow of the separate three voices, harmonic relationships are

much

in

evidence in

this

the forward motion of the counterpoint. deceleration of harmonic rhythm

Harmonic rhythm,

music. It

is,

as a

too, contributes to

matter of fact, primarily through

{from two chords per measure

to

one chord per measure) that

the cadences and phrase endings are distinguished in measures

4,

Ex. 15-6b shows a simple reduction of the Walther excerpt.

through a study of the reduction how harmonic relationships,

and diads (two-note combinations), form a framework

triads

Note also that the principles of three-voice spacing discussed this keyboard composition.

i

12

15-6b. Harmonic reduction of Ex.

Ex.

m

3

«

s

for

^

X ^

It

melodic

activity.

earlier are evident in

15-6a. 4

5

n ^ W ^

-0—^

J.

i y

12.

becomes clear here in the form of

i J

i t*rr

\-

12

11

;«•)

8-9 and

%

r

:>

238

CONCLUSION OF THREE-VOICE COMBINATIONS

Doubling

in

Three Voices.

The harmonic

result of the vertical

alignment of three contrapuntal voices at

any one instant is not always a complete triad, even though triads represent the core unit of harmonic organization. In many instances melodic movement demands the doubling of one note in another voice, often an octave or two removed in register. Such doublings are seen in the Frescobaldi Toccata (Ex. 15-7).

Organ Toccata

15-7. Frescobaldi:

Ex.

Adagio

s

^

^

rlJlrJ-

p

/

I

T'

P

Several such combinations are

15-8.

Doubling

331

:xsz

in

s

331

331

IT"

shown

member

is

usually

of the interval duplicated.

in Ex. 15-8.

three-voice chords.

•-e-

331

m

occurs in a three-voice chord, the resulting sonority

a decorative or cadential consonance, with one

S

r

p

Where doubling

$

fDomi nant /T:s;

'

'r-i'.-

Ex.

n j-^;i

"TT~

^

o

Tl"

ini

^ w

:fe 331

ZCSl

331

331

-nr

~n~

331

331

Although either note of a consonant interval may be^ doubled, it is most frequently the root. Doubling of the interval root usually occurs in cadential consonances whose roots are members of the tonality frame, particularly tonic and dominant. By doubling these pitches the composer emphasizes and helps to clarify the prevailing tonality.

More freedom

has been exercised in doubling

members of decorative

conso-

we have described, are less evident. Either member of a decorative consonance may be doubled the choice is usually determined by melodic considerations. However, where major or minor sixths contain members of.tlie_^ nances, whose roots, as

;

tonality frame, particularly tonic or dominant, the pitch corresponding to tonic or

dominant

will

more

often be doubled.

Common doubling procedures are illustrated in Ex.

15-9.

The piece

is

in

^ minor,

239

CONCLUSION OF THKEEVOICE COMBINATIONS

and both of the endings

opening section of the sonata (which is repeated) are achieved through transient-terminal cadences to the dominant. In both instances the cadential pitch a, the dominant, has been tripled.

Ex.

15-9. Corelli

for the

Keyboard Sonata, Giga

:

^ ^rr

(Allegro).

is m

^^1 ^ r 7yF

^m m s p ^ m ^^ p ^ ^ ,Mt^^^¥^ ^^ m ^

^

7

y y

_

r

^r

r

yyl^

p

P

±± fc

±±: I

^

^m ^

m ^^ ^m ^ J

^^ S^ ^^ XJ^

j)yr}

f-^-^

*

^ ^^

i.

^

fi

^gVj^

s

I

ff

i

'n

^

±3z

f

^^

5

1.

>^HHh

J-

y y

»•

m

J m-

m

important to point out that leading tones, pitches that form tritones, decorative pitches, and altered tones generally are not doubled in three-voice textures. In other words, pitches which suggest continued movement and create It

is

instability are not reinforced.

they are usually located in

Two

When

exceptions to this basic consideration occur,

weak metric

positions, thus attracting less attention.

exceptional doublings, involving the interval of the fourth above the bass,

are seen in Ex. 15-10. Here the doubling of a fourth results from simultaneous use of decorative tones which coincide on weak portions of the beat.

240

CONCLUSION OF THREE-VOICE COMBINATIONS 15-10. Doubling.

Ex.

^

X I

-

-/

J

"

rni

r r ^

T

J

J

J

S'r=f i

r

pS Decorative Patterns.

Decorative activity in three voices

rhythmic activity of

and

in proportion to the

may

be located primarily in one prevailing part, as between two coupled voices, as in Ex. 15-12, or it may

parts. It

in Ex. 15-11, distributed

consistent with

is

be couched in voices of equal activity, as seen in Ex. 15-13 by Hindemith.

15-11. Beethoven:

Ex.

^

^

^S m Ex.

Op. 59, No.

1.

#

«

w g^ 'g^

i

^

^^>^;^^

?:

t JJZ

Organ Prelude.

^Pi ^^ fe

«

^^

m 15-12. Buxtehude:

#

f

m •r

f

CONCLUSION OF THREE-VOICE COMBINATIONS

241

15-13. Hindemith: Ludus Tonalis, Fugue, No. 8. (C) 1943 by Schoft

Ex.

^ ^ ^

r— cfcj

^

*^ ^

&

Co., Ltd., London.

i

•

F

^ J

^^ '

J''i:,, ')^

V

>

P

J n.^ S r

r

*

Cj>

Ex.

aspect of the organization of voices whose function

15-14. Mozart: Piano Concerto

f

^ i

J J

may

represent a color-

mainly accompanimental.

C Minor.

^ ^^^ m ^^^ ^^ J-

A

in

is

r

^^

In some instances, such as Ex. 15-14, decorative patterns ful

J

r

i

U'm

H

^Tj. i

BP ?

Jii

^ ^m J-

i

study of the preceding illustrations by Beethoven (Ex. 15-11) and Buxtehude

and neighbor tones comprise the most common forms of melodic embellishment. That such a statement applies to a vast amount of music may be deduced by analyzing the excerpt by Hindemith (Ex. 15-13). Here, despite a more complex rhythmic and harmonic fabric, decorative pitches are approached or resolved by step. Each independent voice forms a cohesive and meaningful musical line, and the three parts fit harmonically into an intelligible tonal whole. The importance of the tonality frame, d—f-sharp a, as the primary points of pitch focus, can be heard clearly. The importance of passing and neighbor tones in melodic patterns such as the sequence and imitation cannot be overstressed. An interesting sequential use of passing tones is found in Ex. 15-15 from a motet by Ockeghem. (Ex. 15-12) will reveal that, as in two-voice textures, passing

—

242 Ex.

^

CONCLUSION OF THREE-VOICE COMBINATIONS

Ockeghem

15-15.

s

^

Motet, Ut hermita solus.

:

rn f7]

UJtS'-^M' i * rdA PL

"FCS^

#

f^

J

„i I

,

^^

T

r

Double passing tones in thirds occur on the second half of beat three in measure 1 At the same point, the bass, moving in contrary motion, ascends through a passing figure to a. Consecutive dissonances are heard on both parts of the beat, but each dissonance is resolved by step to a member of the prevailing harmony, a d minor triad. A similar treatment of passing tones is heard in measure 2, organized around an a minor triad. Syncopated upper neighbors, moving in parallel tenths, form an entirely consonant embellishment of the prevailing d minor sonority in Ex. 15-16. The importance of members of the tonality frame, here d^ and a, as doubled tones in .

three-voice writing,

Ex.

15-16.

is

significant.

Ockeghem: Motet.

s

m

rT^jTj

^ CJUUS-U^ ^

^ ^m

^

Note that

g^

their triadic

I r

r

r

and b-JIat are upper neighbors to the basic pitches/^ and a^, despite agreement with d^, because of their short duration. The root progres-

example could be expressed

sion of the entire

o

as V'

.

This

is

a good

example of how a composer may organize an extended contrapuntal passage around a simple harmonic framework.

Ex. 15-17.

Alto

Tenor Bass

Obrecht

:

Motet,

O

vos omnes.

m i^ a N f^

m ^ ^ U' L^

? J

^

-J

T

J

P

^ i

I

^

243

CONCLUSION OF THREE-VOICE COMBINATIONS

r^ ^^ ^p

* %

An

n

^n

i-

f=T

interesting analytical

problem

is

encountered

in

^

^

1 P

i f

Ex. 15-18:

^

Ex.

15-18. Neighbor chord.

''

rjr

>

Here three voices employ neighbor tones simultaneously in a homophonic texture. However, considered vertically, the sixteenths, /-^Aar/), d-sharp and a, form a diminished triad in hardly aware of a

The duration of this chord is so brief that we are change of sonority. None of the members of the chord is a basic

first

inversion.

harmonic agreement of several non-basic pitches (in this case usually called a neighbor chord. As we have seen, its relationship

pitch. This type of

neighbor tones) to context

is

is

decorative.

In general, chords (or intervals) of of whose

all

less

members can be understood

duration than the prevailing beat unit, as decorative pitches, are regarded as

of essentially melodic importance, rather than as significant changes of harmony.

on root relationships or tonal function, except in extremely slow tempi, or where they occur as part of a consistent harmonic rhythm. This matter will be discussed more extensively in subsequent chapters.

Such

sonorities

have virtually no

Simultaneous passing tones

effect

may

also create decorative passing chords, as in Ex.

15-19. -*-

Ex.

15-19.

k;,.

^

J.—

1

J

m ^^ # ^^ ijJj r

J

p[j>rc£f-

ft^ #

!•

d^'ii'

244

CONCLUSION OF THREE-VOICE COMBINATIONS

The with

Ex.

can be studied by comparing Ex. 15-19

role of decorative pitches in Ex. 15-19

reduction (Ex. 15-20).

its

15-20. Reduction of Ex.

±^ f^=T

f^¥?

^ When

in favor of

-« T^

isn

jh

all

15-19.

three voices

harmonic

move

color,

f'

r

^

i

:zt tfo-.

in parallel motion, contrapuntal interest

and we tend

is

denied

to hear as basic those sonorities that occur

in strong metric positions. See Ex. 15-21.

Ex.

15-21. Three-voice parallel motion.

Two tive:

factors are generally present in sonorities

melodic motion by

These "chords"

may

step^

and short

—weak

whose

roles are primarily decora-

duration and metric placement.

be viewed as one views pitches of a single strand of melody

which, although not part of the basic melody, fill in and connect more structural points in the line. Their role in the construction of a "finished product" is nonetheless essential.

Suspensions

in

Three-Voice Textures.

Suspension figures account for a great variety of on-the-beat dissonance in threevoice writing. All of the types of suspensions found in two parts occur in threevoice music, but some, such as the 9-8, are

more common

in three voices than in

two.

Ex.

15-22.

st^ 'n^i>

^-^^ Krrnr I -

^ J

^ r

M 9-8

r

J.

(7 -

6)

7-6

i f-f rrv

^9-3 (2-3)

i

nrr

rzi

r

i^ 2-3

"

)

245

CONCLUSION OF THREE-VOICE COMBINATIONS

The

excerpt in Ex. 15-23 contains several suspensions. Perform the example,

paying particular attention to the way the music sions,

Ex.

impelled forward by the suspen-

is

whose resolutions coincide with the intioduction of a new

15-23.

')%

Fischer: Fugue for Organ.

12

J.

C.

3

4

^

^_l

lOI '^

18

17

r

19

^^

n

fe

r

1 1

20

icc:

22

23

xn

-o-

_J: ±jO

S

K

-0-

a 4-3 suspension occurs in the middle part.

sonant with the bass. However, the instability created at is

J J

21

,

r

ZUE

At measure

voice.

this

The

top voice

is

con-

point (in measure

1

1

not solely a product of the perfect fourth between the bass and middle voice.

On

the contrary,

upper

voices.

it

results

Although

it is

parts as a 4-3 suspension, so to speak, of this

from the 2-3 suspension created between the middle and

common

it is

to identify this typical configuration of three

equally important to be aware of the double nature,

and other suspension

figures.

The

voice above the bass that does

not participate in the suspension figure usually forms a consonance with the bass (or lowest sounding part). This aspect of the suspension in three voices is clearly illustrated in

measures

9, 11, 12, 15, 19,

20 and 21 of Ex. 15-23.

We noted in our study of two-voice combinations

that the lower voice sometimes

changes pitch while an upper voice suspension resolves.

common

The "change

feature of suspensions in three-voice textures too.

of bass"

is

a

246 Ex.

CONCLUSION Of THREE-VOICE COMBINATIONS 15-24a. Haydn: Piano Sonata No. 7, 1

(

nr

^M

The

Ex.

i

^

^

^^U

m^

7p

I

^

=nz;

^ 2M

—

i 11

8

J

I

J

J

J

~rn]i-i

J

I

reduction in Ex. 15-24b reveals the importance of suspensions in the excerpt.

12

^ ^ ^^

15-24b. Reduction of Ex. 15-24a.

T!^^=t

3

^ fiU rt=f P

rrr

')7u

a

i

^E^

^

f

^

r

P

7-3

^m f f

^

^-v

§sfit

j-fj

rf P ^

^^

The "change

of bass" pattern

in the excerpt. In

measure

{B'-flat) resolves to a^.

sonance with

a},

2, for

is

J H-J

J

j—-!^

P

#

^ ^

11

J

P

a prominent feature of most of the suspensions

example, the bass moves from

:

to/as the seventh

Since the bass moves to another pitch that forms a con-

(just as the

c

that formed the dissonant seventh would), the resolu-

tion of the suspended dissonance

is

completed. Changes of bass most often occur

motion with the resolution of the suspension. They involve motion to pitches which create a consonance with the resolution of the upper voice. The in contrary

247

CONCLUSION OF THREE-VOICE COMBINATIONS intervals created

by

by the suspension pattern

in

measure

2

would be represented

7-3.

Ornamental Resolutions of Suspensions. Resolutions of suspensions are frequently elaborated through the interpolation of pitches which prolong or embellish the dissonance. In bar one of Ex. 15-25, the resolution of the suspended

e^

has been decorated by motion to two interpolated

and/^ sharp. D^ is the note of resolution of the dissonance, but its arrival has been delayed by the intervening activity. Decorative pitches, consonant or dissonant, which enhance the resolution of a suspension are frequently called changing tones. Ornamental activity, such as the type seen in Ex. 15-25, is not basic to the suspension pattern and need not be included in an intervallic analysis. pitches, a^

Ex.

15-25.

Mozart: Piano Concerto No. 23

in

A

^

major.

m T r^^

p^ ^#^

fl

^

6

A

7-6

7-6

2-3

variety of suspension patterns enhance the illustration

7

(3)

by Walther shown

Ex. 15-26.

Ex.

15-26. Walther:

Organ Prelude.

rzs^

^^'^

l£

I

E

I

ni

m

E^r

as

248

CONCLUSION OF THREE-VOICE COMBINATIONS

The

following

summary

of principles which characterize the use of suspensions

should be noted: and 2-3

1.

4-3, 7-6, 6-5, 9-8

2.

Secondary- suspensions often occur between the two upper voices in conjunction

figures occur in three-voice compositions.

with suspensions above the bass. 3.

The note of resolution is not same level as the dissonance.

generally sounded against the dissonance on the It

frequently occurs in a different octave. This

is

always true with 9-8 suspensions, sometimes in 7-6 patterns. 4.

Suspended tones are not doubled.

5.

Change of bass may occur with the suspension. Suspensions are frequently ornamented by the interpolation

6.

which constitute elaborations of the suspension 7.

Suspensions

may

of changing tones,

figure.

occur as diatonic or as altered pitches.

In the hands of some composers (such as Beethoven,

example) the suspension has been more freely treated. Ex. 15-27 incorporates several unusual suspensions

an interesting three-voice

in

Ex.

15-27. Beethoven:

Other Forms of

The

texture.

Op. 110, Fugue.

Pitch

Decoration.

escape tone, the leaning tone, and the anticipation are

of melodic embellishment in three-voice compositions.

with their use do not in

two

for

voices.

The

dissonant to consonant intervallic

frequent forms

techniques associated

differ significantly in three-voice writing

The same

less

from

their treatment

movement formed by

249

CONCLUSION OF THREE-VOICE COMBINATIONS the suspension,

i.e.,

9-8, 7-6, 6-5, 4-3,

is

created by leaning tones, although they

occur more rarely than suspensions. Accented unprepared dissonances are uncommon until the nineteenth and twentieth centuries, although they can be located in scattered instances before the nineteenth century.

Escape tones, anticipations,

and leaning tones are illustrated in a variety of musical styles in Ex. 15-28. A further similarity between two and three-voice procedures lies in the fact that examples of these forms of decoration occur most often in the top voice.

Ex.

15-28a. Binchois

^

Rondeau, De plus en e.t.

?

5

J.

in

?hS-ffl '^;

Ex.

15-28c.

Bach: Fugue

in

G

minor, Well-tempered Clavier,

susp.

7-6 j

«

X ace.

p.t.

*^

n. tones

m *\

-etonic pedal

JM

^

leaning tone

f'^'M-^J

X

m

unaccented X

e.t.

X

E-flaf.

Ln.t X

in.'i\*r

^

ant.

LM^p

i-

^^

i

15-28b. Bach: Sinfonia

»'•'-

plui.

^m

X

^m Ex.

:

Book

I.

5

5

250

CONCLUSION OF THREE-VOICE COMBINATIONS 15-28d. Beethoven:

Ex.

Opus

18,

No.

2.

d

p.t.

^

X

»

S

m

ga Ln.t X

iE^

Ln.t

X

•,

^

^

i

n^

f^

r r

^ ^ r

The

tone of resolution

*^=F^

usually not sounded along with the leaning tone, there-

sequence in Ex. 15-29 will almost never be found.

fore, the

Ex.

is

»f

^

15-29.

#%^-i^

'S

Exercises.

See Chapter 15 of Materials and Structure of Music 1.

Write ten different spacings of the

D

I,

major triad

Workbook, for

for

more

detailed exercises.

each of three different combinations

of three voices, such as soprano, alto and tenor.

and

2.

Use examples

3.

Analyze

4.

Transpose the tenor (middle) part of Ex. 15-6a up a whole step; then add an upper and lower part in the style of Ex. 15-6, using appropriate decorative patterns. Analyze your work, accounting for chord roots and decorative pitches.

all

in this chapter for sight reading vocally

at the piano.

decorative patterns in Ex. 15-6a.

5.

Use Ex. 15-28

6.

Add two

for aural recognition of decorative pitches.

voices above the bass line in Ex. 15-19. Include examples of every type of sus-

pension in the setting. Transpose the bass

down

a major second before beginning the

setting. 7.

8.

Make

a homophonic keyboard setting of the upper line in Ex. 15-19.

Write a contrapuntal setting (in three equal voices) based on the harmonic reduction in Ex. 15-5b. Use imitative entries in each part.

Ho mophonic Textures

16

of Four Voices;

No n-Chord Tones

In our consideration of musical organization to this point our emphasis has been on combinations of individual voices. We have seen how linear patterns may be combined and how, in three-voice writing, these combinations

produce chords. All music

music one

is

not conceived as combinations of independent melodic lines in ;

line

is

prominent, while subordinate

lines

much

(often in corresponding

rhythms) produce an accompanying harmony. Such textures are called homophonic. We shall consider this term as the opposite of contrapuntal, since the latter describes music in which the separate parts are of relatively equal melodic interest.

homophonic there is one dominating melody and the remaining texture forms a chordal background that complements the important top voice. Notice that the two-voice framework is still a significant structural fea-

The

following example

is

;

ture of the total texture.

Ex.

16-1. Schubert:

3

I

Schwanengesang. 3

252

HOMOPHONIC

Even when one voice

is

TEXTURES;

NON-CHORD TONES

of decided prominence, the other lines certainly

may

be

"melodic," in the sense that they contain some elements of rhythmic or contoural independence. In textures such as the following the overall effect is not exclusively that of counterpoint or of pure

homophony; the result is rather that of a succession some isolated rhythmic activity and lines of

of block harmonies interwoven with

simple melodic distinctiveness.

16-2. Palestrina

Ex.

^^

m

Adoramus

:

m

fe

Chrisfe.

331

-Q-

nrr

^^

8

^

jOO

S

*

fc

o jOlL

3X

nn

^r:

33:

m

331

32:

33: 33:

Example

1

6-3 shows

still

another kind of homophonic texture,

this

one achieved

which are rhythmically differentiated. The lower part outlines simple chords, while the melody unfolds with simple decorative patterns (upper neighbors) around a basic pitch line that belongs to the chords of the lower through only two

lines

part.^

Ex.

16-3.

Beethoven: Sonata Op. 79,

m ^

^¥

i

The accompanimental string patterns. It

pioneered

^

i

I P

and

III.

its

use.

is

is

typical of classic-period works, both as piano

Alberli bass, after the

composer Domenico Alberti, who apparently

figuration of this passage

called

an

HOMOPHONIC

TEXTURES;

NON-CHORD TONES

253

homophonic textures vary from clear-cut combinations of a melody with block-chord accompaniment to less obvious examples in which It

is

clear, then, that

contrapuntal elements are present, mainly as isolated spurts of rhythmic inde-

one or more of the subordinate voices. The common elemen t of all is a singularity of melodic interest and, frequent!)-, a oinnion bond of rhytluaic

pendence

in

(

motior

Textural Considerations

In earlier chapters

we

discussed fundamental principles that govern contrapuntal

For the present we shall be concerned with tones related as blocks of harmony rather than as combined horizontal lines which, as may happen, produce associations.

discernable chords.

It will

be apparent that

many

of the principles related to the

connection of chords have their basis in principles discussed earlier in terms of voice motion. It would be fallacious to regard the ground rules of harmony as unrelated to principles of counterpoint. alized nature

and proceed

to

more

We

shall begin

with principles of a gener-

specific matters that are

determined by par-

ticular circumstances.

Voice Ranges. It

ing to the voice

Thus

four parts

is

customary

to designate the four parts of a texture accord-

names of choral music, even when human voices are not involved. are named, from top to bottom, Soprano, Alto, Tenor, and Bass. (See

page 130 of Chapter 9

ranges of these voice parts in the chorus.)

for the usual

Notation. In notating parts for

any combination of four

instrumental, the score can be "closed," in that

it

consists of all parts written togeth-

on two staves, soprano and alto combined in the combined in the bass clef, as shown in Ex. 16-4. er

Ex.

voices, choral or

treble clef, tenor

and bass

16-4. Closed Scoring.

s ^E^y

Soprano

P^

Alto

TTrr

^-^ P^ ^^^ ^ ^^^

Tenor Bass

f

i

Observe that the stems of individual parts indicate which voice the particular note belongs to. Even when parts cross, this expedient shows the proper orientation of the lines.

Doubling of Pitches. If

we

limit

our harmonic resources

present, a four-voice texture necessitates the duplication of one triad,

and

in

sonority) one

some

to triads for the

member

of each

instances (because of linear factors or the desire for a particular

member might even be

tripled or quadrupled. This doubling

accomplished at the octave, double octave,

etc., as

well as at the unison.

can be

254 Ex.

HOMOPHONIC 16-5. Pitch Doubling

T

tripled root

root

i

1^

^

doubled

^

^

r

^

NON-CHORD TONES

Triads.

in

ii

^ r

TEXTURES;

T-

*

4

^

doubled

doubled

root

doubled

doubled

root

third

fifth

At best, rules of doubling represent the practice of a particular composer, the "norm" of an era of composition, or merely the unique sonority desired by the composer at a particular moment. Furthermore, individual voice motion frequently determines the constituent members of any particular sonority. However,

when

sonority alone

is

the determining factor, the following can

be regarded

as general guides: Triads in Root Position

root doubled

(b)

Major Minor

(c)

Diminished

third doubled (°5 seldom occurs)

(a)

root doubled (or third)

3 (d)

Triads

Augmented

third doubled (seldom occurs in

in First Inversion

root doubled

(b)

Major Minor

third

doubled

(or root)

(c)

Diminished

third

doubled

(or fifth)

(d)

Augmented

third doubled (seldom occurs)

(a)

Triads

any form)

in

Second Inversion

(b)

Major Minor

(c)

Diminished

third doubled (or fifth)

(d)

Augmented

fifth

(a)

fifth

doubled (bass pitch)

fifth

doubled doubled

(or third)

Doubling the root of a major or minor triad emphasizes that chord's stability. In the case of tonic, subdominant, and dominant triads, this doubling procedure also reinforces an important scale degree, 1, 4, or 5. Since these tones remain constant (do not vary with change of mode), they act as the fixed tonal elements of any key. As a consequence, they are often doubled within a four-pitch chord rather than some other tone. As can be deduced from the chart above, certain duplications are generally avoided. For example, we expect the leading tone of a key (when that key has been established) to resolve by step upward. To double this tone in a chord would exaggerate this expectation. ii°

in minor, vii° in

that

is

not

And

in chords containing a tritone (the diatonic chords

major and

in

melodic and harmonic minor) the

a part of the tritone, the third,

is

usually doubled.

member

\ HOMOPHONIC Ex.

16-6.

TEXTURES;

Doubling

M

2J5

NON-CHORD TONES

tritone chords.

in

i f

a

^

^

s

fe

i r

3rd

J erd-

!

3rd

i D:

"ii°6

ii»6

•

a:

VII

ii

In homophonic textures the principles of doubling just cited can be overruled if

sixth is

would be hampered. In Ex. 16-7 the contains a doubled third, even though this third also

the linear progression of a particular voice

chord

{a

major

triad)

the leading tone of the key.

The extenuating

in the subsequent chord (thus not resolving

its

factors are the melody's dip to e

g-sharp leading tone)

and the more

graceful line created in the tenor voice by the step ascension of /-sharp

—g-sharp —

measure 2 contains the doubling of its root, a, but notice further that the third measure contains the V chord again with the doubled third. Once more the circumstances are evident, for both of the ^-

a.

Note that the cadential tonic chord

sharps are a result of

Ex.

16-7.

Praetorius

:

motion

Ich

dank

in the

dir,

in

soprano and tenor

lines.

Lieber Herre.

Spacing of Four-voice Textures

The same

voice distributions apply to four-voice combinations that were dis-

cussed in relation to three voices in Chapters 13 and 14. However, the addition of

another part makes possible a greater variety of voices, as well as a

As we noted

fuller texture.

wider intervals appear more frequently at the bottom of a texture than between the upper voices, except when lower voice couplings are earlier,

between the bass and tenor; frequently between adjacent upper voices, alto soprano,

used. Intervals greater than an octave are found often

they do not appear as tenor

—

Two

—

alto.

basic types of spacing traditionally have been applied to the dispositions of

256

HOMOPHON/C

TEXTURES,

NON-CHORD TONES

four voices: the term "close" applies to any arrangement in which the three upper

members

of a chord are in their closest possible positions. In such arrangements the

soprano and tenor voices normally

Ex.

lie

no more than an octave apart.

16-8. Close Spacing.

The term

open

is

used to denote distributions in which the three upper parts are

not arranged in their closest possible relations. In such arrangements the soprano

and tenor notes

Ex.

Open

16-9.

will usually

H^

rr^

The

r.

iP

'^

more than an octave

apart.

many

If:

"trrr

r

designations

tions that

lie

Spacing.

u ffef^ 'y-hk

(though not always)

of^ close

and

open are helpful, but they are such general descrip-

kinds of spacing are not adequately identifiable by them.

add the term homogeneous

to

We

apply to any distribution, close or open, that makes

use of approximately equal intervals between the adjacent parts of a texture.

Ex.

16-10.

Homogeneous

vrj»i^>>:

can

spacing.

HOMOPHONIC

TEXTURES;

257

NON-CHORD TONES

The opposite of homogeneous, heterogeneous, refers to any chord in which the members are^aced with unequal gaps between them. Notice that most heterogeneous spacings are automatically also

Ex.

open.

16-11. Heterogeneous Spacing.

A

J3 10

r

11

J

¥

^

i

59:

r

i

i

3=51

$

f

33:

r A

which separate pairs of adjacent voices are coupled together (as described in the discussion of spacing in Chapter 1 3) would be a heterogeneous spacing. These kinds of arrangements are more typical of instrumental textures than of vocal. The use of certain heterogeneous distributions depends upon the available pitch range covered by participating instruments; obviously a combination of piccolo, clarinet, trumpet, and tuba possesses greater potentiality for heterogeneous spacings than do the soprano, alto, tenor, and bass vocal choir. Ex. 16-12 contains six different settings of the first phrase of America. Each pasfour-voice texture in

sage has been written to illustrate a particular distribution of voices in close, open-

would be pointless to judge the relative merits of the six settings, for the value of any one type could be decided only in terms of its fulfillment of a particular musical need. Examples (a) and (b) are

homogeneous and heterogeneous spacings.

It

similar to choral textures used for this kind of

maining

settings

might be more appropriate

communal song however,

for other uses.

;

the re-

Each version should

be played or sung several times, followed by a detailed discussion of the various factors that contribute to

Ex.

(a)

its

general musical effect.

16-12. Six Settings of America.

Open homogenenus: common chorda!

^

distribution

rrj f

T f

258 Ex.

HOMOPHONIC

(b)

Close homogeneous; emphasis on brilliance of sonority

(c)

Heterogeneous coupling; sop -alto; tenor

^

^ (d)

/i'

T

i

^

^^

id.

i'

/|i

d

M

i

P^ J:

pr

^

g

^

^^ ^ ^

^1

L

•\

r

r

'

r

I?

$

r

r

i^ J.

m ^TT i

'iJ

^

J

J

^J^U

rr

iE^ f=7f

^

;)J

V

r »pr

i r 1 ^"

r

r

register (somber timbre)

rrr ^^^ i

r^

J

J

J

i i J

5 r

r=r^

Open, homogeneous: emphasis on breadth of sonority, il

r

^^^ ^ # ^^

Homogeneous; emphasis on low

-l£

s f

$

ii'

i

i^U

J.

tm^ rrr )

i'

bass

Heterogeneous coupling; soprano; alto-tenor, bass

J A

(f

ii'

-

If

^

(e)

NON-CHORD TONES

16-12. continued.

'^m


TEXTURES;

fullness of timbre

,J

1.

J)A

f

HOMOPHONIC

TEXTURES;

259

NON-CHORD TONES

Composers control the spacing properties of their music with the same care lavished on chord structure, melodic pattern, and rhythmic motion; the appropriate chord could be inappropriate if its spacing were not matched with the desired effect. In this respect, spacing, individual voice range, and dynamics are inseparable factors. Example 16-13 shows a passage in which all three of these factors are combined in a complementary union that creates a sense of placid solemnity. Note that

four voices

all

spacing

is

lie

within the lower reaches of their respective ranges, that the

and

generally homogeneous,

that the

dynamic

level

is

piano.

16-13. Beethoven: Missa Solemnis, Gloria.

Ex.

P Soprano pax

ho

mi

-

-^

^

—a

-0

ni

-

-

m

bus,

ho

-

ho

-

I

mi

ni

mi

ni

-

m

m bo

bus

P

i

Alto

^ pax

^5^

*

mi

ni

ho

-

«• -

bus,

bus bo -nae.

-

^^

P Tenor

^

i

? ho

pa X

mi

-

-

ni

-

bus

mi

-

n

I

-

bus

b(5

-nae,

1

i

•

\

>

I'll //•fttt It

r^

*


.

r^

X

«

•

pax

The

-

^

u

t^'tt

B ass

ho

,

i

ho

excerpt in Ex. 16-14 illustrates the

way

-

r.

i

mi

ni

-

-

II

bus bo -nae.

a single musical phrase might shift

quickly from one kind of distribution to another. Here the upper and the lower pairs of voices are coupled

;

after a

beginning that

is

open, the couplings

move

to-

gether into a tight formation.

Ex.

Song of Affirmation, Part Reprinted by permission.

16-14. Dello Joio

Soprano Alto

Tenor Bass

iJ

\y-

'i'

i

:

i'

'i'

r

p

i

them

out

like

I

'f toll

i'

bells

I.

Copyright 1953 by Carl Fischer,

Inc.

260

HOMOPHONIC

The

opposite condition, a close spacing

moving

TEXTURES;

NON-CHORD TONES

progressively to an open, could

be equally appropriate in another musical situation. Furthermore, abrupt shifts from one spacing to another are most appropriate when the nature of the passage

demands

variety rather than unity for

its

intended

effect.

In general, a single kind

of vertical distribution prevails within any musical phrase or passage.

Harmonic Succession In homophonic textures chord structure is the main organizational determinant, while in contrapuntal combinations the melodic logic of individual lines emerges

most

added emphasis on the vertical harmonic unit, the way in which chords are juxtaposed becomes an important issue. In some passages the rate of chord change is conspicuously periodic, thereby lending an effect of simplicity to the whole texture. as

significant.

Because of

this

16-15. Schubert: Impromptu, Op. 90.

Ex.

Allegretto

In some works

this consistency

to create a tightly-knit structure.

of harmonic change joins with other elements

The compositions from which

the passages in

Ex. 16-16 are extracted are almost totally organized upon the rate of harmonic

change established

Ex.

in their initial measures.

16-16a. Bach: Well-tempered Clavier, Book

Moderate

Chord changes:

.

#

= 112

I,

Preludium

I.

i

HOMOPHONIC

TEXTURES;

NON-CHORD TONES

261

¥

W.

'rn'M

i'

!>-i

?J).-^

S^

?Jr-J

?>-[

r

r

X

"

5W

^^ iffi-

M.''

^

i

lyi

ik-1

2i).-i

?iri

^ir-i

^^=^^

VI

•''

j

Ifeffl

j^^

gffl^E

SbEgSa ^^S

la/ffl

iiw

?>J i

g

?i)nJ

i

L

J

zr

Si Ex.

16-16b. Mendelssohn: Op. 102, No.

3.

Presto

^

'

-^

i-j)

s

Chord

r r r j

feii L.

I

L.

I

1^i

1

I

changes:

^^ ^^

^^

^

%X%

P

Nonetheless,

this

norm

L

I

1

I

I

iJMi -^^^ I

I

I

strict

sections) a generally

from

I

I

I

m

uniformity

is

not always the case. In most works (or at least

uniform pattern of chord change

occur, in

some

cases to

fit

is

retained, but deviations

particular melodic patterns, in other cases

through an acceleration of harmonic rhythm. is typical of simple and orderly phrases of the classical displays a deviation from an established norm, but this deviation itself

to intensify climactic sections

The period;

passage in Ex. 16-17 it

becomes another norm. Observe that the rate of change of the second phrase twice that of the first, thus producing a kind of "harmonic accelerando."

is

HOMOPHONIC

262 16-17. Mozart:

Ex.

Symphony

G

in

minor, K. 550,

i

ms

rJ

f

^^

^

g:

^

^ T'T rn

t

rnm

i

"S t R

m

^4 &

r

T

>

NON-CHORD TONES

III.

r

-\

TEXTURES,

w^ ^ T r

f

^ri

^m

f

When the rate

^

W*"

of harmonic change

ing voices), a feeling of greater

is

rapid (relative to the rhythms ot'participat-

momentum

is

imparted

to the

whole texture.

On

the other hand, a relatively plodding rate of change effects relaxation.

Contrapuntal Considerations (Voice leading)

Although linear matters are not paramount in homophonic textures, the joining of one chord with another is normally achieved by means of predictable motion from one chord tone to the next. The individual chord members are links in separate unfolding chains of lines, even if those lines are sometimes of negligible melodic interest.

In

Except

this sense, linear considerations are pertinent.

for

unique instances,

parallel motion,

and

it is

all lines

of a four-voice texture do not

obviously impossible for

all

in contrary or oblique

voice

homophonic texture a general balance of all of these

in relation to

in

voices in such a texture to

move

motion

move

one another. In the usual fourpossible relationships

is

maintained in a balanced union. In achieving 1.

this

balance the following principles hold true:

Consecutive (parallel) voices, particularly

fifths

and octaves usually do not occur between any two

between the outer

voices.

—

HOMOPHONIC

TEXTURES;

263

NON-CHORD TONES

16-18. Parallel Motion.

Ex.

^

a

i^^

k=^

J

i

^m#4^

g

3

Parallel octaves

Fifths

2.

f i Parallel

I* S^

r 1

^^

I

i

r

r

f Contrary octaves

fifths

and octaves usually are not approached by similar motion

in the

same

voices, particularly in the outer voices. This occurs occasionally at cadences,

but even here one voice almost always moves by step^to the cadential sonority.

16-19. Similar Octaves and Fifths.

Ex.

m

m m

B

hb^ ¥ 1

A

^^ rf

T

i

J

T

gg f

r

A

tritone created

by two voices normally

earlier, i.e., the °5 contracts, the

Ex.

i

Bk:

ii«

I

5ths approached by similar motion (rare between outer voices)

resolves in the

manner

established

expands.

16-20. Resolution of Tritones.

°5 (contracts)

st

^

^^^ mmor

ifoO vu

+4 (expands)

xc

r

a

+4

?^

t

Similar 8x'es, both voices Similar 8ves, upper voice stepping ( common, particularly skipping { avoided) at cadences)

3.

a

5

: f

+4-

^

^TT~

or

^-

But also:

T m

o5

P5

and

>-o

f vii"

jOZ 18

f

p4

264

HOMOPHONIC

TEXTURES;

NON-CHORD TONES

Voices usually maintain their range identities by not overlapping immediately

4.

into the range of adjacent voices.

Ex.

16-21. Overlapping Voices.

The

5.

outer voices of a texture create an effective two-voice counterpoint; the

inner voices are in

Ex.

Schumann: Freue

16-22.

'$

* r

many

instances reduced to subsidiary lines.

^

dich,

O

meine See/e (Album for the Young, Op.

P

Reduction A

4

SI O'

^^

ii

m

r

J

j-

m^& ^

f

If

r

f

68).

/7s

Basic outer framework

i 6.

When full

linear considerations

complement of chord

sibility

is

7.

it,

every vertical point contains a

tones, root (or prime), third,

and

fifth.

When

this pos-

norm

:

etc.

(The composer's desire

for a particular sonority also

can overrule

of the complete chord.)

W'hen two successive chords contain one note that

some instance more than one),

this

note

is

melodic considerations demand another

f

'o

overruled, a simpler sonority might well result diad, unison, or octave

doubling, this

do not preclude

^

f

is

common

to

both (or in

retained in the same voice part unless

mode

of linkage.

HOMOPHONIC

Common

16-23.

Ex.

tones between chords.

(b)

la)

^

*

A

(c)

i:

>

1 f

V

Bb:

is

265

NON-CHORD TONES

TEXTURES;

.1

me^ Bb:

Bb:

IV

step-by-step working procedure for the

shown

J

in Ex. 16-24.

The

result

is

homophonic

lii

setting of a given

melody

only one of many possible solutions to the given

problem. These settings are planned as simple choral arrangements without recourse to any procedures which would create

The chordal

Ex.

resources deliberately have been limited to diatonic traids.

Melody

^m m

^

(B)

forceful musical statements.

Working Procedure for Setting of Melody.

16-24.

^

(A)

more

Added

ftfp^ ^y^

^m^

7SZ

^

basic pitches for bass voice

^'

M

~=^-J

^-

m

-•

-^ p¥=^ m 2

-•

m- ^•

-•

•

A 1

~i~l

Y-

•

-•

-•

s

(C) Bass voice completed

^

m ±^

s W

Implied

I

V

Nli"

(

+

=

decorative

ii

-^

I

(16)

pitch)

lie (ii)

lii

h^ i vi^

W iii

ivsys

i

I

v

ii

chords:

(D) Basic pitches for middle voices added

i^

^

=f=^

^ i^

•

^

?

•Q

^

^

i

—

266 Ex.

HOMOPHONIC

TEXTURES;

NON-CHORD TONES

16-24. continued.

(E)

Completion of middle voices

(F)

Decorative patterns added for more contrapuntal texture

Non-chord Tones

The

decorative patterns discussed in earlier chapters play an important role in

—or "chordal" —

homophonic by the name

textures.

They

are better illustrated in such contexts

non-chord tones. It will be apparent that

no basic differences separate

the treatment of the decorative tones in two-and three-voice contrapuntal binations from the

ing tone

is still

same

kinds of patterns in relation to a particular chord

a passing tone, a suspension

is still

a suspension. But

;

com-

a pass-

we can now

consider decorative patterns from two standpoints: their melodic (horizontal)

accompanying chord (vertical). Generally these two facets coincide, patterns which form a decorative melodic pattern creating a harmonic relation with accompanying tones that can be distinguished as and

structure

their relationship to the

"non-chordal."

now regard the passing tone as a non-chord tone that is approached by step from a chord member and resolves to another chord member by step in the same direction. The intervallic progression is still basically the same as in contrapuntal W^e can

textures,

forming a

successive chord

members.

m

series o{ stable

—

must be known

unstable

—

stable,

but the actual members of each

in order to separate the

non-chord from chord

HOMOPHONIC 16-25.

Ex.

TEXTURES

;

267

NON-CHORD TONES

Passing Tones.

VI

Neighbor tones fulfill a similar role in relation to a chord they are non-chord tones approached by step from a chord member which return to the same chord mem:

ber.

Ex.

16-26. Neighbor tones.

i^

*

m

D:

The

J.

J.

I5

r V7

^

i ¥

E

r

^r

I

3

J.

IV

a non-chord

approached by step from a chord member and is left by leap. As described first in Chapter 8, it may be left by leap in either direction, but a change of direction occurs most frequently. The leaning tone, on the other hand, is a non-chord tone approached by leap from a chord tone, but left by step. Again the direction of resolution is variable, but a change from the approach is most frequent.

Ex.

escape tone

16-27. Escape

is

tone (usually

unaccented), that

is

and Leaning Tones,

a

te

r IV6

te

^

^ C

:

ill

T ^ ii»

i

16

.

268

HOMOPHONIC

To

continue our review and slight redefinition of decorative patterns,

say that the anticipation as a

a non-chord

tone that immediately precedes chord tone, usually just before a strong beat.

^ S

Ex.

NON-CHORD TONES

TEXTURES;

is

its

we can

repetition

16-28. Anticipation.

i

E minor

The

m

^

i r

r

1.

m^

55?^

V

:

A

C

major:

13

V

following excerpts should be studied in terms of their use of the non-chord

tones discussed thus far.

Ex.

16-29. Mozart: Marriage of Figaro, "

Deh

vieni,

non tardar." c

JMip Deh,

^

I

f

J

f

non

vieni,

tar

I

J^r^

J

-

dar

^i I

t

J.

"1

l

J

y

J)^

l

fi J)J^'f |

^

E

s Ex.

p

-^

m _t-^

16-30. Mozart: Variations on a

:!7.

^')

^ rr h^m ^

J

Menuet by Duport, Var.

1' I.

^

HOMOPHONIC Ex.

16-31.

The

TEXTURES;

NON-CHORD TONES

Weber: Overture

269

to Euryanfhe.

suspension presents a slightly different set of considerations in the light of

our review of decorative patterns textures

we

in

homophonic

and three-voice formed between the

contexts. In two-

described suspensions by noting the intervals

suspended tone and the other voices. With more complex textures, however, it is no longer necessary to determine all of the intervallic relationships. Instead, we

most types of suspensions only by measuring the suspended tone and resolution from what appears to be the characteristic dissonance-consonance

shall refer to its

The following types, two of which are illustrated in most common: 4 — 3, 9 — 8; 7 — 6, and 2 — 3. In many

pattern formed.

Ex. 16-32, are

among

instances this

the

characteristic pattern will be

formed between the suspension voice and the lowest

part of the texture.

Ex.

16-32. Brahms: Violin Sonato

in

G

major,

I.

^

f^^

^-»

^ ^

^m^

(»• :2-

35:

Dissonances often are formed between the suspended note and members of the

chord other than the bass. In measure three of the above example a 7-6 suspension occurs between the highest note in the piano part and a lower voice, in addition to the 9-8 suspension

formed with the

bass.

270

HOMOPHONIC

NON-CHORD TONES

TEXTURES,

Suspensions formed by the lowest voice are measured as before: from the suspended note and its resolution to the upper member of the chord that forms the characteristic dissonance. This type of suspension, illustrated in Ex. 16-33,

of the most frequent.

A

is

one

complete description of the intervals present within

this

For simplicity we can reduce

suspension would be 2\-

figuration to 2-3

this

alone.

7

Ex.

16-33. Pachelbel

Nun

:

lasst oni

Cott,

dem

Herren.

^^

^^

i)frn

J.

J

rule,

r

r

J J i

^^^^ ,

I

t^^^E^

As a

r

r

3x:

composers have avoided doubling the resolution tone of a suspension

more to certain types of suspensions than other because of their particular harmonic context. Where the resolution pitch is a leadpattern. This principle applies

ing tone (as in this

many

4-3, 7-6,

and

2-3 suspensions) composers have rarely doubled

tone in another part.

Pedal Point

Pedal point

—sometimes just "pedal" or "organ point" —

is

an excellent example

of a technique that composers have used extensively, a technique that

any

to is

single musical style. In

its

is

not peculiar

simplest form a pedal figure consists of a tone that

sustained through a succession of chords.

It

usually occurs in the lowest voice but

found occasionally in the highest or an inner part. The term itself implies, however, that its most frequent use is in the bass, for the "pedal" actuates the bass

it

is

notes of the organ.

An

example of this technique is the Perotin excerpt shown below. The lowest voice merely sustains a single pitch, above which the other two voices move in a strictly measured rhythm.

Ex.

early

16-34. Perotin: Three-voice

^^

m

^j:

Organum,

^j

^^

Alleluia.

iJ

:

JJ ^-. ^J ;i f I'l/ i

^

ii-

HOMOPHONIC

The

TEXTURES;

NON-CHORD TONES

tone that forms the pedal

chords that occur above

may

16-35.

may

or

In the following

it.

of both the tonic and subdominant measure 4).

Ex.

271

Haydn: Quartet Op.

triads,

it is

but

m w ^m

it is

foreign to the

i

of the successive it is

a

member

dominant

(as in

^

s

A

member

the tonic; as such

64, No. 2, IV.

J)

^ m g

not be a

r

r

r

Pedal tones are not always sustained. Rearticulated pitches produce the same

harmonic

Ex.

16-36.

effect in a slightly

Haydn: Quartet Op.

S

^m

"busier" way, as in Ex. 16-36.

122

50, No. 6,

^^

I

^

^ 3JZ

«:

# m

DiJQi]

u^nn ^nii n^an

^

fe

7

^ ?

VT

The

tonic

The

tonic pedal often appears near the beginning of a

and dominant pitches serve the pedal function most frequently, particularly in music of the eighteenth and nineteenth centuries. Whatever pitch is used, the pedal tone becomes a kind of static pillar of reference, the associated chordal weavings acting as decorative patterns which prolong motion but do not effect real changes in the harmonic structure of the passage. vious example by

Haydn)

movement

or near the end. B^th are locations in

poser usually wishes to solidly establish the tonic.

An

(as in the pre-

which the com-

examination of the Preludes

and Fugues of Bach's Well-tempered Clavier will disclose his fondness for the closing tonic pedal. Used in this manner the pedal gives the impression that the harmonic progress of the composition is closing, the moving voices are merely elaborating previous material in a prolongation of the cadential pattern.

272

HOMOPHONIC Well-fempered Clavier, Book

I,

the other hand, the dominant pedal

is

Ex. 16-37. Bach:

On

Fugue

The

NON-CHORD TONES

II.

used with telUng effect as a signal of

the return of the tonic key. For obvious reasons, this just prior to a closing section.

TEXTURES;

is

often found in compositions

following passage contains a pedal on the

dom-

inant.

16-38. Reger

Ex.

^

:

I

Toccata

D minor.

M '

^

ff

sempre M.I

^H

in

^

it

w^

£

Gt.

J^

*ttJ*

More than one combined,

pitch

may

2Z

act as a pedal.

as in the following

Sometimes the tonic and dominant are

example.

16-39. Schubert: Der Leirmann (W/nferreise cycle).

Ex.

m ^^

^LLiir ^^

^m ps tS>-=-

In determining the structure of the decorative chords which accompany a pedal, it is

necessary to disregard the pitch of the pedal

itself,

except at those points where

HOMOPHONIC

clearly functioning as a

it is

tions of the pedal

pitch) can be

the

is

way

sounded with

chords which

move over

chords, etc.),

and

pitch

273

NON-CHORD TONES

TEXTURES;

member

of the chord.

One

of the

main

tonal fascina-

which quite foreign chords (in relation to the pedal and yet retain a sense of tonal stability. In this sense

in it

a pedal are decorative chords (passing chords, neighbor

as such they prolong the

harmonic significance of the pedal

itself.

Even more complicated uses of the same basic technique occur. Ex. 16-40 contains a passage in which two violins arpeggiate a C major triad through three measures, under which viola and cello move in parallel minor sevenths. Note again that

it is

the unchanging triad arpeggiation, the pedal, that provides the stable

element; the moving sevenths form a decorative motion.

Ex.

16-40. Shosfakovifch

By permission of the International Music

Quartet, Op. 49,

:

Company, New York.

Violins

S

i.

Viola Cello

^

^^ ^:

^ ^¥^

w

Sinnultaneous Non-chord Tones

Non-chord tones do not always occur singularly. A great degree of harmonic mobility can be created when two decorative patterns occur together, particularly when they are articulated simultaneously. The simple combination of an anticipation along with the resolution of a suspension, for example, produces a sharp dis-

sonance colorfully known as the "Corelli clash." (In spite of the name, by other Baroque composers as well!)

Ex.

f

16-41. Corelli: Sonata

4 g»

S

"Tj

i

T

Op.

m r

m

2,

No.

it

was used

4.

^ p

r

e

f

Other non-chord tones are frequently combined, particularly when they are of of the same type double passing tones, double neighboring tones, etc. Example

—

16-42 contains a double suspension. This type of pattern

when two

lines are

moving

in parallel thirds or sixths.

is

particularly

common

27A

HOMOPHONIC Ave verom

16-42. Mozart: Motet,

Ex.

TEXTURES;

NON-CHORD TONES

corpus.

^^A?*.*^

-7

^ A

^

m

1

J

^

^^

^

more complex combination occurs when an

a foreign bass note. In Ex. 16-43 the

rrt

first

^

entire chord

beat of the final

diminished triad suspended over an arpeggiated tonic chord.

unprepared in the previous chord,

g'),

is

added

to the

suspended above measure contains a is

The

upper parts

third tone (the to

form a more

complete sonority.

Ex.

16-43. Mozart: Sonata

D major,

in

K.

311,

I.

t^

^^ A

f

non-chord figure containing a so-called free

analysis

would be merely a

basic-associate) occurs

foreign to the prevailing chord

shown

tone

is

(which in terms of melodic

when

a pitch that

approached and resolved by

skip.

is

clearly

The cadence

example actually is similar to the bi-chordal effect illustrated in Ex. 16-43; the lower line is merely an arpeggiated tonic triad, part of which forms dissonant relations with the chord in the upper voices.

Ex.

in the following

16-44. Free tone.

^

^W^

^

In some musical passages is

"chordal" and what

earlier

is

it is

not easy to

"non-chordal."

make an

We

absolute judgment about

what

can note such a passage from an

example, shown again below for our present purposes.

—

HOMOPHONIC Ex.

16-45.

—

TEXTURES;

275

NON-CHORD TONES

Schumann: Einsame S/umen (Waldszenen).

f1 We might ask what

—

is

the chordal basis (or bases) for measure

3. Is

the progression

with the c" of the top voice a leaning tone? Or is the whole measure best described as founded in IV, the b flat' and a' functioning as successive passing tones between the basic-associates c" and g'? The answer to this problem is best here

VI

iv,

sought through a basic-melody analysis, as well as attention to the total

set

of

melodic/harmonic patterns. The two lower parts, through skips, outline the IV chord (C e-flat g). The boundary tones of the melody are easily accommodated into this chordal unit, for they are the root and fifth (C G). As a consequence, the entire measure can be described most accurately as a IV chord over which two

—

consecutive passing tones add melodic interest.

In some instances the total

set

When

harmonic structure over another. be chosen if a

choice

must be made.

indicates the probability of

thus making a

of voices will not favor one interpretation of

The

this occurs, the simplest

explanation should

potentiality of a dual (or even triple) analysis

an ambiguous passage,

harmonic structure, anyway. The essential purour understanding of musical

in terms of

precise analytical distinction irrelevant

pose of analysis, after

all, is

organization as an aural

to support

and

to intensify

experience.

Exercises

For more detailed assignments see Materials and 1.

Find several examples

to illustrate

Structure

of Music

I,

Workbook, Chapter 16.

each of the following homophonic textures:

a)

a dominating melody with a chordal accompaniment;

b)

block harmonies with isolated rhythm activity;

c)

two-line texture, the lower outlining chords (similar to Ex. 16-3);

which contrapuntal and homophonic elements are blended. Using the harmonic progression of Ex. 16-22 as a harmonic basis, create piano settings illustrating homophonic textures a), c), and d) of Ex. 1 above. Taking an F major triad as a harmonic unit, see how many different four-part arrangements you can devise using customary vocal ranges, doublings, and spacings; do the same with a d minor triad in first inversion. Using the chord progression of Ex. 16-2 as a harmonic basis, write two different four-part d) a texture in

2.

3.

4.

vocal phrases

(SATB) according

to the guides given for spacing, doubling,

and voice

leading. 5.

6.

Choose passages from music you know from which to describe the patterns of harmonic rhythm. Perform each of the versions of America appearing in Ex. 16-14 by singing the chords in arpeggiated form (bass up) making suitable octave transpositions in order to fit your

own

vocal range.

Dominant, and

Tonic,

Subdominant Chords

and

Position

First

in

Root

17

Inversion;

Dominant Seventh Chord

we

examine some of the relationships that are formed by successive chords and the tonal center of a composition. We saw in Chapter 14 that each scale degree may function as the root of a chord, and that a chord may be identified by the scale step used as its actual root or prime. Descriptive labels, such as tonic, subdominant, and dominant, are convenient to designate chords without naming specific pitches. In this way identical harmonic relations can be described with the same set of terms even though the actual pitches are different. For the present we shall study some of the relations that are formed when In

this

chapter

the chords whose roots are the

shall

first,

fourth, or fifth scale steps are a part of the

musical fabric.

The Root Position and

The

tonic triad

(I

or

First

i)

is

Inversion Tonic Chord.

an important harmonic unit

in

a key.

It serves

the

same purpose in a harmonic context as does the tonal center of a melodic line: it acts as a harmonic focal point. For this reason, the tonic chord appropriately functions as a beginning and concluding harmony; a sensation of inconclusiveness results if final resolution to the tonic

is

absent.

In the following example the harmonic activity is concluded in two different ways once with the tonic and once with another diatonic triad. A performance of each of these endings will demonstrate the inconclusiveness resulting from the

—

delay or absence of the tonic.

276

TONIC. DOMINANT.

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

^ Wr^

Ex.

17-1.

Mozart: Trio

in

i

i

E

Major, K. 542,

*

I

(adapted)

i

*s

^

277

or

m

I

m

w

S -0-

i V7

V^

IV

Compositions frequently begin with the tonic chord. This procedure, illustrated in Ex. 17-2, establishes the tonic immediately. (At times a delay in the initial

appearance of the tonic

may produce

a desirable effect of expectation for the

listener.)

Ex.

17-2.

Haydn:

String Quartet,

Op. 20, No.

6,

M ^^ I.

1^

The

33

structural significance of the tonic chord

is

often intensified by being

preceded by root movement of a descending perfect fifth (or ascending perfect fourth). Such root motions (as in measures 1-2 of Ex. 17-1, and in Ex. 17-2) tend to emphasize the second of the two roots, if rhythmic or dynamic considerations

do not indicate otherwise. The impression of harmonic intensity can be heightened or diminished by the nature of the chords thems^^lves. Generally, the more complex or the more dissonant the first chord, the more conclusive the effect of the second. Inversions of the tonic triad do not produce exacdy the same effect as the root position. Part of this difference exists because inverted chords only have decorative

consonances between the bass and upper parts, whereas root position chords only have cadential consonances between the bass and upper parts.

The

first

inversion of the tonic chord (Ig or

ig)

often appears directly after a root

position tonic, creating the effect of prolonging the tonic

harmony even though

278

TON/C, DOMINANT,

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

the bass changes. This can be seen in measures 1-2 of Ex. 17-3; here the bass outlines the tonic chord,

chord

with

all

The

chords except the second in root position.

recognized because no change of root

Ig

heard between the first two chords, and the second chord contains a decorative consonance between the bass and another part. is

Haydn: Symphony No.

17-3.

Ex.

86,

I.

V

m

ijRf*

^

is

-^-^ f=f ^

i

f

t

f^-^

I

h-

^

1

i

f

16

V7

16

I

1

^

Because the tempo of the preceding example

is

r I\-

Adagio, the motion

I

—

^Ig

is

Sometimes a rapid tempo makes it unlikely that the listener will clearly perceive a change of position, as in Ex. 17-4. In this instance the motion to E-flat in measure 2 adds to the illusion of motion created by the bass line. easily perceived.

Ex.

17-4.

Purcell

:

^ nK a

Dido ond Aeneas, "Shake the Cloud."

^^-t^

u

rrrf

w

^^ S

J

(i

-6h

V

The the

ig

Ex.

is

also present in Ex. 17-5.

95,

Menuetto

^

^

^

r

J

W''

Here

note.

Haydn: Symphony No.

I

i^

associated with the beginning of step motion in the bass that leads

dominant

17-5,

j^^

i

impression of prolonging the tonic chord

chord

to the

is

Hi''

^1

ife=t

*

'.6

IV

TONIC, DOMINANT.

279

AND SUiDOMINANT CHORDS; DOMINANT SEVENTH CHORD

Although Ig (ig) often follows I (i), this does not indicate the use of Ig as a cadence chord. As a fin al cadential chord the most stable form is the r oot position triad. The Root Position and

The dominant

First

triad

is

Inversion Dominant Chord.

often directly involved in clearly establishing a tonic

chord as a harmonic focal point. There are two essential features involved in the motion from dominant to tonic: (1) the root relationship of a descending perfect

an ascending perfect fourth) and (2) the presence of the leading tone (the diatonic seventh scale degree in major keys and the raised seventh degree in minor). Both root movement down a perfect fifth and the leading tone-to-tonic relation are illustrated in measure 1 of Ex. 17-6. fifth (or

17-6.

Ex.

Beethoven: Piano Concerto No.

5,

Op. 73,

Adagio un poco moto

i

M^^

1 fcn

r^^ h

?i^

"

:s:

'"

• ;

X

^

-XI

-X

IT

^L T 1^4 -L

'M*

In major keys the dominant triad a wider range of possibilities exists.

is,

The

of course, major. In minor keys, however, diatonic dominant triad in minor

is

minor.

Although attractive and (to our ears) somewhat exotic when used in a cadence, the minor dominant chord is not found as frequently in simple tonal music as a major dominant. The latter requires a scale alteration the raised seventh degree. Despite the required alteration, the leading tone should not be regarded as an "altered" tone, since it is common property of the melodic and harmonic minor scales. The effect of the minor dominant (v) is effectively demonstrated in Ex. 17-7. ,

Ex.

17-7.

Vaughan Williams: Mass

in

G

copyright owner, G. Schirmer,

^^

i

Minor, Kyrie. Inc.

=? i 1 r f

i^

i

16

V

i

Reprinted

by

permission

of

the

'

Aatidhi

/i]uiun

280

TONIC, DOMINANT.

The Vg

more stereotyped

is

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD in terms of occurrence in musical context

chiefly because of the tendencies present in the bass

tone.

When

resolved it is

the leading tone

up by a half

is

in the

often resolved with greater freedom. This

movement

Ig,

form of the leading

exposed in one of the outer voices,

step. If the leading tone

considerations often govern the

Hne

than

it is

usually

appears in an inner part, however,

may be stated another way: harmonic

of inner parts (doublings, spacings, etcTJ;

most frequently govern the motion of the outer voices which_ constitute the basic framework of the texture. Since the leading tone is the bass note of the Vg chord, the chord of resolution usually will have the tonic note in linear considerations

the bass, a result of ascending half step motion.

Vg both preceded and followed by tonic. As is often the case, the first inversion of the dominant is associated with step motion in the bass. This example also contains a shift of texture from the two-voice imitative writing in the first two bars to the chordal texture of the last two measures. Despite and 2 is clearly e. the thinness of the texture the chord root in measures

Example

1

7-8 illustrates

1

Ex.

17-8.

Rameau

Rigaudon.

:

^ ^^

ms

^^

i

^

f-g-r

g

V

An

exception to the preceding occurs

the leading tone

does not layed or

Ex.

17-9.

mean is

is

tt

O

^^ y^i

is

ignored

m m

^ p^^ I

V6 V

I

16

I

Judah.

m

ii

^^

IV

V

i

followed by V. In such a case

that the resolution of the leading tone

/*

^ra

V6

x6 the root of the chord m- another chord

Handel: Judas Maccabaeus, Rejoice,

^

ititz

is

i

heard in another voice.

S^ T^

moved

when Vg

fe^ rr

e=t

i

V|I

;

member. This

it is

simply de-

AND SUiDOMINANT CHORDS, DOMINANT SEVENTH CHORD

TON/C, DOMINANT.

An No.

Vg occurs at the opening of Beethoven's Quartet, Op. 59, Ex. 17-10. Although a measure of silence interrupts the harmonic

effective use of

2,

shown

in

motion, the leading tone

Ex.

281

is

eventually resolved to the tonic.

17-10. Beethoven: Quartet

The Root Position and

The subdominant

First

in

E Minor,

Inversion

Op. 59, No.

2,

I.

Subdominant Chord.

often encountered preceding the

dominant in the terminal cadence. In this common progression the subdominant note directs motion toward the dominant, approaching it by step from below. The melodic cadential line of 4-5-1 occurs frequently in bass lines and is demonstrated in Ex. triad

is

17-11.

Ex.

17-11. Melodic 4-5-1

The subdominant to the

dominant:

it

in

bass

line.

however, does not appear only as an approach chord also precedes the tonic directly at cadences or elsewhere in triad,

a phrase.

A

wider variability in the triad quality is one of the characteristics of the subdominant. Ajt^hpugh tonic and dominant triads are relatively consistent as to their quality in a major or

appear

minor context, the two forms of the subdominant (IV or

iv)

music with considerable interchangeability. Conditions influencing this usage undoubtedly include the melodic use of the raised sixth scale degree in minor keys (necessitating a major triad when harmonized by the subdominant) and the in

frequent nineteenth-century practice of lowering the sixth scale degree (by a semitone) in major keys.

282

TONIC, DOMINANT.

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

17-12. Brahms: Sehnsuchf.

Ex.

.h=^

m

^ 17-13.

Ex.

S

j^

J'

fi

"

i#

r

«i

^

?

V7

IV

Schumann: Symphony No.

211

Finale.

s

:2i

J I

-&-

E

f ')^
2,

^

5

J

J

i

J

S

331

^

V7

IV (6)

l^^^=d=4

i

V7

I

subdominant chord appears in much the same context in connection with an ascending or descending diatonic scale line in the as Ig bass or an arpeggiated bass Hne. Ex. 17-14 illustrates the first of these procedures. In

its first

inversion the

—

17-14. Handel: Concerto Grosso,

Ex.

Op.

No.

6,

1,

I.

Allegro

fe^ fQ r^

±E

-•

13^i

§

A

S

P=»

fc

^^

more complicated treatment of ivg

is

rrs

A nnip i^ f

C\

i)

?^^ I

J

g^ i IV6V7IV6V6

I

seen in Ex. 17-15, the complexity due in

The essential harmonic progression of this merely a weak terminal cadence from ivg to i^.

part to the elaborate use of suspensions. excerpt,

shown

in Ex. 17-16,

is

This basic progression, however,

is

elaborated and prolonged for several measures

on the cadential

i^

before the fermata.

before

it

settles

TONIC. DOMINANT.

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

17-15. Mozart: Concerto

Ex.

M^\

p-

r

in

C minor,

j^f-r 'f

491,

K.

i

283

I.

' ff i

^^ ^

1^

<SPfl

o

>t-

n^

a!

J

r

'^

?

ivo

Ex.

iv

iv6

iv

17-16. Basic harmonic progression on Ex.

^ ^ i

V\,

(f,

17-15.

1*^

IV'

i '

subdominant chord,

17-17.

6

4

move by

step,

it

often

in

E-flat

Major, Op. 44,

^

# i

i

XTQ-

resolution of IVg

upwards

this bass line

17-18. Schubert:

Sonata

in

is

-0

to

^

A Major, Rondo.

1

0-

~ma-

IV'

I.

#

)

IV

Vg can be seen in Ex. 17-18. The ultimate the tonic, which in this case is somewhat delayed.

^

a^f

)

i

f iv6

Ex.

to a root position

II.

^m ^ ^ ^^^

j)

melodic goal of

moves

as in Ex. 17-17.

Schumann: Quintet

^BS

The

'S

9^

If the bass pitch of the ivg does not

Ex.

JV6

V^

16

284

TONIC. DOMINANT.

The harmonic two

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

structure of the last measure in Ex. 17-19 can be interpreted in

different ways:

it

can be interpreted

as a IVg, or the c" (the "root")

makes

interpreted as a delayed accented passing tone (which lodically, the latter analysis

17-19. Bruckner: Mass

Ex.

m

S

in

F

Minor, Qui cum Patre.

1.

r2

r

f

^M=#

1

(IV6)

J. S.

VI

7-20 both ivg and IVg are juxtaposed in a texture with considerable (It

should be remembered that on the organ pedal

would be employed which would double

17-20.

I'

4

contrapuntal independence.

Ex.

Me-

f

r

In Example stop

the root).

seems more musical.

^^h^

i

e

can be

Bach: Chorale Prelude, Ach, w/e

this line

an octave below.)

fluchtig.

^^ Manual

'

Pedal

^

Y^i* J .

s=^

I

P iV 6

jy6

^

£

i^ V6

Although most of the examples shown thus

far in this

chapter are excerpts from

approximately 1650-1900, we should not infer that the harmonic relations illustrated are an exclusive property of this period. Much contemporary music, as the following example demonstrates, reveals similar harmonic organization.

t

TONIC, DOMINANT,

Ex.

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

285

Copland: Sonata for Violin and Piano. (C) 1944 by Aaron Copland, copyright owner, and Boosey & Hawkes Inc., Sole Licensees. Reprinted by permission.

17-21.

t

jn

P

$

M

—

-9

^^-

1E3 ^T-r

'SL

s

^

I

i V

IV

The

I

following phrase, dating from the middle of the sixteenth century,

The

clearly in d minor.

chords

V

IV

I

—

all

final

cadence emphasizes

root position triads

D

is

and the other

as the tonic,

— belong to the diatonic materials of

this

key and,

in their total effect, affirm the tonality.

Ex.

17-22. Palestrina

m

:

Ven/, Sancfe Spiritus.

^

P¥

331

J

i:

9tFpg

A

A

i

)V

iy

:i\

Example 17-23

presents a picture

more

Here the choice of

in a chordal style.

m

J

J

19

1*

V

"X

,1

typical of sixteenth century compositions

one key

although e minor is the Complicating factors appear, however, in the second and third measures the use of the minor dominant and the emphasis upon G and C suggest other alternatives. It seems clear, though, that the cadence, viewed against all that pre-

most

is

difficult,

likely.

;

cedes

i-V rather than

^

Ex.

it, is

17-23. Ingegneri

f

55??

§

s

:

iv-I.

£cce quomodo.

i -r

fr

^fW-ff^ * 331

J^k^^sU.

r^

f^

a

tBT

286

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

TONIC, DOMINANT.

The Dominant Seventh Chord.

Together with major and minor

triads,

other more complex sonorities also have

seems apparent that if the triad may be described as consisting of the piling up of two thirds, the process may be carried one step further the

dominant

as root. It

produce a four-tone sonority known as a "seventh chord". In this section we shall concern ourselves with but one of these, the dominant seventh (V,), a "majorminor" seventh chord type which we will abbreviate as Mm,. The final measure of Ex. 1 7-24 contains a dominant seventh in block form. From to

this arrangement we can readily see the reason for its name. It has as its basis the major triad on the dominant D F-sharp A to this is added the minor seventh C above the root D. Hence, the term "major-minor" (Mm) seventh, the first factor

—

—

;

referring to the quality of the triad, the second to the type of seventh.

seventh chord

Ex.

is

found on the dominant, we shall

17-24. Mozart: Concerto

in

G

Major, K. 453,

•»•» # «R ^^

y<'^

1

»^

1

J

^

j-

The seventh

of the

Mm,

in the previous

example

is

e£

introduced without melodic

preparation. Often, however, the seventh of the chord In addition, the resolution of the seventh

Ji

^

^

H

^E^

this

as V,.

it

I.

i

i£ 4

refer to

When

down by

is

step

melodically prepared. is

directly related to

the decorative (non-chord) character of the harmonic seventh.

Early occurrences of recognizable is

Mm,

chords are found

introduced as a passing tone above a dominant root.

The

when

the seventh

introduction of the

seventh with the dominant triad intensifies the motion to tonic because the

seventh forms a tritone with the third of the dominant chord (notated as a

diminished

fifth

in Ex.

17-25). It

is

the subsequent resolution of the tritone that

creates the effect of increased melodic activity.

Ex.

17-25. Tye

:

Come, Holy Ghost.

f^ ifiv ^ f

^

i

^

p

TON/C, DOMINANT.

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

287

In addition to passing tones, the seventh of the dominant seventh often results

from a suspension. Such an introduction of the seventh, by preparation voice, demonstrates the traditional treatment of the dissonant seventh:

by step motion or prepared

Ex.

in the

^

same

voice,

Hoh

same

approached

and resolved by descending

17-26. Scheldt: Chorale Prelude, Allein Goft in der

step.

sei Ehr.

L

S

^-

^^ X i

w

P

r

f

^^

in the

J

~rr

-&.Ka

-1

J.^

In Ex. 17-27 the dominant seventh

is

seventh must be regarded as a chord

introduced in such a

member

way

that the chord's

rather than as a result of linear

and approach (by leap) confirm the fact member of the chord and not merely the result of

activity. Its metric location, duration,

that the seventh

an integral

is

linear impulse.

Ex.

17-27. Monteverdi: Ohime, je fanto awafe.

i,'/i'ii"i'i'

'J

^ The

A

J.

m

:

J -.

jJ'

t

~a

^^ i-~r

resolution of the major-minor seventh chord

is governed largely by the memembers. Perhaps the most important result of this is the tritone formed by its third and seventh, the leading tone and fourth scale degrees respectively. When the tritone is notated as an augmented fourth, it usually resolves by expanding to a sixth; when the tritone is spelled as a diminished fifth, it

lodic treatment of

its

usually contracts to a third. This results in the

tone and

t

he downward

upward

resolution of t he leadingresolution of the chord seventh, both by step.

|i

288

rON/C, DOMINANT,

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

17-28. Resolution of the V7.

Ex.

o5

Bt:

>•

3rd

6th

Bk

V7

This resolution pattern

V7

sometimes not adhered

Often a composer will resolve the leading tone downward to the fifth of the tonic chord in order to obtain a complete triad on the resolution chord. This is seldom done, however, when the leading tone is in an exposed melodic position.

Ex.

is

17-29. Variant resolution of the Diminished Fifth

to.

the V7 Chord.

in

o5

Harmonic Cadences.

Harmonic progression

is

but one of the means by which the composer can

create the feeling of conclusiveness that he desires at the cadence. earlier that a single

melodic

line

can attain a convincing and

We

satisfying

observed

cadence

through certain manipulations of pitch and duration, and these same factors produce similar effects in two and three voices. We noted also that merely a cessation of motion can produce a cadential efTect. In recognizing cadences in harmonic texture it is important to remember that chordal succession alone cannot produce a cadence it must be coupled with other ;

factors

— reduced

motion, metric placement,

etc.

—

to achieve this condition.

We

attempt now, however, to identify various types of cadences with greater precision than before (as, for example, in melodic cadences), since we are now con-

will

cerned with the entire harmonic content of the music.

Cadences that we designated as terminal abound in the music of the seventeenth, eighteenth, and nineteenth centuries but in several subvarieties. One of the most frequent of these is the authentic cadence, a cadence produced by movement from

dominant

to tonic. This rather general description leaves a great deal of variety

in the exact procedure used

by composers. Possible variants

dominant sonority (V, V7), the soprano

line (including

exist in the type of

such cadence

lines as 7-8,

—

—

TONIC, DOMINANT,

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

2-1, 2-3, 5-8, etc.),

examples

Ex.

r

and the bass

illustrate various

line (including 7-8, 2-1, 5-8, etc.).

The

289 following

approaches to the authentic cadence.

17-30. Beethoven: Septet,

Op. 20, Menuetto

I.

^

^

VI

Ex.

17-31. Mendelssohn:

P

LJ

Symphony

t^

17-32.

^ Z

Ex.

,

A Minor

1^.

(Scotch),

f

I.

t^

tf'

,t:

p

^^ is^

Hfl^f Ex.

in

V^

in

A Major,

^

ip^p^ m

m

^

Mozart: Requiem, Offertory,

^

-*

i

r

^ tit Do

-

mi

-

ne

Je

-

su

K.

Domme

Chri

~J^

I

m p It

ieiu Chrisfe.

-

ste

I

"\

V^

114, Menuetto.

^

17-33.

*

#—

p

Mozart: Symphony

1

I

X

^m

290 (^

1

Ex.

TONIC, DOMINANT.

17-34. Buxtehude

:

Instrumental Sonata, Jesu, Meine Freude.

o

yg=^i

^ff^

f

^^

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

J

J.

-iHi

il

f M.

A second type of terminal cadence ment from subdominant is

known asplagal, which is produced by moveThe downward root relation of a perfect fourth

to tonic.

is

characteristic of the plagal cadence

"Amen"

following

many hymns.

In

and may its

clearly be recognized in the typical

effect the plagal

clusive as the authentic cadence, often following

clusion of a

movement

cadence

is

fully as

an authentic cadence

con-

at the con-

or composition. Ex. 17-35 clearly demonstrates a plagal

cadence concluding a composition.

Ex.

17-35. Brahms: Alto Rhapsody.

n

fe Sein

Herz.

^^

f7\

I

Occasionally the tonal center

The

tions that

Ex.

331

:xjl:

IV

17-36.

r^

A

final root is

movement

is

not clear at the end of a composition as in Ex.

suggests a plagal cadence, but there are indica-

the tonic.

17-36. Bach: Cantata No.

161,

My

inmost Heart doth Yearn. i7\

',:-<''

AND SUBDOMINANT CHORDS; DOMINANT SEVENTH CHORD

TONIC. DOMINANT,

Progressive cadences

may

more

also be classified

suggesting continued motion in a

number

291

precisely into different types,

of different ways.

A

frequent manifesta-

which the final chord is the dominant. Since composers have approached the dominant in any number of ways, there are countless varieties of half cadences. In Ex. 17-37 the cadence is little more than the tion of this

is

the half cadence, in

V—

reverse of the familiar authentic cadence

Ex.

17-37. Mozart:

Mass

in

C Minor,

K. 427,

i.

Dom/ne Deus.

^ mm^ »

\%

ij

^

p

Other diatonic

(or

fejgp^

^

?

r

tr

f

1

even chromatic) chords

may

precede the

final

dominant

chord, however, as in the following.

Ex.

17-38. Schubert: Winterreise, Der Wegweiser.

fcm

m^

as the

of 2

ivg

commonly

f="

f

^

^^ The

$

w

m

? iV6

occurs in a particular species of half cadence^ that

V

is

known

"Phrygian cadence." Its name stems from the typical cadential melodic line found in the Phrygian mode. The characteristic features of this cadence, 1

—

illustrated in Ex.

1

7-39, are

first

the chordal progression ivg (or

iv) to

V, and second

the contrary motion between the outer voices, expanding or contracting to the

octave of the dominant. This cadence

is

common

in

minor

keys, less frequent in

major.

*

Another kind of progressive cadence, the

deceptive, is

discussed in Chapter 21.

292 Ex.

TONIC. DOMINANT,

AND SUBDOMINANT CHORDS, DOMINANT SEVENTH CHORD

17-39. Handel: Concerto Grosso,

jJK!

1

tf^i

Op.

^^m

6,

No.

2.

j'J e

J-

Phrygian cadences are often seen as interior cadences, less often as terminal cadences. Occasionally, however, Baroque composers used Phrygian cadences at the

end of one of the inner movements of their sonatas, concertos, or a close harmonic connection with the following movement.

suites,

suggesting

Exercises

For more detailed assignments see Materials and 1.

2. 3.

Structure

of Music

I,

Workbook, Chapter 17.

Write an eight measure melody in G major which clearly outlines Tonic, Subdominant, and Dominant chords. Use passing and neighbor tones to decorate basic pitches. Then apply the same procedure to writing a melody in b minor. Practice spelling I, IV, and V chords in a variety of major and minor keys. Listen to a recording of Friihlingstraum, by Schubert, and identify the I, IV, and V^ chords used in the opening section of the song.

4.

Write an eight measure piano piece in A major, using an essentially homophonic texWrite in | meter, allegretto, creating two 4 measure phrases, both of which illustrate the chord sequence I, IV, V, I. (Use V or V^ as desired). ture.

5.

Make

several settings of a bass line consisting of 4-5-1 in different major

keys. Write for

4 voices

Mm^

in

and minor

chordal and contrapuntal textures.

chords on different roots.

6.

Practice spelling

7.

Write out V^ chords for four voices in at

least five different spacings.

Resolve each chord

to tonic. 8.

Practice writing

9.

Listen to the slow

and

identifying V-I

and IV-I cadences

in different textures.

movement of Symphony No. 39 in E-flat, by Mozart. Note particularly subdominant and dominant-seventh chords. Connect the following chords in a major and then in a minor key. Write in \ meter, the treatment of

10.

SATB. I-IV-V^-I-iv-I-V-IV-VjI. Use decorative pitches to effect smooth chord connections.

Inversions

of

78

thi

Dominant Seventh; Harmonic Rhythm

we

examine the inversions of the V7 chord, pointing out the characteristics of each and studying their approaches and resolutions. Our concern will be almost entirely with melodic movement, since the use of different inversions of this chord does not involve any changes in the typical root progressions. The differences are those of bass motion, approach to and resolution of the seventh of the chord, and the treatment of certain characteristic intervals in In

this

chapter

will

the chord, especially the tritone.

As with triad inversions, we shall indicate these seventh-chord inversions by means of figured bass symbols. Since we are dealing with a more complex sonority, however, the figurations must be more complete. For the four positions of the dominant seventh (and for

all

seventh chords in general),

we

will use the following

figured bass symbols.

Ex.

^ 18-1.

m

Figuration of inversions of the V7.

^

a -e-

-oxt;

V7

331

331

V6

ISH

V(6) 4 s

'S

(I) 1.3

.

\J

In Ex. 18-1 the figures in parentheses are unnecessary to the identification of the chord and, consequently, are generally omitted both from the figured bass

and from the analytical symbols. Note that the numerical the interval of the seventh (or

its

inversion, the second)

is

relation that represents

always included

respectively.

293

— 7_6_4_4 5

3

2

294

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

In the resolutions of these inversions, two melodic factors governing voice motion are important. We discussed in earlier chapters the tendency of the members of the tritone to resolve in an outer voice

—

by

step,

and the

intensification of this tendency

soprano or bass. This same tendency

is

when found

present in the dominant

seventh chord, in root position and inversions.

The seventh

is

a dissonance. It

is

dissonant not only with the root of the chord

but with the third as well, even though these relations are mild by contemporary standards.

The tion

is

seventh of the V7

approached

is

in a limited

number

of ways, and

its

resolu-

virtually restricted (with a few exceptions noted later in this section) to a

downward

step.

In

descending resolution, the seventh possesses an active

this

tendency as strong as the leading tone. The interval formed by these prominent "tendency tones" is significant in itself, since it is the tritone the most unstable of intervals and the one that most urgently

—

The

harmonic context may be observed in Ex. 18-3 in "x" and "y," the two voices moving in contrary motion by step according to their tendencies. An exceptional resolution of the same suggests resolution.

typical resolution of this interval in a

interval (in similar motion) occurs at "z."

Ex.

18-2.

Beethoven: Violin Sonata

P^

in

C Minor, Scherzo. tr-

3m

^ ^ ^^ ^ ?

"27

j|

J

J^

^

^

v

Several patterns are possible in the approach to (or "preparation" of) the seventh. In Ex. 18-2 one of these

is

illustrated

— by step from below.

In addition

often approached by step from above,

by leap (usually from below), or it may appear as a suspension from the previous chord. These approaches will be illustrated later in this section. Certain inversions are seen more frequently with one or another particular approach; these will be noted as we proceed. We will not dwell at length on the V7, since its use has been amply illustrated in an earlier chapter. One characteristic, however, should be noted unlike its inversions, which are almost invariably found in complete form, the V, appears occasionally with the fifth missing. In four- voice textures composers have doubled the root in such cases. Authentic cadences in four voices that employ V7 fall into one of the following categories If both the leading tone and seventh resolve according to their tendencies, either the V7 or the I will be incomplete. Composers someto this, the seventh

is

:

:

times sacrifice this melodic convention to achieve complete chords, as in the final progression. In cadencing

omitted the 18-3.

fifth

and

upon an incomplete

tonic triad, most composers have

tripled the root, as in the second progression

shown

in Ex.

INVERSIONS Of THE DOM/NANT SEVENTH; HARMONIC RHYTHM

Ex.

295

Four-voice authentic cadences, complete ond incomplete.

18-3.

^^

"X"

"Y"

Incomplete

± a

a ffi

J

I

f

^

Both Complete

"Z"

Incomplete

1

i T

4-

f

The Ve Chord 5

In

its

approach and resolution, the Ve

tion possibilities are

more

is

similar to

V,,.

Here, however, the resolu-

limited, since the leading tone (in the bass)

and seventh

generally resolve by step according to their tendencies. Thus, the only frequent

chord of resolution

is

the tonic, as illustrated in Ex. 18-4. In this

example we

see

the characteristic tritone between the outer voices.

Ex.

18-4.

^

n»

^ r—f ^

Haydn: Quartet Op.

..

J-

50, No. 6,

I.

i

T

m^

-e-

-&-e-

P

^

v|

Since this resolution the approach

is

f=T

standard, most of the differences in the use of

(»

#

i»

Ve appear

is often preceded by l\\, a progression suggested by the 6-7-8-scale line in the bass, as in Ex. 18-5. (This also allows the seventh to be prepared in the same voice in the previous chord, thus introducing the dissonance smoothly.)

in

Ex.

18-5.

R.

to this chord. It

Strauss: " Breit ijber mein Haupt."

(

7th prepared

)

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

296

One

Ve

chord" between two tonic triads often the two outer voices move in contrary motion in and out of the of the most frequent uses of

is

as a "neighboring

;

tritone as in Ex. 18-6.

18-6. Tschaikovsky

Ex.

:

Violin Concerto,

P

^ra

I.

i

3=«

f

^

^^

^

Occasionally

one or more of beat of the

last

Ve

does not

its

members

move

J

J

V8

I

J

directly to the chord of resolution but suspends

as in Ex. 18-7.

The chord change

is still

measure, but the resolution of the individual voices

on the is

first

staggered

rather than simultaneous.

18-7.

Ex.

Haydn: Quartet Op.

54, No. 2,

II.

m r^^ f « t^ ^

i

rr^

nrr ^^ ^

^^

J

^

==j

vS

When

the leading tone

ticularly strong

emphasis

less

common

Ex.

18-8. Bruckner:

is is

approached by leap from above, placed upon

its

Skip to

l.t.

7,

II.

it is

i'

as in Ex. 18-8, a par-

resolution. This type of

than the preceding examples, but

Symphony No.

(i)

extremely

approach

effective.

is

297

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

An Ve is

obvious exception to the upward resolution of the leading tone occurs followed by V7. In this case the bass note

then resolves instead of resolving directly. This tion, since there has

moves down is

to the

when

dominant and

not actually an irregular resolu-

been no change of harmony; the resolution

is

merely delayed.

^ ^m ^m ^^^ Delayed resolution of Vb chord.

18-9.

Ex.

=i

$ ^

j=^

i-

^

V|

(V?)

T

The V4 Chord 3

The

We

\'^4

is

least frequent of the inversions of the

perhaps the

shall see, in later chapters, that the

common of V4

is

as

dt.

I

passing chord

V|I6V4

Some unusual

We

second inversion in general

and seventh chords. One of the most between I and Ig (and vice versa).

position for both triads

18-10. Mozart: Quintet, K. 516,

Ex.

dominant seventh. is

the least

typical uses

III.

I«

voice-leading procedures appear occasionally in connection with

most circumstances composers have chosen to resolve the 7th downward by step. When resolving V4, however, this procedure often has been abandoned in favor of a stepwise upward resolution, as in Ex. 18-11. This produces

V4.

have seen that

in

a resolution of the tritone in similar motion, which sequential melodic pattern precludes the

more usual

is

seldom found. Here the

resolution.

298

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

Schumann: Piano Concerto, Op.

18-11.

Ex.

^

54,

d5 to

^UJ

'h

F

Ur

p5

i

pt.45

31 t" In both Ex. 18-10 and Ex. 18-11 note that the (the root of the

V chord)

is

common

tone between

kept in the same inner voice; this feature

is

V| and

I

character-

of this progression, although

it is not always present. In Ex. 18-12 a different use of V| occurs. Here it is the concluding chord in an unusual type of half cadence (iii -Vl).

istic

—

Ex.

18-12.

Haydn: Quartet, Op.

64, No. 4,

I.

The V^ Chord In our discussion of V^, the third inversion of the dominant seventh,

we

will note

four types of preparation of the seventh. In resolving this chord the presence of the

seventh in the bass virtually dictates that the chord of resolution be sonority that allows for the step resolution of the seventh. In this carries out

its

strong melodic tendency. There are no other

V| its resolution the manner in which of

;

is

We may now

extremely stereotyped.

the chord

is

way

Ig

or another

the bass line

common

treatments

turn our attention to

approached.

Ex. 18-13 illustrates one of the most frequent seventh preparations: from below

melodic context the seventh appears to be treated like an upper neighboring tone. For this reason, when the chord seventh is approached stepwise

by

step.

In

this

from below and resolves boring tone figure."

to the

same

The melodic

particularly noteworthy.

tone,

it is

said to be prepared

interest of the

middle parts

in

by the "neighthis example is

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

Ex.

18-13. Brahms:

Symphony No.

3,

299

I.

±=^ ^^ m 4 aj=^ ^ .B^^ s ^E^ ^^ tfr

r

r

tfr

r

v|

I«

r

16

Another frequent type of preparation occurs when the seventh is approached by leap from below in Ex. 18-14 from the tonic. The seventh here takes on the character of the leaning tone, since it is approached by leap and resolved by step.

—

Ex.

18-14. Beethoven: Coriolan Overture.

W^

z:

mnv 1^^ mrm r=T^ V

.^

r

i

*

Still

?

^ ^

another approach to

V^

is

^

rnfm rr"^ 16

2

illustrated in Ex. 18-15.

treated as a suspension, prepared

The seventh

here

is

by the bass note of the preceding chord. In this way the dissonance of the seventh is subtly and smoothly introduced. Obviously the chord of preparation must contain the fourth scale degree in the bass if this type of preparation

Ex.

18-15. Pachelbel:

is

used.

An Wasserflussen Babylon.

—

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

300

The

fourth type of preparation

passing tone between

V and Ig, as

by step from above. Here the seventh acts as a illustrated in Ex. 18-16. In this example a further is

exception to the usual resolution procedure of the V7 occurs.

The seventh

ferred to another voice (in this case the bass line) before resolving. Since

of chord occurs, the listener

18-16.

Ex.

Wagner:

Lohengrin,

"Ha!

no change

Dieser Stolz."

^m

i-^-i

^

trans-

not conscious of an unresolved dissonance.

is

s

m^

is

u f=

V7

A characteristic feature of the

18

^ 2

resolution of the

V|

is

the

upward leap of a

perfect

fourth in one of the upper voices, usually the highest.

18-17. Beethoven: Piano Sonata, Op.

Ex.

^^ f Til 'y-^\

(^

13,

III.

32

t

ciP^

=^

i

I I*

—

—

We

have noted three ways other than downward by step in which the seventh when it actually resolves upward as in of the V7 or one of its inversions resolves the resolution of V^ (see Ex. 11); (2) when the resolution is delayed by some type of suspension pattern (see Ex. 18-7) and (3) when it is transferred to another voice :

( 1 )

;

(see

Ex. 18-16).

another exception to the usual resolution occurs when the resolution is ornamental. The upper line of Ex. 18-18 leaps away from the seventh to a leaning Still

tone E-sharp on the resolution tone

first

beat of the next measure before returning to the expected

F-sharp. This

procedure

a decoration of the predictable resolution.

is

similar to No. 3 in that

it

is

merely

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM 18-18. Beethoven: Quartet

Ex.

Op.

18,

No.

3,

301

I.

V|

The

viifi

Chord

The diminished

triad

on the leading tone bears a marked resemblance

to the

dominant seventh chord, since all of its members are also members ofV,. Walter Piston and others have argued that it is actually a dominant chord, and that its root is missing (this root would be the dominant). One cannot deny the similarities between vii° and V,, but we must regard this triad as a separate chord in its own right. As discussed in Chapter 14, we shall regard the lowest member of this chord as

prime, for the sonority does not possess a root.

its

Like most diminished triads,

The

first.

chord.

Ex.

A

bass thus

is

not a

member

^^ J y-¥^ i

f viie

18

A Major,

is

in

any inversion other than

shown

in Ex. 18-19.

I.

m

i

T

:

I

in

appears

of the prominent tritone that characterizes this

typical progression involving viig

18-19. Brahms: Violin Sonata

M:tf

vii° rar ely

P

—

-(•

(•-

-^

302

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

This chord

The obvious

is

used frequently as a passing chord between

I

and

Ig in

Ex. 18-19.

between vii| and V^ account for their frequent interchangeability. Their sound is virtually identical, creating an aural problem in distinguishing the one from the other. In most contexts viig and V| are equally similarities

appropriate, for they create the

same aural expectations.

Ex. 18-20 and Ex. 18-21 illustrate customary doubling practices in the vii|. These procedures, however, apply equally to any diminished triads, \ yhen either r oot or third is in the

one

member

that

soprano, composers have^preferred to double the thirdj^lhe

not a part of the tritone)

is

customarily doubled

when

it is

.

The

fifth

of the chord, ho wever,

is

in the soprano. Obviously, melodic considerations

caiTprecIude one or the other of these procedures.

Ex.

18-20. Pachelbel: Aus iiefer Not.

m

s

^

r

1 r

I

i

r vns

Ex.

18-21. Buxtehude

Herzlieh fhut mich ver/ongen.

:

S^

S -J

^^ r

r V*

In writing the

;-;J

i •s

XT

r

16

vii|,

particular care should be taken not to double the chord's

— the leading tone —

mentioned many times in previous chapters. Despite the similarities between the vii° triad and the various inversions of V,, composers have preferred to use the dominant seventh in all but one inversion. Ex. 18-22 illustrates the various possibilities and the general preference. Surprisingly prime

for reasons

INVERSIONS OF THE DOMINANT SEVENTH

;

HARMONIC RHYTHM

enough, there are very few exceptions

Ex.

18-22.

Comparison

r

dominant seventh and

vii°

inversions.

s

s

331

=8=

Preferred to

Preferred to

-elOI

icn

n

n

v1

Vii°6

Harmonic Rhythm

— Further

selecting the roots their function.

V|

VM"

movement

more is involved than merely of each chord and placing them within the key to determine

This process

is

of a piece,

important, but

it

does not consider the relative rate

of speed with which the harmony changes. Since as well as the

vir

Study

In studying the harmonic

harmonic aspect of music,

can be defined simply as the

It

seems hkely that the

vii^

i

-I

m

of

vii°

f

or

to these conclusions. It

was a decisive factor, as well as the greater of the chord when the dominant tone is present.

exposed tritone in both functional stability

and

303

rate

it is

this factor involves the

aptly called the

temporal

"harmonic rhythm."

of harmonic change.

The

next two examples represent diifereni stages in the harmonic rhythm from the same movement. In Ex. 18-23 the rate of change is extremely slow, since the

same

basic chord structure

adagio tempo. Ex. 18-24

changes occurring

Ex.

is

— the tonic triad —

in

is

prolonged

complete contrast to

much more

this

for

4^ measures in an

with perceptible harmonic

rapidly.

18-23. Brahms: Violin Concerto,

II.

16

V

304

INVERSIONS OF THE DOMINANT SEVENTH, HARMONIC RHYTHM

Ex.

18-24. Brahms: Violin Concerto,

Ex.

18-25. Harmonic reduction of Ex. 20-24 (solo line omitted).

'P

^j

^

^ h^/1

(

W

^

'1

• I

|

,j

,H

II.

^ Brahms

an accelerated harmonic rhythm to heighten the intensity and excitement, along with the increased rhythmic activity of the various voices and the dynamic crescendo. All three elements combine to propel the music toward the climax. These examples also demonstrate the extremes of variability in harmonic rhythm that can occur within a single composition. Further study of this movement from the score will prove valuable. Such a harmonic simplification is helpful in plotting the harmonic rhythm of complex passages. The reader should practice making similar reductions from other examples in this chapter. Examples can be found of compositions which demonstrate even faster and slower harmonic rhythms than those of Ex. 18-23 and Ex. 18-24. When a single underlying chord is prolonged for an extended period of time, harmonic rhythm as such ceases to exist. The harmonic flow is static. On the other hand, when the harmonic rhythm becomes as rapid as in Ex. 18-26, the harmonic changes may cease to be separately audible. This can produce the effect of a harmonic "blur" in which the separate chords are used not as "functional" progression but as passing chords. It is often possible, as is the case here, to detect a simple harmonic background in this rapid shifting of chords. In

this latter

passage (Ex. 18-25)

uses

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

Ex.

18-26. Reger

:

305

Kyrie e/eison.

Molto agitato

A common rate of change tions in

Ex.

moderate

18-27. Viotti

^i

:

illustrated in Ex. 18-27

which

is

typical of composi-

tempi.

Violin

Concerto

in

^m J-i

/7S

d

F^

z:

Tempo

is

of performance

enters into the problem

is

A Minor,

I.

^^ ^ TTTr

m^ ^

i rr

ri

always an important factor in harmonic rhythm.

It

two ways: harmonic structures that would be tempo must be considered as basic units a slower tempo. If, for example, the harmonic changes

in at least

dismissed as "passing chords" at a rapid in the

harmonic scheme

at

of Ex. 18-26 occurred in

still

slower tempo or in longer note values, their effect

would be considerably different, and their harmonic separation as individual chords would be more apparent to the listener. Tempo can also influence the rate of harmonic change in another way: extremely slow tempi often seem to demand a faster harmonic rhythm than faster tempi in order to sustain the motion of the music. Conversely, fast tempi often necessitate

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

306

a slower harmonic rhythm so that the separate chord changes will remain distinct say nothing of the convenience to the performer). Thus harmonic rhythm

(to

creates

The

an analytical problem use of pedal point

rhvthm. Not onlv does

its

for the listener

and a practical one for the composer.

when

a further consideration

is

studying harmonic

use render the inversion of a chord meaninarless, but

it

can also "camouflage" the harmonic rhythm. Our ears depend upon the bass so much in identifying a harmonic progression, that the basic harmonic framework is

obscured

Requiem

is

when

a pedal

is

present.

The "pedal fugue"

of Brahms'

A

German

a prime example. This composition employs a rich and varied harmonic

—

however, over a tonic pedal sustained throughout the movement by the bass instruments. The beginning of this movement is quoted in Ex. 18-28.

vocabulary

Ex.

all,

18-28. Brahms:

A German Requiem.

I Tenors

prJpr

ulTjf

When

the predominant harmonic

established, one

may draw some

rhythm of a particular composition has been

conclusions regarding

its

use as a creative techni-

We

have already seen that an increase in the rate of harmonic change can be used to produce a crescendo of harmonic activity as effective as a dynamicor textural crescendo. It is not surprising to note that the speed of harmonic rhyth in rn ost que.

m

when

compositions increases 18-31

and Ex.

18-32, each

ap>proaching a cadence, Ex. 18-29, Ex. 18-30, Ex.

from a different era of music

history,

demonstrate

this

technique. Ex. 18-29 and Ex. 18-31 illustrate a cross-section of harmonic rhythm

from

interior passages in the respective compositions. Ex.

reveal a faster rate of harmonic

Ex.

18-29.

J.

G. Walther

:

rhvthm

Concerto

in

at cadences in the

18-30 and Ex. 18-32

same movements.

B Minor (interior).

^^

^

307

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

Ex.

18-30.

G. Walther

J.

^m fc^

i

Concerto

:

^ T ^ rr

^^^=^

^y- ^-^

aa pT^

p

.VT

18-31. Franck

V

•

:

Symphony

f

J

L.

Symphony

in

D Minor,

^i^

I

^

n.

'

L

^m J

U

(cadence).

^^

iiJ (!

(interior).

P^

121

18-32. Franck:

)-ll|i

I

i

J

Ex.

r

D Minor,

in

1 f

,V7-

IV

^^

Ex.

B Minor (cadence

in

taz

J

J.J

^

^

.

h
L

We

can make other observations about the use of harmonic rhythm as a determinant of musical form. Its rate is noticeably faster in formal sections that are developmental rather than expository. Likewise, sections that display an uncertain or unstable tonality often

make

use of a relatively rapid harmonic rhythm.

A

com-

poser frequently differentiates between his thematic materials in a composition

by

setting

them

in differing rates of

harmonic motion.

In contrast to these procedures, a composer often chooses a slow harmonic rhythm for sections in which a theme is stated as a whole or in which a single key

emphasized. Obviously

harmonic changes are relatively slow. Thus harmonic rhythm can be an agent of form in music and can influence both thematic and tonal aspects. is

it is

easier to reinforce a tonality if the

:

308

INVERSIONS OF THE DOMINANT SEVENTH; HARMONIC RHYTHM

Melodic motion is another element that can influence or be influenced by harmonic rhythm. When the melodic element is prominent or very active in a composition, a slower harmonic rhythm is often present. The reasons for this are clear: a too rapid harmonic change would obscure the melodic patterns and might inhibit the choice of melodic tones. Conversely, sections in a fast harmonic rhythm rarely display a strong melodic element. These problems emphasize the fact that melodic and harmonic interest within a single section are rarely of equal significance; one or the other usually predominates. Exercises

For more detailed assignments see Materials and 1.

Structure of

Music

I,

Workbook, Chapter 20.

In textures of four parts, resolve various root pxjsition and inverted versions of dominant sevenths to appropriate versions of the tonic chord.

from music several passages that contain examples of dominant seventh chords and inverted. Study these, noting chord of resolution and melodicmotion of resolution in each voice. If the texture in question has less than four voices, what chord member has been omitted? If more than four voices, what member has been doubled?

2. Select

in root position

3.

4.

5.

6.

Write an original passage of three phrases in which the two interior cadences occur on inversions of the dominant seventh chord. Examine the harmonic rhythm of Beethoven's Sonata for Piano, Op. 2 no. 2, Scherzo and Trio. What (if any) differences exist in the harmonic rhythms of the Scherzo and its Trio? Do the harmonic changes coincide with the metric accents throughout? Compare measures 1-4 and 17-20 of the Trio. Does harmonic rhythm differ? Practice playing \^, \"|, \\, in both major and minor keys. Play in four voices with any member in the soprano, then resolve with appropriate voice motion to the tonic chord.

To

the two-chord progressions of (5) above,

possible to precede the a.

7.

dominant chord with one of

b.

Suspension

c.

Neighboring tone

d.

Leaning tone

Using the following progression

^

Make up

9.

it

the following figures:

Passing tone

erties that arpeggiates the

8.

add a preparaton,- chord which makes

3

is

iv/i6/

as a guide, improvise a

melody of simple rhythmic prop-

given chords

V^

/i

similar progressions in major

and minor keys

for the

same

practice.

Continue the aural practice suggested in recent chapters, concentrating upon recognition of the dominant se\enth chord in root and inverted positions. Learn to identify these both as isolated sonorities and within progressions. Melodies for sight singing and melodic dictation should incorjKtrate the outlined Y. chord.

10

and hearing of intervals, concentrating on dominant seventh chord.

Drill in the spelling, writing,

in the

relations

found

Second-Inversion Triad

The

19

I

student of music literature will notice that triads appear

often in second inversion than in either root position or

first

inversion.

and

first

inversion contain at least one

probable

major and minor cadential consonance

reason for this exists in the intervallic structure of the chord triads in root position

A

less

:

between the bass and upper parts (specifically, root position contains both a perfect fifth and a third; first-inversion triads contain a third and one decorative consonance a sixth). Only the second inversion contains no cadential consonances above the bass; it is constructed entirely of decorative consonances (the sixth and

—

the perfect fourth).

The

Hence

it is

a

less stable sonority.

perfect fourth, in particular, sets this inversion apart.

treated as an unstable interval throughout

much

has not been used above the bass without

some

The

fourth has been

of music history

and normally

special treatment to cushion

its

by step motion, resolution as a suspension, etc.). Whatever the reasons behind this practice, we find relatively few second-inversion triads in contrast to a profusion of root position and first-inversion sonorities. When second inversions are used, they are generally the product of non-chord tones. The three uses of six-four chords we will examine are the "cadential" sixfour (I5), the "passing" six-fours (V| and I^), and the "embellishing" six-four effect (introduction

(IVS).

The Cadential

By

1^

most frequent use of any second-inversion triad is as a preparation for an authentic cadence; hence the label "cadential." In this context the tonic is the only chord found in the ^ position. Its approach and resolution demonstrate the restrictions composers have placed upon its use. This harmonic cliche is illustrated far the

in Ex. 19-1.

309

SECOND-INVERSION TRIADS

310

19-1.

Ex.

Mozart:

This example of tones: the tone.

To

E

Sonata

Violin

in

Minor, K. 304,

E

can easily be interpreted as a combination of non-chord suspended from the previous chord and the G an accented passing

continue

i^

of reasoning

this line

merely an embellished

\^,

Examples such

have led

as this

However, not

The

is

— — \'

harmonic progression is from ivg some musicians to deny that this usage of the

i.

six-

all.

examples of the cadential

all

logically conclude that this

I| are as easily explained.

Ex. 19-1

though, the salient features found in virtually every occurrence of the

cadential I^. six-four

we could

that the "real"

four chord produces a tonic function at

illustrates,

I.

One

of the most significant of these

is

the metrical placement of the

— usually on a strong beat, resolving immediately

to \'

on the next beat.

and the fourth generally resolve, as they do here, down by step to the nearest tones of V. Another chracteristic is the doubling of the bass note (the dominant) in another part. These same features are notes that form the intervals of the sixth

present in Ex.

Ex.

19-2.

2.

Haydn: Quartet Op-

^

•?—

9,

No.

Menuet.

2,

3

rnsT^pi

J:

P

^m

r-

rfy

J

£

i

*

2

i

16

15

f= V

^

i

^ r

This example also demonstrates the metrical placement of the Since the resolution

is

directly to

measure), I^ often occurs on beat

V

I^ in triple meters.

(found customarily on the third beat of the

can be found on the first beat as well. in an unusually thick texture of six voices.

2. It

Ex. 19-3 illustrates the cadential

i^

This example should be analyzed carefully to determine whether the same princi-

"

SECOND-INVERSION TRIADS

377

and melodic motion apply under conditions of greater textural Aside from this, however, the characteristic features of our previous exam-

pies of doubling

density. ples

Ex.

may

Bach: Six-voice Ricercar, "The Musical Offering.

19-3.

K

ft''

>

!

be seen.

» »

^ t

J

i

J-

njz

^ r

i|

r rft=g

[^^^

i=a

#

ffi

r

12

more homophonic texture. The high registers used strings, and tenor soloist) increase the effect of the

Ex. 19-4 illustrates the If in a

example (in the flute, progression and emphasize the ethereal mood suggested by the

in this

Ex.

19-4. Berlioz:

text.

Requiem Mass, Sonctus.

m^ n

-

a

P

tu

a

-

f m glo

^^ ri

-

a,

glo

-

l7\

»

ri

-

a

I

g tu

-

iea= Vr-

=5^

z^

S

v The

previous examples have illustrated the standard resolution from \\ to V. Ex. 19-5 contains an unusual treatment of \% in which it occurs at the culmination of a prolonged pedal point on the dominant, (during which there are several other

and

examples of

l\),

the parts

also interesting: the

parts.

A

is

resolves to

further unusual feature

the choral

and orchestral

parts.

I

without

first

proceeding

V. The voicing of

to

dominant pedal appears only is

in the orchestral

the complete absence of leading tones in both

:

312

Ex.

SECOND-INVERSION TRIADS Beethoven: Missa Solemnis, Kyrie.

19-5.

Soprano Alto

Tenor Bass

Orchestra<

n

i

^^

i^i

V

n The

following

summary

n of the characteristics of the cadential I| should be

helpful 1.

Usually occurs in a strong metric location.

2.

Has

3.

Resolves to \' or \\.

4.

The bass is doubled in an upper part in a texture of four or more parts. The upper voices, other than the doubled note, usually resolve down by step.

5.

the

dominant tone

in the bass.

Passing Six-four Chords

The second-inversion

triad

is

sometimes formed

as a link

between two more basic

chords (basic because of their duration, metric location, or other factors) or in extended examples of similar motion. In cases such as this, as in Ex. 19-6, the entire sonority

chord.

It

however,

is

may

frequently of very short duration. In plotting the harmonic rhythm,

it is

19-6.

Stamitz

^ ^ i

r

harmonic unit has been formed. chords are found on the tonic and, less frequently, on the dominant.

helpful to recognize that a separate

Passing six-four

Ex.

be viewed as an aggregate of non-chord tones or as a decorative

:

Sinfonia

r

in

E-flat

Major.

^^

fe

IS

iv«

i|

i

rr

*—H^

# f

313

SECOND-INVERSION TRIADS Ex. 19-7 also illustrates a typical passing

I5.

chords, passing six-fours occur most frequently in

In contrast to cadential six-four

"weak"

(metrically unaccented)

locations.

19-7. Corelli

Ex.

m ^

Ex. 19-8

6 4

6

is

less

No.

6,

11,

"

Sarabande."

^

^ 6

6

obvious because of the presence of

but the passing six-four

19-8.

Ex.

^^

Concerto Grojso, Op.

4^£U 5

tones,

:

is

similar in

Handel: Concerto Grosso, Op.

all

No.

6,

many

accented non-chord

other respects to the earlier examples.

4.

^ff?^-n^ Mm^m W LJ

rij^ls

n ^ n n ^s

^

6

rj;

c-'r

cj-

6

It

6

6

a

r p

7

6

4

Examples of V^ used

in passing are rare.

V^ appears

The

following, however, illustrate the

from Ig to I or vice versa. In most similar circumstances composers prefer harmonizing the ascending second scale degree with V^ or viig. The reader should experiment with these three sonorities to distypical procedure:

cover their relative tonal

in passing

effects.

justify detailed conclusions

Examples of V^ are not numerous enough

about their doubling,

etc.,

but the general melodic

principles governing the use of six-four chords usually apply effectively.

Ex.

19-9.

Haydn: Quartet, Op.

m 9^

p

r

74, No. 3,

III.

r

r V6

4

to

^

3M

SECOND-INVERSION TRIADS 19-10. Beethoven: Piano Sonata,

Ex.

Op.

2,

No.

3.

m^^^^^ ^^^ ^^ ^

^

s^

V|

l«

Embellishing Six-four Chords

A

an "embellishing" chord, or, described from a melodic viewpoint, as a double neighboring tone grouped over a stationary bass tone. In this context IV| is the only chord that appears with any frequency. As in the final cadence of Ex. 19-1 1, it is used to prolong the final tonic third frequent type of six-four treatment

is

as

chord.

Ex.

19-11. Embellishing Six-four chord.

16

I\'

Numerous examples

many

vflS

I

(lV|)

I

of IV^ can be found in works from the Classical period. In

of these the chord occurs virtually at the beginning of the movement, as in

Ex. 19-12. In this context

it

helps to focus attention on the tonic note

tends to establish solidly the key of the movement. In an obvious sense, as a

functions

pedal figure on the tonic pitch.

1^ ^ ^^ Ex.

it

and thus

19-12.

Haydn: Symphony No.

g rr^

m

iv»

102, IV.

U

M1

,

;

SECOND-INVERSION TRIADS

A

similar, yet

measure

example appears in Ex. 19-13. The IV5 occurs measure and again in a more prominent and extended role in

more

briefly in the first

315

elaborate,

three.

m ^

Ex.

19-13. Cannabich

:

Sinfonia

in

Major,

B-flat

II.

w

fei

r^

r

m^k^

^ fe:

Other Uses of Six-four Chords

Music thoroughly embedded

major-minor tonal system has sometimes used the suspenseful effect of the I^ as a preparation for the c adenza in instrumental concertos. The orchestral interlude that precedes the cadenza customarily ends with a I^ sustained by a fermata, as in Ex. 19-14.

Ex.

in the

19-14. Beethoven: Piano Concerto No. 4,

$Sr ^—n-l

')-it

v

I.

CN

^

(O

h 2:

f

f

n r

21

z:

u

+ <SPfl

^i The harmonic progression interrupted by the cadenza is resumed at the end of the cadenza. The soloist usually ends with a trill or some other prolongation of V thjs resolves

some

with the entrance of the orchestra on the

I

chord. There are, of course,

striking exceptions to this procedure,^ but they are in the minority.

The appearance

of six-four chords can be a useful aid in harmonic analysis,

especially in the sometimes difficult

problem of determining the key. Since they

are relatively infrequent, a six-four chord of even a beat's duration usually appears

within a context of tonal stability and often points unmistakably to the dominant of the key. In the absence of other evidence, it seems most logical to interpret an isolated six-four

1

chord as

I^, unless the

Sec Beethoveiis Piano Concerto No.

3, I,

context clearly contradicts this analysis.

bar 481 for a brilliant and unusual exception.

376

S£cond-;nv£rs;on triads

Cadences ending with a six-four chord are not common in music of any period. An unusual example of such a cadence occurs in Ex. 19-15 (the cadence is, of course, an interior one) The cadence appears to be the result of the extended dominant pedal point in measures 4-6. .

Ex.

19-15. Verdi: Aida, " Ritorna Vincitor."

In Ex. 19-16 a six-four chord appears as the structural climax of a section. Al-

though the overall tonality of

this

excerpt

not as clear as eighteenth and nine-

is

teenth century standards would

demand, the relationships between the individual most part, the most traditional of all root relationships chords are, for the the fifth, and the chords are mostly major minor triads. The enharmonic perfect and spelling of the six-four chord {g-sharp — a-flat; d-sharp — e-flat) appears to be for the

—

convenience of the eye in

Ex.

19-16. Bartok

its

organization of the melodic

line.

Concerto for Orchestra. Copyright 1946 by Hawkes by permission of Boosey & Hawkes Inc.

:

& Son

(London)

Ltd. Reprinted

+

sm

^p m i

8^a

i p

m S

i

s

f^

BZZ

i

^m ,

\

mfr

I

't

izg:

¥i

^

t

i

^

toeJ

Vm

=a

In Ex. 19-17, \\

M^^W^ is

ES

z:

again used as a cadential chord;

a surprise after the minor implications of the

"^^m

Q

^

t**-"

B

its

major quality comes as

flats in the

previous measure. Al-

SECOND-INVERSION TRIADS

317

though the chords in this excerpt are more complex than the diatonic triads we have been studying, the cadence on the G major six-four chord clearly confirms

G

as the tonal center.

19-17. Barber: Hermit Songs,

Ex.

"The Desire

^''i>

y

\

,

J^iJBJ-

JM^iiJ-

7

l

^iiJ-

Parallel Six-four

=

J^LW-'J-

^

^

^m

5 ^;

Reprinted by permission

Inc.

fY

fY

W^^

J'JiJ'

m

^m

Hermitage."

for

of the copyright owner, G. Schirmer,

5 -o-

^ ^

Chords

motion in similar sonorities is a favorite device of many late nineteenth century and early twentieth century composers. We find six-four chords used in this manner, along with triads in other inversions and more complex chords. An Parallel

obvious example of

this

technique occurs in Ex. 19-18, in which the motion

is

chromatic.

Ex.

19-18. Debussy: A4ar/oneffes.

^m A

i

different purpose seems to

chords in Ex. 19-19.

The

A

%

have motivated the inclusion of parallel six-four

disjunct character of this excerpt suggests that the melodic

was provided with an accompaniment of six-four chords. The spelling of the individual chords (most of which are major) testifies that they were conceived as line

blocks of sonority rather than as the results of three separate melodic strands.

—

:

378

SECOND-INVERSION TRIADS 19-19. Bloch

Ex.

:

Sche/omo. Reprinted by permission of the copyright owner, G. Schirmer,

Inc.

(Celesta doubled by flutes 8^0 sopra)

j

-i

grj

\

mm^ h wa ^^

.

Renaissance composers sometimes used six-four chords with complete freedom. Ex. 19-20 shows a passage in which the three upper voices form parallel six-four

chords over an intermittent pedal in the lowest voice. As a matter of fact, contrary

motion

entirely absent

is

^

Ex.

19-20. Obrecht

i'

gE^

from

this

excerpt until the final cadence.

Miaa Graecorum.

:

^

^

I'J.'Mi'^ f

jnj

i

e

P

j

j

-

-o-

^ j_^

p

Exercises

For more detailed assignments see Materials and 1.

Structure of

Music

In music of various composers, find several examples of the

I,

Workbook, Chapter 19.

main kinds of second-inver-

sion chords discussed in this chapter {cadential, passing, embellishing). Also find examples

which do not 2.

fit

the definition of these three types.

Write several textural v^ersions based on the cadential pattern shown below. Do these in major and minor keys and in different meters. Write the two-voice outer framework first for three- and four-voice examples. CiQJ^ Progression: IV-IB-V^-I // or iig-ie-V^-I // ^ Write a four-\oice homophonic setting for the following chord progression:

(jr

minor

—

^,,—

:

J i

ij

\j>:>\j

ij'

V

iv«

(b) I-I\-6-I

(a)

ij);)|j

iv«

IV

At the piano, play the following progressions

^

.^

in

VJ

i

iJ>;>iJ iv«

^

ij>j>ij iv|

major and minor keys

IV,-I6_V,-I

I-Ii-Ie Improvise an arpeggiated melody based on a progression such as the following. Be sure that the lowest note of each arpeggio pattern corresponds with the given inversion. Choose keys that make this comfortable for your own voice. Progression:

Sample:

Bp major: lah

I

/IV«

/

Ig

/

\1

/

(C)

Ig

/ I //

319

SECOND-INVERSION TRIADS

Do

6.

and with your major instrument. Ear-training procedures Clontinuc the following drills from previous chapters. a. Recognition of intervals, melodically and harmonically b. Recognition of triad quality, soprano and bass factors c. Harmonic dictation for Roman numeral designation and chord inversion d. Harmonic dictation for Roman numeral designation and one or both of the the

same

exercise at the piano :

outer voices e.

Melodic and rhythmic dictation with continuation of syncopation and increasing complexity of

f.

rhythm

Intensive drill in rhythmic reading

and sight-singing

'O

-

(p,'+.

.

n

.t

1^

(,

Ternary

Form ;

20

The Supertonic

Chord

In music, as in are used, each having

its

all

own

of the arts, various fundamental formal designs

particular characteristics.

musical design depends largely upon the position. In earlier chapters

and unify the smaller

we saw

sections of a

way some

that repetition

melody;

this

is

The comprehension

patterns recur within a is

of

com-

frequently used to unfold

also true of the larger parts of

most formal structures. Formal plans can be understood by the ways in which they incorporate repetition and contrast. One common scheme involv-es a restatement of all or part of an opening section. Simply stated, such musical structures follow the plan of statementcontrast-restatement. The trademark of this particular symmetrical structure is "three parts," two of which are the same or similar. Depending on the length of the total composition, each part contains at least one or more phrases. Frequently the return of material appearing earlier serves to "round off" a composition rather than give the impression of a distinct section of "return." This

practice can be obser\^ed in

many

of Ex. 20-1, the fourth phrase of the second phrase

is

is

folk

melodies and popular songs. In the melody

a slightly altered version of the

minimized

(1)

by the

similarity of

its

first.

The

contrast

rhythmic structure

to

by the use of a transposed version of the cadential pattern of the first phrase, and (3) by the importance assigned to g-sharp and /-sharp in the first two the

first,

(2)

measures of both phrases. Since these similarities exist, the third phrase resembles a bridge that links the first two with the last; it does not have an impact comparable to the beginning portion of the melody.

320

TERNARY FORM; THE SUPERTONIC CHORD Ex. 20-1.

German

^ i,

h

'I

I

Folk

n

321

Song.

^

*•

|¥>.r]j. ^iiij:pr

,


^

5

-)j

i

j^

*:*

i

II

2.

ii

j

rjj-JiJjj.

j,^

^f r^^- I

t.

|

As

is

often the case in melodies of this type, the third

balance the

first

and fourth phrases actually

two. Thus, even though the principle of return

is

present, the

two equal parts, a ba A similar design is the basis for Ex. 20-2. However, the interrelationships we observed in Ex. 20-1 are not as immediately evident because the element of contrast is more striking. For example, the phrase that begins on the second beat of measure 8 brings into play a new rhythm, a wider range, and a change in overall pitch direction, as well as a change in the established phrase lengths (four beats instead of eight). However, the accented non-chord tones that appear on the first beat of nearly every measure are retained, as are the basic accompanimental figure and the upbeat beginnings of each phrase. formal design that results

Ex.

20-2. Beethoven:

is

divisible into

Piano Sonata, Op.

^ .^ ^ ^M m ^

0-0-0-

f^P

F \

||.

"Rondo."

-#

f •

•

ife *=#

||

n-nm

f

f

7,

:

Y

r>rr ^

m

f

f f

m

f=t

f 0-M

322

TERNARY FORM, THE SUPERTONIC CHORD

Ex. 20-2. continued.

^^m ^1^ a s

m A The a

I

^^

a ^

^-0^

?-r¥

1||«

1V ^

|>

^

5

•

two-part design that incorporates a restatement of earlier material in

second part this

^

«_^

^Ek

p-*^ 5

is

the embryonic stage of ternary form. As the

name

ternary impliesT"

formal plan involves three distinct sections, instead of the two discussed third section frequently

literal

restatement,

is

a

full

earlier.

restatement of the opening section, or

distinctly separated

it is

its

if

not

from the contrasting middle section. length, and the contrasting material

Each of the three parts is more or less equal in is more than a mere bridge, linking statement with restatement. In contrast

to the

similar two-part design with restatement, the middle section in ternary form fre-

quently impresses

us, as

the initial section. This several phrases are

is

a definite and separate musical unit, as strongly as does particularly true

combined

to

when we

produce each

listen to

compositions in which

section.

Ex. 20-3 displays clearly this division into three parts.

The change

of

rhythm

measure 9 gives the impression of a change of tempo, even though this need not be the case. Furthermore, the elaborately "decorated" melody of the second section adds to the contrast, counterbalancing the emphasis given to the rhythmic at

motive (J

Ex. 20-3.

J

J

Schumann

)

of the

first.

:

Album

for fhe

Young.

a.

1.

m frm Itm

^ ^W^^

r»

IQ

^ W

TERNARY FORM; THE SUPERTONIC CHORD

323 i\

v^-^

ji ijgrr^fl"l-^>

k

^^^^^^ ^^ r

I

^

f

^

r

T^

eS

J

i

iafr

^ rJ-'V>

^^ U ,

f'^j

"J

iij

r=r^

iij

i

z:

^

^Pl

jj^

r

i

7

S^ i^^

^

t^

^antfrt jr

|.

p-^r?

:P

I*

ss — —;a^-fi;

U

]t=«

•g iS g ^

^

(

^

n

ff

I

Even though the increased activity in measure 9 is immediately apparent, other factors work hand in hand to produce contrast. The entire composition is in D, but the section beginning at measure 9

produces a significant

major instead of ^ minor. This mutation contrast with the opening section. Since D major is associated

only with the second section,

it is

is

in Z)

another factor that delineates the form

when

the

measure 17. Furthermore, the upper part in measures 9-16 uses a larger range than the preceding, and is characterized by triadic outlining. In this instance the opening accompanimental figure is used in each section (with some modifications), as in measures 9 and 17. initial tonality returns in

The

restatement (measures

varied by changing the register (measures 17-20) and by doubling the melody in octaves (measures 21-24). This heightens the effectiveness of the return by avoiding the monotony of a literal restatement. Frequently, however, the third section of a ternary form is a literal repetition of the

first.

If this

is

1

7-24)

is

the case, the restatement need not be written out.

On

the con-

324 trary,

TERNARY FORM; THE SUPERTONIC CHORD it is

often indicated

by da

capo {D. C.)^ at the

times the indication Dal segno {D. S.)^ in Ex. 20-4. This

means

is

found at

end of the second section. Somethe end of the second section, as

that the repetition begins at

"the sign" appears) rather than at the beginning. thing like the following:

Even though Ex. 20-4

ABA.

some indicated point (where

The

sign usually looks some-

.^* is

longer than Ex. 20-3,

its

formal design

is

the

same

basic

Similar relationships delineate the larger sections, but there are notable

For example, two distinctive accompanimental patterns are used in the Chopin. The first, measures 1-16, is distinguished by a durational accent on the second beat in the inner parts, nullifying the upbeat pattern of the lowest part. differences.

In the second section, measures

1

7-33, the

pattern, as well as a change in the

rhythm

rhythm

is

distinguished by a

of the melody.

And

downbeat

as a final confirma-

between the two sections is achieved by modulaa new tonal center. In Ex. 20-3 tonal contrast was produced by mutation.

tion of sectioning, tonal contrast tion to

Ex. 20-4.

Chopin: Mazurka, Op. 33, No.

2.

m

^ u-

^

^^ ^ r

rr

^ r

^

^

Repeat from the beginning, or "from the head." Repeat "from the sign."

^ r

f

— TERNARY FORM; THE SUPERTONIC CHORD

M m ^m ^^ f

^h ^ ^

r^,i

\

^^ ^^

jj

r

r

^ ^s Skt

f^

fei^r

m

^S

t

f

r

^P T^

st^^^^

^&

=fe

S^^

^ ?g

t tt

P

m

*

I

J

P^ vo

*"^

^

i»—(^

?

^I

fct

Fine

^

^=«

ai^za:

^Itrr^

i ?i

^

r

r

si i ^ g^ ^

i

i

P

r

r

> J^ji

i-

rr

Ij-j

325

5

4

mis i

3 1»

fe

a:«

•VJ

••

^

#

f

I

Pii^

a^^ja

2-

i

^

ai

m r D.5. a/ Ftne

Another factor is present in Ex. 20-4 that tends to overshadow the other formal elements as a determinant of form. This is the change of texture. The overall texture of both the Schumann and the Chopin examples is homophonic.

We

noted

in Ex. 20-3 that the pitch

range increased in the second section.

This increase alters the texture slightly by changing the space between the melody and its accompaniment. In Ex. 20-4 the textural change in measure 18 is more pronounced because the accompaniment changes character and is moved to a different register.

The number

of parts

is

essentially the

same, but spacing starkly

326

TERNARY FORM; THE SUPERTONIC CHORD

distinguishes the textural "top" from "bottom." thirds (measure 24

Our

and following) represents

The motion

still

in parallel sixths

and

another change of texture.

discussion has emphasized the overall plan of ternary design, as well as

some of the

demarcate or produce contrast between the sectional parts of the total form. As a matter of fact, it is very difficult to describe a piece of music without taking into consideration both the structural plan and the smaller factors that fill out this plan. Generally speaking, many compositions have a ternary structural design, just as many buildings are basically rectangles. However, we know that architects have adapted the rectangular structural principle to many factors that

different situations,

and

similarly, the ternary principle of statement, contrast,

and return has been used

A

many

in

quite different compositions.

cursory examination of Ex. 20-3 and Ex. 20-4 reveals in both cases a basic

ternary plan, but a closer look at the structure of each section shows that the processes of unfolding are not the

same

in both pieces.

Thematic material,

tonality,

rhythm, and total length are obvious differences. Another difference is the way each section closes and connects with the restatement. The B section of Ex. 20-3 closes with a half cadence that is combined with a definite rhythmic halt.

The

listener's

demand

for

a return to the beginning prob-

ably results from the instability of the half cadence and the extreme rhythmic

end of the contrasting section is not signaled as boldly because the rhythmic activity in the upper parts continues through to the beginning of the restatement. The two sections merge (elide), and it is not until the return is in progress that we become aware of it. Even though other points of comparison and contrast have not been touched, the reader should examine and compare other design factors of the two contrasting sections. In summary, ternary design consists of three distinct sections: statementzrzcmz^ trast restatement Each section may follow a particular formal pattern of its own^ and each section usually has a different tonality. The statement frequently closes with a terminal cadence, as does the contrasting section. Sometimes the contrasting section closes with a progressive cadence or merges with the restatement. That is, finality is avoided at this point to enhance further the cons equent retu rn to ateriaL_ of an earlier statement. contrast. In Ex. 20-4 the

—

.

m

The Supertonic Chord In Chapter 14 we learned that triads can appear on any scale degree. also seen in previous chapters that the triads

on the

first,

and fifth scale are major triads. In

V

e.g.,

this sense these three triads

confirm the scale basis of a composition.

triads of the

major keys,

harmonic spectrum can be

I,

IV, and

identified initially

have

fourth,

degrees delineate the mode,

in

We

by

The

their quality

other

(i.e.

as

—

327

TERNARY FORM; THE SUPERTONIC CHORD

major, minor,

Our

etc.).

In

this

chapter

we

discussion will focus primarily

though

The triads

use

its

is

one of these, the supertonic? appearance in major and minor, even

will discuss only

on

its

not restricted to these two scales.

supertonic triad

is

minor

major key, setting

in a

it

apart from the major

IV, and V. In Ex. 20-5 the second scale degree appears as the bass note

I,

measure 5; it is also the root of the chord. Since G is the tonic of this excerpt, the minor triad on a is supertonic. However, the relationship of the a minor triad to the tonal center is not strongly confirmed until the G major triad is heard in measure 8. Thus, in retrospect, it can be related to G and understood as ii. The ii chord also contains the fourth and sixth scale degrees, so it can be used to in

harmonize either the second, fourth, or sixth

Ex.

20-5. Beethoven

m

:

Piano Concerto No.

Vivace Orchestra

^\

^^

pp

I

n

V

4,

V

J-U

-^

I

f

VfV t Mzza:

^

i*

=E3E ^F=n

Ei

i

£

:•:

•

Ff

P

£

i=5

—w-W

m m 9

^m

i

III.

B

I

&

'

58,

^^ :

^m

Op.

scale degree.

wt

3

h

I <^\ \\

^1 r,

In minor keys the supertonic triad seen that the diminished triad triad, that

its

is

less

is

diminished. In previous chapters

stable than either the

characteristic interval, the diminished

to a smaller interval,

and that the fundamental of this chord

sense.

Supertonic literally

fifth,

means "above

the tonic."

we have

major or the minor is

is

a

generally resolved root in

only a broad

328

TERNARY FORM; THE SUPERTONIC CHORD

In Ex. 20-6, the lowest note, the prime, of the chord

is

doubled

after the resolution

—

of the leaning tone g in the soprano voice. The diminished fifth {/-sharp c) moves to an octave (B b) in similar motion, making clear that /-sharp is in fifth relation

—

with the root This

is

b.

The

characteristic resolution pattern of this interval

minor when the

often true in

ii°

functions in the

in major, in root relation of a fifth with the

Ex.

Loewe

20-6. Carl

The second is

:

Der Pilgrim vor

scale degree

is

Si.

Just.

same way

is

not used.

as the

ii

chord

dominant chord.

Op. 99, No.

3.

frequently the root of a major triad. Because a tritone

created between the third of this chord and tonic, a major triad on the super-

tonic has a different relation to tonic than

its

unaltered counterpart. Therefore, its

often magnified. It will be discussed in detail in Chapter 24.

structural role

is

Ex. 20-7. Bach

Chorale, Ermufre dich, mein schwacher Ceist.

:

f

^

^ The

^ $ LM i

i^ U f rr L^A

XV^f

T:

difference in sonority quality distinguishes

however,

this

It

ii

(or

ii°)

from

I,

IV, and

V;

does not explain the tonal relationships that can exist between them.

Because of the tones in common,

dominant.

i f

has two tones in

ii

(ii°) is related

common

to

both the subdominant and the

with IV, one tone in

common

with V.

329

TERNARY FORM; THE SUPERTONIC CHORD 20-8. Supertonic chord.

Ex.

m

'

Wr¥^J rd^

C:

^T5th

Sa ?^^ m |

^

c

:

Another strong relationship can be estabHshed between ii and V, because their roots form a fifth relationship. This is the same root relation that exists between V and I. The roots of IV and ii are a third apart, a relationship that is not present between any paired arrangements of I, IV, and V. One important structural role of the supertonic chord arises because it has a tone in common with V and because its root forms a fifth relation with V. Root relations by fifths tend to define harmonic activity, as in the V-I progression. This is also true when ii moves to V. If a half cadence is used to demarcate the end of a section, the use of ii before V emphasizes the harmonic caesura because of the root relationship.

chord frequently appears in an unaccented metric position when it precedes V. Consequently, V is emphasized both by the root relationship and by the rhythmic placement. Both of these factors appear at the end of Ex. 20-9,

The

ii

Ex. 20-9.

Mendelssohn

P^

:

Song Without Words, Op. 85, No.

a

5.

J^

^

• #V

0-0-

*

Ml

m

mum

»#

it

si

m

s

0-0-

^

t^ P

P

IV

In Ex. 20-9,

is

ii

preceded by IV. Thus

each of which has at

V

to

because

Sometimes tivity

it

has

one tone

common

in

V

with

it.

In this sense

ii

can link IV

elements with both. it

precedes V^, but the ac-

of the other parts adds complexities not present in Ex. 20-9. Notice that the

lower two voices

move

the supertonic

doubled rather than the

Ex.

I|

appears between two different chords,

ii

common

rhythmically accented. In Ex. 20-10

is

ii

least

ii

is

20-10. Bach:

m

^^

in contrary

motion

to the

upper two, and that the third of

root.

An Wosserflossen Babylon.

^J

r

n.nj r

r

CJ^

'

ii

r V^

I

330

An

TERNARY FORM; THE SUPERTONIC CHORD

analogous rhythmic formation

exists in

Ex. 20-11. Both

IV and

ii

have the

same duration, and the duration of V is equal to IV and ii combined. Consequently, because of duration and because of being preceded by ii, V is emphasized as the cadential chord.

Ex. 20-11. R. Strauss: Nichfs,

Op.

10,

No.

2.

By permission of the

International

Music

Company, New York.

Vivace

As

its

root position form, the

first

inversion

(iig)

of the supertonic triad frequently

move in part. How-

precedes V. In the three-part illustration (Ex. 20-12), the two lower parts

dominant is reached (measure 3) in the lowest instead of a subdominant root, the fourth scale degree (measure 2) forms the

parallel thirds until the ever,

third of the supertonic chord.

^

TERNARY FORM; THE SUPERTONIC CHORD

Ex.

331

20-12. Mozart: String Quartet, K. 464,

^ ^

^ ^^

^

m

m

i

fct,

P

g'

<

P

IM

II

V7

6

move

In Ex. 20-13 the upper three parts

When move

Ex.

the fourth scale degree appears as in contrary motion, creating a

20-13. Kuhnau

:

iig

motion in measures 1 and 2. bass in measure 2 the upper three voices in similar

chord.

The Baffle Befween David and Goliafh.

m ^ ^^ ^

f

^

.

^

i

f

f

succession

iig

—

k ^

16

iis

The

^ f

—V represents a fusion of the patterns IV—V and —V beii

cause the bass motion up a second

and V, and because the

fifth

is

root relation

is

also present.

In

this sense,

are used interchangeably to harmonize the fourth and sixth scale

precede V. The bass motion up a second iig

instead of

IV

between IV iig and IV degrees, and to

characteristic of the root relation

is

an important melodic

provides the harmonic element of the

factor; the use of

fifth relationship,

while

still

retaining the melodic second of the bass line.

A simple discussion.

experiment can be performed with Ex. 20-14 to bear out the preceding '\\% is used in the realization of the keyboard part; consequently,

Here

a in the violin part (end of measure 4)

is

a passing tone.

332 Ex.

TERNARY FORM; THE SUPERTONIC CHORD 20-14. Corelli: Violin Sonata

i^

\

J

in

C Major,

Lir

i

J

i

^=^

^=# ^f^ rr^

Q

^

p

i

itF IV

If we

frr r .

^N=^

?=T

^

\r

r

i

|

p^

III.

V

11°

would be a passing tone. Either chord could be used. However, iig creates a change in harmonic rhythm that corresponds to measure 3 and supports the drive to the cadence on V. change

Ex. 20-15.

Vln.

ii|

Corelli: Violin

^^ §

i

to iv, b

^ ^

j

Sonata

in

C Major.

ciJ

r

I

^=^

s

rr

s

III.

r

^ ^^

Lf r

* i

f

i

^

9

^r^

i?F=

p

^

V

IV

The occurrence

of

iig (iig)

is

often characterized

by the harmonic

sixth

between

the two outer voices, placing both the root (or prime) of the chord and the fourth scale degree in

prominent

positions. Consequently, instead of the characteristic

harmonic diminished fifth of ii°, an augmented fourth and some other part.

Ex. 20-16.

Brahms: Symphony No.

(rM

4,

is

created between the prime

IV.

SI

^

^

zsb

JV«

i°6

IZ

:a^

ini

i

;.

TERNARY FORM; THE SUPERTONIC CHORD In this excerpt

The

moves

ii|

bass motion in

motion 2

to

i;

333

therefore, the

augmented fourth

measures 2 and 3 outlines 4

—

1,

resolves typically.

supporting an upper voice

— 3. The motion by step in the upper voice balances the motion by skip in

the lower voice.

A

ii|

chord

in a

major context

is

shown

in Ex. 20-17.

The middle

chromatic motion, has considerably more independence than

part, because

minor supertonic had been used. Notice that the augmented fourths in the upper two parts (*) move by similar motion to other augmented fourths. Here it is the descending chromatic pattern of the middle voice rather than the iig that makes the of

its

if

the

diminished supertonic inevitable.

^^ ^ ^ ^ ^m 20-17. Chopin: Mazurka, Op. 7, No.

Ex.

T

^

The it

ii

f

r

2.

rr

f^^T^

SPi ^

r^f

ISZ

^^

¥

chord's relation to the dominant

is

performs. In other contexts the supertonic

one of the important structural is

roles

frequently decorative in character.

That is, it is used for creating linear harmonic motion rather than as a structural harmony in conjunction with V and I. This more decorative function is illustrated vividly in Ex. 20-18.

From measures 2-6

all

The

root

Missa Je ne demande (Smijers

Ed.).

position, unfolding the phrase sequentially.

consequently

Ex.

ii

moves

20-18. Obrecht

This excerpt

:

of the chords that appear are in root

movement

is

down by seconds;

directly to tonic.

noteworthy because the two-voice outer framework is a succession of parallel fifths. This relation is subtly nullified because the upper voice moves down a third before moving in contrary motion to the next harmonic fifth. is

also

Oblique and contrary motion are the prime organizing forces in Ex. 20-19. Beginning in measure 5 the root movement ascends by seconds, leading to I\' in measure 7. Consequently, ii moves to iii (see Chapter 21).

334

TERNARY FORM; THE SUPERTONIC CHORD Brahms: Piano Sonata, Op.

Ex. 20-19.

5,

V.

m

^m

?

^m 5"

A

similar root relation

is

illustrated in Ex. 20-20.

Each of the chords

is

in root

Tonic does not become clearly defined until measure 3. Since ii is used to harmonize the sixth scale degree,/, it moves directly to tonic (*) in measure 1. In measure 2 the harmonic succession ii V is formed by the bass part. However, ii remains in effect in the upper parts. Therefore, the supertonic and the dominant

position.

—

chords merge.

Debussy

Ex. 20-20.

:

Bruyerei. Permission for reprint granted by

copyright owners, and Elkan-Vogel Co.,

^m ^^ ^a

Inc.,

Durand

et

Cie.,

Paris,

Philadelphia, agents.

m^n^

^7^-^: (iii)

u ^7-^^—7-^: ii

f:

=:

^:

I

Root movement by seconds is an important organizational factor in Ex. 22-12, Ex. 22-13, and Ex. 22-14. This type of root activity results in a melodic, rather than a "harmonic," lower part, Lengthy passages of root motion exclusively by seconds can create harmonic instability because none of the successive chords have tones in common. However, other factors, such as duration, may at any point give sufficient emphasis to one of the chords in such a series to produce stability.

The

ii

chord also

is

used to create chordal elaboration,

e.g., it

may

be a neighbor

chord. In Ex. 20-21 parallel tenths become a feature of the vertical ordering that begins with the second beat of measure

measure

7.

Even though

5,

and that continues

there are only three parts, root

to the first beat of

movement by seconds

is

TERNARY FORM; THE SUPERTONIC CHORD clearly present.

The

ii

chord

is

335

syncopated

;

therefore, the

the unaccented part of a beat. Since similar motion

a neighbor chord. As an embellishing chord,

ii

is

reappearance of

involved,

ii

I is

embellishes

plays a prominent role, for

rhythmically prominent with a syncopation, and the

b'-JIat in the

on

I

as

it

is

upper and g in

the lower part are the pitch apexes of the phrase.

Ex.

20-21. Obrecht: Missa Forfuna Desperafa, Kyrie.

Ses xn

m:

^^ J.

i>

J-

s

ll r

ii^' i

^^

nA f

3t

mM

n

J

J

J^ p

r-

^^

^

^J=^ UUm ^^ $ ^w^ jj

I

J

^ r

II

Root movement down a second sometimes occurs cadentially, resulting in the progression ii I. Since I is the harmonic goal of this pattern, it is a type of terminal cadence. Furthermore, ii I most closely resembles the plagal cadence, because the supertonic chord has two tones in common with IV. Therefore, it can be described as a supertonic plagal cadence, to distinguish it from the usual IV I plagal

—

—

—

form.

Ex.

20-22. Hindemith

:

Mafhis der Maler,

I.

(C)

1934 by

B. Schott's

Soehne, Mainz. Renewed

1961. Reprinted by permission.

t^

i^

fi-

— -e-

r^

^^

S2 2^

(m)

The first inversion supertonic, as part of a terminal cadence, also creates the supertonic plagal cadence. The plagal nature of the iig I cadence is primarily a result

—

336

TERNARY FORM; THE SUPERTONIC CHORD

of the prominence given to the fourth scale degree. This explains

a supertonic plagal cadence. In both cases

this cadential

why

ii

—

I is also

pattern results from the

and the first scale degrees. The secundal root of the more common IV I cadence.

relationship between the fourth tion modifies the effect

Ex.

rela-

—

20-23. Supertonic plagal cadence.

^

Er

g

^

N

lie

Exercises

For more detailed assignments see Materials and 1.

Listen to

Structure

and study through compositions such

of Music

I,

Workbook, Chapter 20.

as the following. Isolate those musical

elements that play a prominent role in creating the ternary design of each work, a.

Schumann:

Traumerei

Rachmaninoff,

Debussy, La fille aux

d.

Mozart, "E amor un ladroncello" {Cose fan

and

Prelude,

Op.

3,

cheveiix de lin

Spell, write, play,

3.

any diatonic scale. Use the harmonic rhythm of Ex. 20-5 in a

tutte)

sing the chords that could appear

2.

Write

No. 2

b. c.

on the second

scale degree of

as the basis for a four-part vocal composition.

contrapuntal texture with or without a

text.

(A B A) composition for a combination of four different instruments. Create a middle section that does not rely upon tonality change to provide

4. Write a short three-part

contrast. 5.

Reduce Ex. 20-12

to a two-voice

framework. Then use

this

framework

as the basis for

a

six-measure phrase for piano. 6.

Write a new melody for all or part of Ex. 20-4. Then create a new accompaniment melody you have written.

for the

Submediant and

21

MiBdianf Chords;

Chord Relationships

Several examples in the preceding chapter included chords not

or sixth scale

The

were either the third degrees. They represent the only two diatonic triads, iii and vi, that

directly related to our discussion.

roots of these chords

we have not yet discussed. The quality of both the mediant and submediant

triads differ, like that of

ii

and ii°, from I, IV, and V, making possible an immediate qualitative distinction. Other distinctions will become apparent as we examine the appearances of iii and vi in various contexts. The Submediant Chord

In major the submediant sixth, first,

and

is

a minor triad.

third notes of a scale,

and

is

The submediant chord

used to harmonize any of the three.

In Ex. 21-1 the sixth scale degree appears as bass in measures

a chord root only in measure

Ex.

1

and

1.

21-1. Beethoven: Piano Concerto No. 2,

IV«

V«

Op.

contains the

19,

II.

I

337

3,

but

it

is

V

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

338

example the repeated g (the third scale degree) in the upper part is harmonized by both I and vi. The association of the two roots with g results in a change of harmonic rhythm that would not be present if only the tonic chord had been used for the first two beats. In a minor key the submediant triad is major in quality. Like its counterpart in In

this

major,

it is

frequently associated with melodies that contain successive repetitions

of the tonic note. As a consequence,

VI

is

used frequently to create an active

harmonic rhythm. This is seen in Ex. 21-2, where VI alternates with 2, even though the voice part remains on the same pitch.

Ex. 21-2.

J^TJ

Schumann: Dichterliebe, "Die

J

<j

f

I

^^t /^ it.,L

W'

pp

J

J

}

i

li

^ t

..

alten,

^

j

I

measure

J'J^J-

J

^

J*

[•

^

K''

1

i=t

I

II

jt

p 44

M

V

cjl:

in

bosen Lieder."

j j

I

i

between i and VI makes it possible to continue the pattern of harmonic rhythm begun in the first measure. Furthermore, this relationship is part of the alternating major triad minor triad pattern that begins in measure 1. The submediant chord shares tones in common with tonic, supertonic, and subdominant, if we include only those triads previously discussed. These tonal relationships are illustrated in Ex. 21-3. In Chapter 20 we did not show the relation of the supertonic chord to the submediant; here we can see that such a relationship ii, in major, is analogous to ii exists. As a matter of fact, the root relation of vi and V I. Notice that in minor the root VI and the prime of ii° are a diminished This

shift

—

—

—

fifth

Ex.

'>

apart.

21-3.

Ti 3rd

C:

—

I

vi

ir^-13 3rd Vi

n^-u

\

\%\\\i m\AjiVy-h% \

5th IV

vi

w

o5th I

VI

VI

iv

vi

ii°

339

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS In major or minor the submediant chord

is

frequently a part of a chord succes-

movements

sion that culminates with the dominant, usually with successive root

by fifths. The half cadence that ends the first phrase in Ex. 21-4 gains harmonic prominence by the preceding root motion. The ii chord is structurally important because it relates directly to the dominant and in this excerpt vi plays an important ;

structural role because of

Ex.

21-4.

its

root affiliation with

Haydn: The Creation,

Part

No.

I,

ii.

3.

^

i^ n Wf

iJ^ j^ iEi rrrr ffff

U P^ ?

J 1

^^

11

^

f

V7

Here

vi

is

preceded by

next with at least one

I; thus,

each of the chords in measures 1-4

common tone.

is

related to the

Furthermore, root relationships by

occupy

fifth

most of the phrase. In Ex. 21-5 IV appears between vi and ii, producing root movement in thirds. Consequently, each chord in measures 1 and 2 has two notes in common with its

immediate predecessor. Notice

also that the

ent in the supertonic plagal cadence,

common

tone relationship

is

not pres-

and that the phrase does not contain any

fifth relationships.

Ex. 21-5.

Wagner:

PU

^

Parsifal.

i

J'

^

331

a:

IV

-o-

^

^ -a

Ak

s

w

1 I

ii

The submediant chord also appears root movement by a second, thereby

in the role of a neighbor chord,

omitting the possibility of

Ex. 21-6 shows vi as a neighbor to V, clearly indicated by to

V. Notice that the resultant motion by step

phrase.

in the bass

its

and

common

creates tones.

durational relation

adds variety

to the

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

340

^ m

Bach: Ermvfre dich, wein sehwacher Geist.

Ex. 21-6.

^

I

n N

1^-r

.^^

S^ G:

^

f

r

IV

I

The melody note marked (*) in could be harmonized with the I chord. By using vi, however,

vi

appears to "replace"

measure 2 of Ex. 23-7 the bass line in measure 2 conforms harmonic color.

Ex. 21-7. Bach:

to

I.

measure

1,

as well as

adding a different

Aus meines Herzens Grunde.

m s

f

V

Vi

In some contexts

r

i

r 1

^^^ r

r

5

$ i ^i

f

^

1

^f

^

?

r

VI

The appearance

IV

of vi as a cadential chord creates a particularly striking effect.

ends the second phrase (measures 5-8) in Ex. 21-8. The earlier harmonic and melodic activity of this phrase "predicts" that it will probably close on tonic, as It

does the

V7 move

first

phrase. Furthermore,

we have already heard the melodically outlined we expect the same resolution of the V7 chord

measure 4, so in measure 8. However, V7 resolves deceptively to vi, rather than to the expected I chord. Since the expected harmonic pattern is evaded, harmonic deception results. The cadential succession V vi is called a "deceptive cadence," and is one to tonic in

—

other type of progressive cadence.

—*

341

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS Ex. 21-8.

Beethoven:

Op.

Trio.

11,

I.

Allegro con brio Clarinet in

Bb

rrirriii

J

Cello

/ /

i I

•/

te^ I

p^

nqrz

^

:qZ)

TS-

/

^^5: tP

3: -e-

^

1^

I«

More

fe

'/

''Vi^rTJi'' r'^-^Jj

Piano

f

g

a tS

^

3j: a:

— fe

-o-

V7

IV

VI

tonal activity leading to the expected tonic chord generally follows the

deceptive cadence. In Ex. 21-9 a cadential

deception afforded by

vi intensifies the

vi

appears in measure

eventual appearance of

I,

8.

Here the

as well as en-

hancing the immediate repetition of previous material. Unlike the major-minor relation formed in major, the deceptive cadence in minor involves two successive

major

Ex.

triads^

21-9.

Haydn:

String Quartet,

Op. 76, No.

^

i

^^

m

^ ~?"

'^

d:

2,

IV.

ff=JF

^ ^ ^

P

342

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

Ex. 21-9. continued.

^M.

i

^m 1^^ %

r

m

?

I

v

VI

P f F

^ ^ £^

V—vi,

Therefore,

p

n

J

ff

f*-

p

^

I«

Since the root relationship between

common.

I

V

and

vi

is

a second, they have no tones in

Hke the succession of

all

chords whose roots are a

second apart, generally involves considerable contrary motion. The third of the vi chord (the tonic note) is generally doubled when it is preceded by V or V,; the root obviously also can be doubled. In minor the root of

doubled when

VI

is

usually not

preceded by the dominant, because the leading tone would then resolve to a tone an augmented second lower. Ex. 21-10 gives the usual doublings for both major and minor. it is

21-10. Doubling

Ex.

submedicnf chords.

in

Root

^

f w

m^ F:

V

-e-

Third doubled

doubled

i

^

W

f

^ V

vi

tKl

-&-

i*:

^

vi

I

mi

t±:

^

m f:

«

S

te

\l

-^ 9

V

VI

—

y

VI

^^ VI

VI

Third doubled

fe

$ 1=f

VI

VI

343

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS In Ex. 21-11 the

Here

vi

is

vi

chord ends the

preceded by

V'^,

and

also

phrase in harmony with the tonic note.

which harmonizes the second degree. Since the leading

tone appears in the upper part, a descending line

first

it is

moves

resolved to tonic.

The

fifth

of the

V,

is

part of

Consequently the third of

to the tonic note.

vi

doubled.

is

Symphony No.

21-11. Schubert:

Ex.

f±

i

5,

i m^ n f7 '

r

mM rn

1 i r^

^ ^ g

^ m ^^ n

rr=r

E\>:

\nvi

I

The Mediant Chord

The mediant

is

contains the third,

a minor triad in major and a major triad in minor. Since fifth,

and seventh notes of a

scale,

it

has two tones in

it

common

and V, and one tone in common with VI (vi). In minor keys the mediant sometimes an augmented triad, when it incorporates the raised seventh degree;

with is

I (i)

rare occurrence barely justifies attention.

its

Ex. 21-12.

Mediant Chords.

irVt

'):

C:

I

In

|

p:i

r):,

m^'K

III

many

„

l

„

iPO i^ I

I

harmonic

V

IE

or

m

!

or

^i^ in+

mediant chord is similar to that of the submediant, i.e., it frequently moves to or from the tonic, subdominant, or dominant chords. In Ex. 21-13 the iii chord appears three times. In measures 1 and 3 it connects I and IV, and in measure 4 it connects V with IV.

Ex.

respects the

21-13. Brahms:

Symphony No.

role of the

4,

3

i

KJ

:*

—

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

344

The primary organizing

principle of Ex. 21-13

the lower part in measures vallic structure.

as

shown

and

2

is

contrary motion. Furthermore,

a mirror of the upper;

Fewer chords could have been used

in Ex. 21-14.

rhythm of measures

whereas

1

is

and

1

in Ex. 21-13

The 2

result,

is

however,

now

J

Jin

it is

is

IJ

support the melodic e.g.,

line,

the harmonic

J

J

In addition, the half step root relationship between

Ex. 21-14.

has the same inter-

quite different;

J

IJ

to

it

iii

and IV

is

eliminated.

Reduction of Ex. 21-13.

^

^

f^-^i

.^h

J

i

P

m

:*

I

^

^£

--.

27

^:

chord is in a prominent metric location; however, it is part of an upbeat pattern that deemphasizes its location in the measure. Since iii is used to harmonize the seventh degree, and since the V chord contains the lowered In Ex. 21-15 the

iii

seventh degree, an alternating major-minor triad pattern

Ex. 21-15.

Revel: Trio, right

IV.

is

created.

Permission for reprint granted by Durcnd et Cie., Paris, copy-

owners, and Elkan-Vogel Co.,

Ill

IV3

Inc.

Philadelphia, agents.

V

In Ex. 21-16 the harmonic rhythm of the second phrase creates a distinctive contrast with the first. In addition, the appearance of both VI and III produces a brief skirting of the relative major tonality. Notice that the root movement of VI III is similar to iv i. Since this similarity exists, we can say that the iv i.

—

of measure 3

pattern

—

—

is

is

a sequential continuation of vi

iii;

that

immediately repeated at a different pitch

is,

level.

a systematic harmonic

345

SUBMEDIANT AND MEDIANT CHORDS, CHORD RELATIONSHIPS 21-16. Mozart: Requiem, K. 626, No. 8,

Ex.

^

i

J

I

Jesus."

i^r]

^

rt

^u g:

"Domine

J-3J

LJU

f

CUT

^^ ^aaj ^m ^* J

J^

V«

VI

Vi

ffl

I

J-^

^m The

III chord appears

between

been harmonized with either

i

i

and

V

i

i^^;i

in Ex. 21-17.

J

^

#-=:

p

The melody could have

or V. Interpolating III enhances the harmonic

structure, and maintains the harmonic rhythm established in the preceding two

measures

(iJJ IJJIJJ

movement

J^-v^

).

Notice that the resulting root

outlines the tonic chord, thereby confirming the tonality; also note that

each of the chords

Ex.

IJ

is

related to

its

successor with at least one

21-17. Brahms: Piono Sonata, Op.

m tj P

e^

J

fe:

vf'. m

S

331

331

331

33=

33=

Roots:

by thirds

in the

are shared with

iii

chord precedes tonic

in a

33=

331

of

tonic triad

cadence. This places root

important terminal position. The two tones of the I

(root

and

third of

iii

V

i5

Outline

Sometimes the

tone.

1,

^ ^m s ^ a

common

equal third and

fifth

of

I)

iii

movement

chord which

create a

smooth

—

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

346

on chord repetition. The presence of the leading tone chord provides the one factor that makes this relationship progressive.

relationship that borders

the

iii

Ex. 21-18.

Bl»:

iii

I

in

cadence.

I

iii

Ex. 21-19 and Ex. 21-20 illustrate terminal cadences involving

iii

—

Both

I.

examples are similar in cadential effect, but there is a notable distinction: in Ex, 21-19 the I chord is melodically outlined, whereas in Ex. 21-20 the iii chord is melodically outlined. Thus, even though the cadential harmonic pattern is the

same

in

both excerpts, the terminal motion of each melody has a different char-

acter because of the chordal outlining.

Ex.

21-19.

R.

Strauss: Ein Heldenleben, Op. 40.

fc

^^

f

Ex.

m

(I)

ff *'"

i

1

VI

^

i

iAs-

W'

No.

I

I

III

10,

molto

" dim.

^

i9-'

21-20. Brahms: Intermezzo, Op.

^p

e

~o

cresc.

P

Et:

^

-^

3.

r^t

i^-i

W

^

ifl-S^

4^

5^ 9^.

'9-.

Sd.

B:

The augmented mediant (HI) is generally found in positions similar to III. Any differences that result are produced by the augmented triad's distinctive

347

SU6MEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

and rootlessness. As we have observed in previous chapters, the inclusion of augmented or diminished intervals in diatonic tonal structures implies greater quality

tension, because resolution to a point of stability seems desirable.

Since the leading tone

is

member

a

of the triad,

IIP generally

resolves to chords

that contain the tonic.

21-21.

Ex.

Augmented mediant.

t^ i

i

m

^ ^=T

m^

e:

in+6

Furthermore, share in

21-22.

Ex.

it

i

^

m ni+

IV

has a tonal kinship with

i,

VI, and

V

VI

because of the tones they

common.

Augmented mediant.

«ll— y

f

i

in+

II

lljL

Jl

l

II

m'

I

ljl

¥ VI

ni+

In Ex. 21-23 111*6 is approached by contrary motion between the two outer parts. A logical chord at this point would have been Illg, but instead the tenor moves by step from a to g- sharp in the first measure. This forms the augmented sonority of the chord, at the

same time directing attention

to the a that follows

of G-sharp — A

propels the texture on the second beat. This leading tone action forward through iv to the dominant that eventually cadences on tonic.

21-23. Bach: Chorale setting, "Herr, ich

Ex.

habe missgehandelt." I7\

SJ r

^ a:

I

r

J

J

r

r

r

T i m+6

^ IV

V

f -> i

348

As

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

in

most unstable

Thus

tion.

triads, the tones

the third of an

doubled are those that do not suggest resolu-

augmented

triad (the note

E

in Ex. 21-23)

is

generally

doubled.

The augmented mediant

frequently precedes V, producing the effect of an

em-

bellishment of that chord. This possibility exists because of its close similarity with

V, and

their

common

bass tone

when

III"^ is in

passing activity in Ex. 21-24, Ill^g would

Ex. 21-24.

first

inversion.

Without the

directly to tonic.

Chopin: Prelude, Op. 28.

i ^^

^

ri f

^^: S

* ni+6

The

move

the

v^

i

and the

harmonic

situa-

tions that are similar to their root position counterparts. Since the root of the

chord

first

inversions of both the vi

iii

chord appear

in

does not appear in the lowest part, the resulting effect of harmonic change siderably

of

I

weakened

in

some

contexts. For example,

remains in the lowest part. Even though there

is

if vig

a

is

con-

follows tonic, the root

root change,

the tonic note,

harmonic motion. The result resembles a harmonic embellishment of the I chord rather than a change of harmonic function. Stated another way, the tonic note resembles a pedal, and any chordal change above it must be decisive to change the basic pattern of harmonic rhythm. because of

Ex.

21-25.

its

tonal predominance, nullifies the effect of the

I— vie.

=§=

S

tf^=^ VI 6

—

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

The

first

inversions of both

and

iii

349

are often used in passages that unfold the

vi

musical materials sequentially. In Ex. 21-26,

iiig

up of greater and

I

and IV. Its use here coincides with the established pattern that alternates root position and first inversion chords. Therefore, even though the roots change in every measure, the harmonic rhythm, because of alternating inversions and root positions, is made

Ex.

lesser accents,

4

J-

\

21-26. Mozart: Piano Concerto, K. 413,

sTinii

J-

J-

appears between

IJ-

IJ.

J.

\

(

J*-)

nn-n

J

T

-rri i ^

r

f VU

I

'-^

'y\

2nd

4th

Analysis of

I

I.

/

F:

vi

4th

roots:

^

i 'f

fE^^^^Ur

w^

m/ ^ ^

— rt ^^ m

J 7

f

•

r^

f 16

IV

iii'

I

_IL

2nd

Ex. 21-27 has two important features. First

and dominant pedals tion of

I— V

2nd

4th

in

measures

1

and

2.

is

the sequence formed over tonic

Superimposed on

this

a kind of "sub-progression" that accompanies the melodic sequence of the top voice. is

in

strong root relaharmonic sequence

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

350 Ex. 21-27.

Massenet: Manon, Act

A

at the

dominant

level

result if I

At

vii°

I

second feature of Ex. 21-27

which, though terminal in

Scene

I

— — of V — IV —

Notice that the succession of

sequence

III,

is its

use of vi and

iii

its

monotony

inversion chords including

found together with a scalar motion lodic forces outweigh harmonic progression. This

by seconds, the lack of common tone

that

would

in their stead.

in the lowest part.

tions

followed by

as interior cadential chords

the passage of the

had appeared more frequently first

is

iii.

effect, relieve

times, extended passages of

measure

vi in the first

When

results partly

relationships,

this

iiig

and

vig

occurs the

from the root

are

merela-

and the absence of strong

bass progression. Passages such as that of Ex. 21-28 bear a direct relationship to

the practice of fauxbourdon^ in the fourteenth and fifteenth centuries. In such passages

harmonic relationships that are cadential

fore, this

Ex.

kind of

movement extends

IV8

iiie

iSee Chapter

ije

!3.

je

vii'^

vje

avoided; there-

or lengthens a phrase by sequential patterns.

21-28. Mozart: Piano Sonata, K. 279,

C:

in character are

ve

III.

IVs

iije

ije

je

(iv)

V

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

The

use of the submediant

diatonic triads. As

we have seen,

351

and mediant triads completes our study of the iii (III) and vi (VI) frequently occupy a secondary

harmonic

role; in other contexts they contribute a fair share to the structural

aspects of

harmony.

Tonal Relationships of the Diatonic Triads

Now

that

numerous

we have

studied

all

of the diatonic triads,

tonal relationships existing between them.

we should

consider the

There are two

significant

any two chords: the pitches (if any) shared by both chords, and the kind of root relationship formed between the two. Each triad of a single scale has at least one tone in common with another triad from that scale. Any two triads having as many as two tones in common are closely related. If they have one tone in common, they are less closely related. If there are no tones in common between a set of two triads, they are not closely related. Three principal types of root relationships may exist between any two triads. They are fifth, third, and second. The root relationship of a fourth (like IV I) is an inversion of the fifth, just as root relationships of a sixth and a seventh are inversions of the third and second, respectively. Triads whose roots form a fifth relationship have one tone in common, such as V I and IV I. If the root relaIV or I vi, there are two tones in common. But if the tion is a thirdj_as in ii root relation is a second, as in V- -vi, there are no tones in common. -29 sTiows chord refationships to tonic when roots are related by fifths. The vii° chord is not included because the leading tone does not function as a root, and the I V is not included because it does not support the tonic as the root of its relations hip. In minor the ii° chord would precede V. The ii° often is used in the same manner as ii in major; therefore, in minor keys root succession by fifths could begin with the iv chord, followed by the VII chord and continued as illustrataspects about the relation between

—

—

VI

ed, III

Ex.

—

—

vi.

21-29. Chord relationships.

C:

The is

(ii°)

—

ill

VI

ii

V

I

tonal relationships in major of each triad to

shown

in Ex. 21-27.

The

leading tone chord

is

I

by root movement of a third

included in this illustration, even

though the leading tone does not function as a root. The rootlessness of the ii° chord in minor makes it similar to vii° in major. This should be kept in mind when relating this illustration to minor keys.

-

SUBMEDIANT AND MEDIANT CHORDS; CHORD RELATIONSHIPS

352 21-30. Chord relationships.

Ex.

i Mio~«

3 C:

vi

IV

The summary

V

(vii°)

li

I

that follows shows the tonal relationships of each triad in both

major and minor keys. Root relationship by second is omitted because it is created by the roots of any two adjacent triads, with the exception of vii° in major and ii° ill

minor.

Summary

/

of Tonal Relationships Between the Diatonic Triads

One Tone

Common Minor

Major Tonic

V

Supertonic

vi

Mediant Subdomi-

vii°

IV V V VI vi

vii°

I

Root Relationship

Two Tones in Common

in

Minor

Major

iv

V

iii

IV

-sttrn^^

vi

vii°

VII VI VII I

V

I

vi

ii

ii°

viii°

Minor

Major

VI IV

III iv

3rd

iv

Major iii

Minor

vi

VII

V

—

i

vi

VI

V

I

VII

vi

ii

I

i

iii

ii

—

—

Ill

V

VI

ii°

—

IV

VI

III

— V

i

VI

nant

Dominant Submedi-

I

ii iii

ii

i

III

ii°

iii

VI

I

VII

III iv

i

Leading

IV

iii

iv

III

ii

V

v

ii°

IV

I

ant

VII

—

i

III iv

V

tone or subtonic

Exercises

For more detailed assignments see Materials and

Structure of

1.

Sing and spell the mediant and submediant chords in

2.

Use the melodic material from measures 16-measure piano composition

3.

4.

1

and

Music

all

I,

Workbook, Chapter 21.

diatonic keys.

2 of Ex. 21-9 as the motivic basis for

a

in ternary form.

Reduce Ex. 21-11 to a two-voice framework. Then elaborate this basic frame a "new" four-phrase work. Reset the melody of Ex. 21-16 with a "faster" harmonic rhythm. Incorporate

to create

all

of the

diatonic chords into your setting. 5.

Write an experimental composition that uses a preponderance of chords other than subdominant, or dominant, Make a formal plan, and sketch in the chordal forms that will serve as the basis for a phrase or section. tonic,

6.

Write a three-phrase vocal composition. Use the following plan: position chords; second phrase, parallel

root position

and

minal cadence.

first

first

first

phrase, only root

inversion chords; third phrase, alternating

inversion chords. Close the example with a mediant to tonic ter-

Through-composed

22

Form /

Mutated Chords, Harmonic Sequence

one principle of organization in most musical designs. However, there are compositions in which the repetition of larger formal units, such as a period or a section, does not occur. Broadly speaking, this means that no Repetition

is

two parts of such a composition are identical in all respects. If this were adhered to consistently, the composition would be a series of contrasts without any sense of return or "rounding off" of the whole form. The creation of a unified musical design depends upon many factors; large scale repetition is only one of these. Compositions in which each section is essentially different are sai d to be through-composed^, to distinguish them from repetitive structural schemes. Through-composed compositions may contain several contrasting parts or sections; however, total length

is

ultimately limited by the listener's reten-

tion capacity.

Compositions based on the formal principle of non-repetition generally do not contain exact restatements. In Ex. 22-1 none of the four phrases is precisely like another {abed); even so, it is a balanced structure. Each of the phrases is only externally different; within the separate phrases similarities exist that create unity. Ex.

22-1.

Slow

inyUl'.P^

'

The German form

\

r^m

^

v^

PC rr

i

-^^^-i

i

of this term, durchkomponierl, appears frequently in books that discuss musical

form.

353

354

AH

THROUGH-COMPOSED FORM four phrases have a similar contour, various rhythmic patterns recur,

and each

phrase begins with an upbeat. In addition, the tones focus decisively on A as tonic. Thus, even though this melody does not contain repeated phrases, other factors help to produce unity.

The through-composed formal design is used

also for compositions that are longer

than the melody of Ex. 22-1. Simply stated, the duration of a composition

mined by the length of each

is

deter-

through-composed composition each section will comprise several phrases. Within each section repetition of phrases may occur, creating unifying elements within the section that differ from those found in all subsequent sections. section. In a longer

In Ex. 22-2 the four sections are clearly delineated by changes in meter, tonality,

accompanimental patterns, texture, and rhythm. These major external differences make the form (abed) easy to comprehend as through-composed.

Ex.

22-2. Schubert: Der Jungling auf

dem

HiJgel,

Op.

No.

8,

1.

Not too slowly

Voice

Piano

f

'

m ^^ s ^'

.g Ein

i

p r

r

Jijng ling auf

"*

^

-^

^

pr

r p ward der Augen

5

a

M

t

k

—:fe

*l* * p T' dem Hu

*

p Spiegel

¥

ihm

triib

4

^

1

^r

seinem

gel mit

-

p

i

Kummer

r^r-S saB;

wohl

fi^

-i-

If

^

^

P

cj'p

und tranen

^

f 7

j

J p

i

-

rr naB,

f'

i

^/PC;'^

wohl ward der Augen

^ ^

s

^

rr

r

r

r

# ;

355

THROUGH-COMPOSED FORM

o

f^rlrr

p

Spie

ihm

t f

-

gel

a^

p

r

'

tranen

triib unci

s

f^r

^

naB

-

fe

ri—

MA ^ PP

m

wi

f-

#-=

/7\

s

(•

-0

9-"

-.

i-

It

i

MaBig ^^=^

^~^

^^

Z2I i

PQ-CT

r

Sah fro

J^rr ;^

,>

:

heL'am-mer spie

am

len

grii-nen Fel

fe^ ^^ p^# Jq^ ^^ ^^^ f^ -

-

d*

^ ?=^

i-—^J-—j)

^

r

>

^^

hang.

i

i

^-'^i^J-''^;)

fH^#^#^

sah fro

^^1^^: J—^--^

-

he Bachlein

J.-^jJ.-^;)

i

die Schmet-terlin

lang;

-

ge

S

* d

j.—^J,J:-^J)

^^m

mm ft^Pi

quil

len

-

das bun

J^V-'-.j

^^ F^^ ^m

W^^

sen

so

-

gen

*-*^

#•»

)

-

te_Tal

ent

Jr-;j^

j)

P^^ am

^m

ro

i^i "•

-

ten Blii

-

^^T^

ten

I

— — — —

Jr-jJr^;,

J.— ;J—-^ Jr^J J.—

T

r

'

mund.

^ wie

i

i

Mor

—

r

r

pcj-xJ -

gentrau-me

fe r

Jr— j>J.-^i>

>

r

"r

»

r

»

P flo

-

gen

m r

«—

r

die

-

l

;i;>;i Lf^^CJ

Wol ken -

in

^^#

dem ±jt

—

—

«

356

THROUGH-COMPOSED FORM

Ex. 22-2. continued.

1^'

'jr

r und

'

Rund

^Liin^

al

^^ ^m ^^^

^^^^ C\

r

^j^

>

i

Gliick,

mm

nur

in

^

£

P C

al

schwammi n

les

-

[p J] J^ij.^-i

Jr—xj^r-^j,

^^ ^^

* j^Mcrpp^Y

Herz hin

sein

und

ter

-

\^ri

J^ij^i

Jr-^J,Jr-^j>

^m

^^ mm

mun

war so

les

-

-pn''

r

p

unter sah nicht

-

^

^

s ^^ ^^

i i

H

Freu

der

$

:#^

£

zft:

*

:

^

de

-

h

;J

1

fTS

^^_J

^

UJ)

^^

^

^'^^ I

Freu

^^

sah nicht der

Blick,

^

J^

i>

^

de

-

Blick. r7\

S

dimin.

1

^^

1^

#

3i:

IS

•»

•«*

—ir rn

• i'p y

Langsam ^j' #'

'

l

j'j! 0' m-

j'. •'•

i

^^ ^'PP'^'r

j' w

1

Ach! dumpfesGrab-ge-lau-te im Dor-fenunerklang,schon

i

r

^ f'

^ ^

m.

r

r

p

1-^

i?p

«

te

•

pr

r

r

—

4

j'pi^'PP'

Jif

j'.i'j! ton-

^—*

—r^^ ^p

^'r

i

p

—

«'

M P^P

p-p^P'

aus derWei-teein kla- gender Gesang; sah nun die Lich-ter scheinen.den "^'

pr -*

r

4-

r

p'fpr

pTpt

r

r

~4

«-

-#

-#

r

r

3

#


THROUGH-COMPOSED FORM

f ^ ^m

357

pM

pp-p^r ^pic'p p-pr

p-

schwarzen Lei-chenzug, fing

bit- ter

man,

an zu wei-nen,weil

4

-V

I I

T

w

r?

r chen

-

*!

^^2-p

p

man

sein

^f

m R6s

well

i ii

crcsc.

i''

^»p p

r

sy

trug.

-^j'liii^-

tee|.

I

^ t=^

f)ij).

To- tengraber kam,

S ^^ ^

^

j^F'

J

i

li

;>;)j)r

i^^^g'

^Y

'i^

und gab der Er-de wie-der,was Gott aus sel-ber nahm.und

T rrff

p

der

i

^"^

«i^^^ iV * P^

'

te

i?p

F

-

denSarg man nieder,

lieB

Jetzt

#^^

I

Jun^jurM) I^^TiJV^iy * S' d d

^

H-4fi

f

f

fi-''

— >—

,-«

5 i

^^

ii^

»

—y^ 0' 0- S' J'J'JT

%

p-

P

-0

i^f

der, was

Gott aus sel-ber nahm.

M#tfl s

i«^

'>-^}

f

} iJ

l|J

4

E ni f^^

i«

t

3 ^

-0

Etwas geschwinder

^'

^

'

p

'

^ Hi*

i

r~p cjp

Da schwieg

^^ .

i

a*

i

(T*

I

gab der Er-de wie-

^

J'

J'P

f!

r

•#

des Jiinglings

g

*

*'

J

i>J

i

M

r' Kla

-

ge,

und

ic;p be

g

PP

M

^-^

^

^ r

-

-0

^

p

tend ward sein

358

THROUGH-COMPOSED FORM 22-2. continued.

Ex.

^^

p schon am schbnern Ta

sah

Blick,

cjMf

p If

^J

J

*

p

m Ji

'

r

'LTp

r Ster

-

^

I

ar J

'f Mond

^J ^

S J

ho

J

r

The key

he

J'j

^

J'

^

da

las

J

er in

1=1

*rjj

r ^^

den

^

JiJ

J

i

r

^ ^

Schrift,

^

^

p[j i

pif

r

J

r

2

der

^ ^=^^=^

r

^

PCJNf

^

ir"

p

J

^

y

nung

Hoff

^J ^

^jg^

r

r

r

r7^

^^ ^ « i

r

r

her auf- ge- schifft,

J

^ p nen der Hoffnung ho- he

t

Gliick.

i

E

r

t

i

i

f

r

p Und

'

^

'J

'

1

^

ka- men, der

wie die Sterne

p

Wie der sehens

ge des

r

^

Pc;f'

^

^

S

r r

-

Crp

i

p

^ *H^

i

y

^

Schrift.

j=

i

i i

I

r

pr

p

*
*

t^

r

basis of this song,

e

Cg

G,

is

^

f 1

f^

1

^^Ff

f

p

f

p v:;

a crucial factor in the delineation of the

whole design. The use of both g minor and G major contributes to the unity of the composition, through retention of the single tonic, and counterbalances the contrast of tex*;ural change.

The

potentials of this design principle are limited only by psychological prac-

359

THROUGH-COMPOSED FORM

which there is no repetition at any level, motivic, phrase, or sectional. However, that would be the exception rather than the rule. The disjjn guishinp feature of through-composed de sign js large sectional contr asts. These gross contra sts often are softened by transferring ticality.

It

would be

possible to create a form in

cTiaracteristic patterns

Mutated Chords

7-1

from one section

and

to another.

7-VI

mediant and submediant chords add new dimensions to the harmonic palette. Chordal unfolding also is expanded by using chords that result from chromatic inflection, such as the minor tonic and the In the previous chapter

we saw

that the

minor subdominant in a major key. Incorporating the chromatically inflected third and sixth scale degrees into the musical fabric gives the impression of "mixing" elements of both the major and minor modes. Initially, the resulting chordal

and melodic

digressions are local, or "coloristic," in effect; structurally, these

digressions prolong

harmonic

activity.

Frequently the progress of a composition is enhanced when repeated phrases are mutated by chromatic inflection. As in Ex. 22-3, the effect is that of juxtaposed

modes, but the

total impression

structural tonal relationships.

is

On

a blending that does not distort or change the

the contrary, the mixture increases the available

tonal possibilities.

Ex.

22-3.

Haydn:

String Quartet,

Op. 64, No.

^ ^ V w

3,

I.

^Sp f

P

•>

i

''

^ ^ n

f

i

'^ r

^

>

^^ ^ 5

mt^

E

i {^^r^-^

^m^

^E^ ^?=^

f=^

y

,

J)

y

-0-

^^^'i'^-

f

^

360 Ex.

THROUGH-COMPOSED FORM 22-3. continued.

^ ^^^e ^

P

^^^

l-z^Z-J--'^^^ wr^*5t*v*it*

•^

^^^

P

^ When

"27

i

i

'l-zJ

these digressions are set in close proximity, as here, the result

is

a fusion of

complementary elements, obscuring the more distinctive qualities of each. It is probably more accurate to designate compositions in which elements of both major and minor appear consistently as major-minor. Any chord containing notes whose tonal roles are flexible may appear as a mutation. Both the mediant and submediant are particularly suited to mutation because their roles in the establishment of tonality are less direct. As mutated chords they add to the harmonic spectrum by making available sonorities that are more different but

closely associated with other tonal contexts.

In Ex. 22-4 the elided phrases represent a prolongation of V.

The

deceptive

harmonic activity in measure 4 is intensified by the appearance of the B-flat major chord, a mutation of the diatonic vi. It is created by the chromatic inflection of the third and sixth scale degrees, and changes the root and fifth of the triad by lowering them a half step.

Ex.

22-4.

VI.

VI.

Via.

Vc.

Haydn: Quartet, "The Lork," Op.

64, No. 5,

III.

THROUGH-COMPOSED FORM

Like

its

36?

The

used to create a deceptive cadence. vi in the

deceptive cadence

heard instead of a minor

major second, and regional chromatic

The

'VI prolongs harmonic

diatonic counterpart, the

I,

we

when

triad, (2) the root

(3) the inflected third

motion

and

is

third.

is

is

by minor second rather than

sixth scale degrees bring into play

activity.

the

is

same

as the diatonic vi. If

as in Ex. 22-5, both the diatonic

and the mutated

"VI

is

directly

spellings of the

third scale degree are juxtaposed. Furthermore, the resultant root relation

major

it

perceive between ^VI and

the result of several factors: (1) a major triad

is

non-cadential use of 'VI

preceded by

difference

activity

This combined with the chromatic inflection produces a

is

a

third rela-

tion.

Ex.

22-5.

Brahms

Symphony No.

:

3,

I

Third_relation

is

present

II.

W

W

I

when chord

roots are

^thnd^part.

volved have two tones in coinnioii, a diatonic third relation the other hand,

if

is

exists, e.g., vi

the chords inxoKccl oiiK ha\c one tone, or no tones in

a^ "ch romatic" third relation chords

If the chords in-

exists.

IV; on

common,

In a ll chromatic third re ations one of the l

diatonic, the other a mutation (or chromatic).

In Ex. 22-5 "V'l both prolongs the influence of the tonic pitch and also focuses attention on the plagal cadence. In part, this attention

is

a by-product of the

362

THROUGH-COMPOSED FORM

lowered sixth scale

step,

both as root of ''VI and as the third of

iv in the cadential

pattern.

The mutated mediant

To

create the

one half

''III,

also

used in the same

both the root and the

Like the ''VI,

step.

is

fifth

way

as

its

diatonic equivalent.

of the mediant triad are lowered

adds another sonority to the harmonic palette.

''III

When'' III precedes V or V, a cross relation may be created by the juxtaposition of both the diatonic and the mutated seventh scale step, as in the second measure of Ex. 24-6.

22-6.

Ex.

Dvorak

:

String Quartet

A-flat,

in

|.

li^f^J ^m ^J f

^^^ At:

*^

V^

IE

±i^

t— tL

m

1

¥^=^

VI

I

B

r

^^

The 'III chord is in third relation to both I and V, and has one tone in common with each. The ''III also bears an interesting relation to ''VI because of their root relation of fifth

The

and

their

common

tone.

purely coloristic roles of ''VI and

are sometimes regarded with

''III

attention than their structural roles. In Ex. 22-7 the cadential activity

by introducing ''VP before proceeding

Ex.

22-7. R. Strauss: Die Nachf,

Op.

10,

is

less

heightened

to tonic.

No.

3.

By permission of the International Music

Company, New York.

^

zt

rtft? ^

33 zr

Bt:

At

first

bVI

glance

it

appears that the cadence

is

both deceptive and authentic.

How-

harmonic motion is completed, ''VP is heard as a chromatic embroidery around I that is reminiscent of non-chord activity. Earlier in the chapter we stated that consistent use of mutated chords produces

ever, after the

363

THROUGH-COMPOSED FORM the cfTect of elements

mixed from two

different tonal sources.

seen thus far has always involved juxtaposition. In involves both juxtaposition

Ex.

and superposition,

some

The

process

we have

rare instances the mixing

as in Ex. 22-8.

Copyright 1941 by Russischer Musikverlag, Symphony of Psolms, Renewed 1958. Copyright & Renewal assigned to Boosey & Hawkes Inc. Revised Version Copyright 1948 by Boosey & Hawkes Inc. Reprinted by per-

22-8. Stravinslcy:

I.

mission.

The simultaneous mixing

of different harmonic elements

Such stacking of diverse elements

also a possibility.

is

carries the practice of mixing to

its

logical further

development.

Ex.

22-9. Bartok

:

String Quartet No. 2,

1948. Copyright

I.

Copyright 1920 by Universal Edition. Renewed

& Renewal assigned

to

Boosey & Hawkes

Inc.

for the U.S.A.

Reprinted by permission.

Violin

I

P

Violin n

e ^m P

Viola

dolce

i

dolce

M

fi

£

r^^

i pizz.

Cello

m

tr

r r r se:

2

2

3

iU-

#

T-

T»

9—

m.

1

364

THROUGH-COMPOSED FORM

Ex. 22-9. continued.

In Ex. 22-9 a harmonic groundwork o( A major chords. Stacked above this predominance of

is

A major

clearly outlined is

by the

cello

the octave pattern of the

violin that definitely outlines a minor.

Harmonic Sequence

The harmonic sequence

is

created by repeating a systematic root pattern at

successively different pitch levels.

Some

skeletal versions of several patterns used

in this procedure are given in Ex. 22-10.

22-10. Harmonic sequence.

Ex.

O O ^J C3H m n ^-O^ o XE

^W

\\i\i\\\'^\\^


g

u

on""Qoo IE --0zaz

TlvvTu

i\'

V

I

g

an.

I I

4th6th4th6th

Vi II

8«««g' III

I

V

III

VII°V

ft

n

JCE

^^W

m

m^^-^ jCX EC

I

I

3rd 5th etc.

O O 3X IX -&-

I6i\'v0°6iii vjeii I

1

^&w

v^i

I

4th 5th etc.

In Ex. 22- 10a the sequential pattern involves root movement up a perfect fourth, and its repetition a third lower. The pattern is broken here when root movement

by a second appears between IV

—V.

In Ex. 22- 10b a pattern involving roots related by thirds

monic sequence. Each unit of the sequence is connected by tionship, and the interval of repetition is a third above.

is

the basis for a har-

roots in a fourth rela-

365

THROUGH-COMPOSED FORM

and root position chords are alternated in Ex. 22- 10c. The resulting root pattern is by fourths and fifths. Notice that in a harmonic sequence the First inversion

leading tone "functions" like a root. Consequently, the vii% chord status

determined by

Each of

its

prime relation

is

repeated

is

two chords. The number of

a matter determined by compositional necessity.

become dull if repeated too often, while another bears melodic and harmonic interest.

pattern might

because of

its

The phrase

in Ex. 22-1

1

assigned a

to the other diatonic triads.

these illustrations involves a pattern of only

times a pattern

is

One

repetition

opens with a harmonic sequence. The pattern

is

based

on the chord root relationship of a fourth and a bass pattern of root movement up a fifth. The melodic sequence is carried out between two different parts and is continued through measure 3, but the harmonic sequence ends in measure 2.

22-11. Handel:

Ex.

Organ Concerto

in

F

Major,

Andante

t

V

$

(^

i^

(J^)

%

%

%

<

s^^^^

^^ P# ^ ^ ^

i

^

mm 'y-'i!

<''

m

m

J'l W¥=^

Bt:

The harmonic The root pattern

VI

pattern treated sequentially in Ex. 22-12 contains three chords.

up a fifth, down a second the interval of sequence is a minor third below. Since a minor dominant chord is used, the sequence contains only minor chords, whereas the initial statement contains only major chords. is

;

366

THROUGH-COMPOSED FORM 22-12. Brahms: Piano Sonata, Op. 5,

Ex.

^ •

'^^'i^

-<9^

5;

im m

I

I

^

pattern begins with

a root

when

repetition can be the

I

— V7 —

Ex.

vii°,

Album

Harmonic sequences relations

w

first

(V)

inversion chords are used.

The sequen-

indicating again that the leading tone functions as

Leaf,

Op. 124, No.

4.

often involve non-diatonic chords.

harmonic replica

—equal

When

this

occurs the

sonorities as well as duplicated root

In Ex. 22-14 the basic harmonic pattern

is

sequence has the same structure transferred up a second.

22-14. Beethoven: Plana Sonata, Op. 81a,

f^^

^^ Eb:

^p

£ vi

—of the original statement. I; the

^

appears as part of a harmonic sequence.

it

22-13. Schumann:

Ex.

3

IV

In Ex. 22-13 both root position and tial

12

^

^

'^

ji

At

I.

I

yi

III.

gf^

^^ ^^^

Harmonic sequences play an important formal discussion here

is

merely an introduction

detailed studv will occur in

Book

II.

role in

^ ^m

many

compositions.

to this aspect of organization; a

* Our more

.

367

THROUGH-COMPOSED FORM

Other Examples of Harmonic Parallelism

Harmonic parallelism places chords in a relationship more melodic than harmonic. As such, the individual root relationships are less significant than the total pattern as a sweep of motion. As in harmonic sequence, a systematic root pattern emerges. Sometimes an entire phrase is organized by parallel chords, as in Ex. 2215.

Ex. 22-15.

Puccini:

//

m MM

f^

^ O

ter

e

-

^

Tofaorro.

ni.

in

-

mo

na

-

ra

-

ti

^!

§S

,

buo

^m na

sera

b

m

JL

1

y

f

F

P

In other contexts a series of parallel chords creates variety w^ithin the phrase, as in Ex. 22-16. In both Ex. 22-15 and Ex. 22-16 parallelism incorporates first inversion chords exclusively.

22-16. Brahms: Variations and Fugue on a

Ex.

Theme by Handel, Op.

24, Variation

f .^-^-^m

M imif^itir

n

^ m^

'^

B\>:

.

[rn

V

I

Parallelism

is

second)

is

i==*

16

ije

lije

IV6

v6

IV6-

not restricted to inverted chords^ or root is

by

major. In this excerpt

harmony because

-

^

Z^ V

In Ex. 22-17 root movement

!.

movement by

I

seconds.

and each of the chords (except for the difficult to distinguish between melody and

thirds,

it is

V6

the interval of the third characterizes both.

Refer also to the examples of parallel second-inversion chords in Chapter 2 1

—

368

THROUGH-COMPOSED FORM 22-17. Debussy: Preludes, Book

Ex.

I.

soir." Permission for reprint

and Elkan-Vogel Co.,

^P

H^

Inc.,

"Les sons et

les

parfums tournent

granted by Durand et

Cie., Paris,

dans

I'air

du

copyright owners,

Philadelphia, agents.

^^^=^=^=^-

mm

M

r

H

Hi

i

f

a

i

,

|i|

im n

accompany a chordally outlined melody in Ex. 22-18. Because measures 3-5 constitute a harmonic sequence, some of the roots form an augmented second relationship. Notice that the effect of the parallel movement is Parallel fifths

partially counterbalanced

by the contrary motion of the melodic pattern.

Mikrokosmos, Book V, No. 139. Copyright 1940 by Hawkes (London) Ltd. Reprinted by permission of Boosey & Hawkes Inc.

22-18. Bartok

Ex.

:

& Son

^ ^m ^

ty-^-

m w ^m

m

#

^^ More complex

5

p

i

'rrt

m

f

motion found in Ex. 22-19. In this passage the parallel chords move above an ostinatd^ figure. Both factors create a static harmonic rhythm. parallelism and ostinato sonorities are involved in the parallel

—

'

A

short pattern reiterated at the

same pitch

level.

THROUGH-COMPOSED FORM Ex. 22-19. Stravinsky:

Rife of Spring,

"Dance of the Adolescents."

^^

^^

FU.

Horns

Bass

369

f^A

Clar.

Vic.

>

m^'r

%^

k^^

^j

j -

^ -

»

Exercises

For more detailed assignments see Materials and 1.

Make

a detailed analysis of Ex. 22-1.

What

Structure

of Music

I,

Workbook, Chapter 22.

other patterns than those mentioned in the

chapter are used to unify the composition? 2.

Write a 16 measure through-composed composition for piano that uses a key scheme such as the following: G-flat major, parallel minor, G-flat major.

3.

Spell

4.

and sing mutated chords (i, iv, III, VI) in all major keys. Listen to compositions such as Brahms' i?/!a/;iO(/)', Op. 1 19, No. 4. Discuss the use of mutated

chords. 5.

Locate, sing through, and analyze several through-composed compositions.

6.

Create various harmonic patterns that could be treated sequentially. Use one of the examples in this chapter as your model.

Binary

Form

23

In shaping their compositions composers have often used a two-part

many

which employ this formal design of two distinct sections which often (but by no means always) contain similar material in both sections. The grouping of two (paired) dance movements such as the Pavane Galliard is perhaps an early manifestation of such a trend. B inary form is most associated with dance movements found in instrumental and keyboard works of the eighteenth century, as we shall note later in this chapter. It IS also important, however, to note that two-part forms can be found in vocal music, ensemble and solo instrumental music, and keyboard works of other periods

or binary form. There are works from

centuries

—

as well, including the current era.

tion

is

Furthermore, the principle of two-part organiza-

often found as the basis for sections of compositions as well as entire pieces.

The themes

of variation movements, for example, are

commonly ordered

in

binary form.

theme from a movement whose subsequent variations retain the structure, harmony, and melodic outline of the opening and its accompaniment. Note that the passage is arranged in two eightmeasure periods, A and B, each of which is repeated. It is common to regard the second section as a logical "answer to" or continuation of the first. A letter representation of the form of the example would read AA BB. The letter B denotes contrast between the two sections, in this case involving rhythm, contour, harmonic

Example

fi*

23-1 shows the statement of the

progression and texture.

370

BINARY FORM

Ex.

371

Op.

23-1. Beethoven:

Andante con moto.

57,

Andante con moto

.
In contrast with the preceding illustration, binary organization encompasses the entire

movement shown

A', rather

than B.

two main sections of differing lengths, measures 1-21 and 28-50, separated by a six measure interlude (Adagio), which in effect joins the first section with the second and prepares for a modified return of the opening. Note the similarity of materials in measures 1-4 and 28-31. A comparison of the completion of section I (A), which is not repeated, with section II (A') will show that the second half of the piece, while making use of materials easily traceable to section A, constitutes more a logical outgrowth and continuation of A than a contrasting section it is therefore labeled in Ex. 23-2. This piece consists of

;

Ex. 23-2.

division of

/

Shostakovitch: Prelude No. 18, Op. 87.

MCA

Inc.,

Moderate

New

(J

=

©

Copyright

York. Used by permission.

88)

A-/^'

cri

A

1/1

MCMLV

by

MCA

Music, a

372

BINARY FORM

Ex. 23-2. continued.

^^^ ^^m

10

^^ ^

PT C m

dim.

^

n. -9

fl

^nz:

i?±i

^'''

^

[jf'^

^

^

ZJI

dim.

i j

I

^

15

- J.[> #

*

T^

'f~

20

i

i cresc.

^^?

*

jr

1^^

^

W^

r

rr

»

ritenuto

355=^

^

Adagio

(J

ii

1p j:^?

=

f

r

66)

^^

s

25

i r*-

i-

»

i,o

sub i to

ra accelerando

WZ,i-?-

'^

f

i^

P

^ ^^ ^^ ^ />o<:o

P

dim.

M

a

poco

^

!!'

^^

t\>Moderat o con primo (J = 88)

W^

fcK^JPP

c?

i

^.

liJplil '

^

9 %

p^

^^^^J^

^^''

21

35

cre5c.

i5? -pj.

s

:s:

BINARY FORM

373

/vvUrtu>^

')^

J' t i

^g ^S

Hi'

19-

^

g

f-?

\fr

^

Z2

further study of this piece will

f^f show

a

^^

^ id

m ll'

A

50

-1112 ^i^i^i ^

m S

zz

'r—f

that terminal close

^-

is

^ zz

r

avoided in measure

D

major region that begins the Adagio and which moves by dominant pedal (C in / minor) to a reassertion of the principal tonality (/minor), coinciding with the beginning of ^'. 21 in favor of a shift to the

The simplicity of the plan of this movement testifies to the usefulness and easily comprehended structure that typifies most binary compositions in which continuity and overall unity, as opposed to contrast and developmental display, are desired characteristics.

Baroque Binary Form

A

particular manifestation of the binary principle appears in much music written during the Baroque period. This is the only specific type of binary construction to achieve

widespread currency, and then only in the seventeenth and eighteenth

centuries.

This form plan is significant not only because it was the prevailing small form for over 200 years, but also in that it was the direct recursor of the sonata-allegro p forrrk In these centuries the binary form was widespread, appearing in the separate

movements of rees, forlanas,

the dance suite (allemandes, courantes, sarabandes, gigues, bour-

menuets

etc.) as well as in

sonata and the concerto.

the various

movements of the instrumental

r,

%

374

BINARY FORM

Many

of our observations on the nature of this form will apply equally to other

compositions in two-part structure. specific descriptions are

Two parallel

d ivisiv e

It should be understood, however, that these based upon Baroque binary compositions such as Ex. 23-3.

general aspects are almost always present in this type of form: an obvious

between the two sections in their use of thematics, and an absence of strong contrasts such as those found in the ternary form., A certain basic "same-

ness" of themes, texture, register, tonality, etc. often characterizes the binary form.

This quality

is

readily apparent to the listener. Both of these attributes are clearly

demonstrated in Ex. 23-3, which

Ex. 23-3. D. Scarlatti

:

Piano Sonata

a piano sonata by

is

in

Domenico

Scarlatti.

B Minor.

^

([iczc^Miz/^

$

h 1

^^=^^

»

m^ n^

mi

-^

i;^.'-"--

rn^fin

15

m

m

m

^

±=^ .

c.

'\?ff^\^

20

tr

m^

p

jj

^

A Ai.

F

SP

JJJ

JJJ ,

B d

'

^

f*

jij ^ I j^j

m

m

m

25 .

P

375

BINARY FORM

t

30

y^ ^^^^

=

^

m^

^ f\^^\

^¥=i^

^^

n

?

^

k^jj^

^ or-

V

p'

i;

I

^ s^ i m ^m ^^

^ ^^ ^ ^^ ^^ ^^ n 1r

'^^'1

1

\

40

(

.

...-fence

45

^^

£

iiU

f^

AYOA^l^j

p # s ^^ ^ S ^ tt4r^t,ux1b

55

—

#-#

a

^-(^

^ #-^

P

p

^

^^

^ ^

a tr

i

J

!lp

#,tr

60

i

m m

.£1 65

*

^^

Oa

p

LiLr

P^

^eMM?<^

mw

it

i Fl

I

/"^

D

376 Ex.

BINARY FORM 23-3. continued.

klTT

^^te

/^

A

-jl

?

^^ ^^

^^

.

^ ^ ^ ''^

- • (

75

«^

:^

^ ^ ^^ ^ ^ ^^ f^^^ ^ ^ 80

fe^

t=m.

^-^-»

P

q?^

^>-m-^

85

-

^

0'

^^fr

f

V^"!

^J^J

!

The

^=±

l±±.

tonal relationships of binary form also generally conform to a

pattern such as that unfolded in this example.

The

bi-partite design

is

common

frequently

confirmed visually by the use of double bars at the end of each section. Since each section

same

An

is

usually repeated, a formal arrangement of

letter

is

understanding of the formal design

thematic fragments.

complete

A A A'A'

is

produced (the

used because of the basic similarity of the thematic material).

themes,

The fragments

is

facilitated

(or "motives")

by extracting the important

shown

in Ex. 23-4 are not

but they comprise the significant musical ideas in the

first

section

(measures 1-47), and they recur in the second section in recognizable form.

comparison of the thematic outlines of these two large sections similarities (and differences) between them.

will

make

A

clear the

—

J

^

377

BINARY FORM Significant thematic fragments

Ex. 23-4.

from Scarlatti

:

Sonata

in

B

Minor.

a (beginning --

^

— jy

J ^F

o: i, a P^

1

^

b (measure *f

1

m

ll

*

d

—

1

J

J.

V

^

^

p

m

—

J

1

U

SS

7)

P= = !^

W~^~W

^

i

i c

N

^

*=s

(measure 29)

^ ^

d (measure 35)

^^

?

^

The thematic outhnes of each section are very similar. Fragment (a) occurs in much the same form at the beginning of each part (measures and 48). Similarly, 1

fragment

(d)

is

the thematic basis for the last part of each section (measures 35

and 75). The principal difference between the two halves of the form is the order of appearance of fragments (b) and (c) they are reversed in the second section. Compare measures 7 and 67 and also measures 29 and 62. From this analysis we can conclude that the two sections of this binary movement are quite similar almost parallel in many cases. The interchange of position of the two middle motives in this example is not typical of the form, although other examples of the same arrangement do exist. Our analysis has not accounted for every melodic fragment, but it has been thorough enough to disclose the basic thematic similaiity of the two sections. ;

—

378

BINARY FORM

Before leaving this example, however,

we must

consider the tonal design, a factor

equal in importance to the thematic outline. Examine

composition again,

this

analyzing for keys and the relationships between successive keys.

apparent that the key scheme of the two sections does not duplicate the same neat parallelism of the thematic design. Section A begins in the key of b minor, changes to D major in measures 25 and 26, and remains in that key until the double It

bar.

is

The

tonality at the beginning of section A', however,

major and

is

not clearly defined (G

D

major are both possibilities), but it becomes stabilized in b minor, arriving there in measure 55, and it remains there until the end of the sonata. The tonal direction of the second section is reversed, in a sense, as the following diagram

indicates:

Tonal diagram of Section

Tonic

is

Section A'

to contrasting

key

Contrasting key or

(?)

to tonic

tonal indecision or instability at the beginning of the second sec-

many

present in the majority of binary movements. In

sible to rule out

all

but one key at

showing key area.

relationship

between keys

is

it is

somewhat

cases

it is

not pos-

In the analysis of compositions

this point.

this characteristic tonal ambiguity

The

Sonata in B Minor

:

A

The apparent tion

Scarlatti

sufficient to point out the general

different

when

the composition be-

major key. In that event the contrasting key is almost always the dominant^ example D major to A major). The minor key to relative major key progres-

gins in a (for

sion of the Scarlatti

is

the rule, however,

when

the basic key of the composition

is

minor.

To summarize ment of

the general characteristics of binary form, the thematic arrange-

the two sections will be parallel, but the tonal direction will be reversed

in section two. This latter statement will

The above elements hardly exhaust

apply almost without exception.

the

list

of possible factors which contribute

to the perception of form in this or any other composition. Considerations such as

changes of texture,

register,

cadences, phrase structure, phrase extensions,

many These may not

contrapuntal factors, sequences, melodic contour, harmonic implications, and others affect our mental image of the structure of a piece of music. all

them

—-along with

some degree

to the total

be of equal importance in any given composition, but

countless other factors not mentioned

— contribute

in

all

of

experience of musical form.

Among

A

the other significant form-producing factors in Ex. 23-3

change of texture

gun, and

this

is

new formal The addition

often the signal that a

occurs in measures 29 and 62.

is

texture.

or thematic unit has be-

of the octave in the right

hand against the continuous sixteenth notes in the left hand marks an important change from the previous texture and attracts attention in both of these locations. Aside from

this

one change, however, the remainder of the composition does not

method of delineating formal sections. Cadences play an important role in defining

use this

the breaks between sections.

An

—

379

BINARY FORM

obvious example occurs in measure 34 and again in measure 75, each bringing the

mark

previous material to a terminal cadence. These

the points of arrival for the

keys in which each of these sections concludes.

An

element that

not readily apparent often serves as a unifying formal device.

is

Such is the case in measures 1-10 where the left hand part is an ostinato, repeating the same two-measure fragment again and again. Similar figures appear in at least two other locations in each section, particularly near the final cadence. Notice also the use of augmentation in measures 7 and 8; both hands play the same melodic fragment but in differing note values. Suggestions for further analysis of this composition will be given at the end of this chapter. Binary and Ternary Forms Contrasted

The

main differences between the binary and ternary principles apply virtually always to movements in these forms, Although all of these contrasts will not apply to every composition, enough will be present to indicate clearly the following

proper category.

^C

BINARY In two sections,

1.

each

set

double bars and repeat

TERNARY ^^'^ off

by

1.

signs.

In three sections, the third of which is

a literal repeat of or

the

Each of

2.

the

two sections ends

different key than that it

3.

4.

in

in a

2.

which

is

similar to

first.

Each of

the

three sections usually

ends in the same key in which

begins.

it

begins.

There is little thematic contrast between the two sections.

3.

There is considerable thematic contrast between the first two sections.

In the conventional

4.

The opening thematic

opening

thematic

binary,

material

the

material in-

variably returns in the tonic key

does

not recur in the tonic key.

at

the

beginning of the

final

(A)

section.

Rounded Binary

A basic element of almost all musical forms is the return or restatement

of opening

material near the close of a composition. This element, prominent in the ternary design,

is

absent (except in terms of key return) from the binary form as described

above. In the Scarlatti Sonata, the opening theme does not return intact in the tonic key.

The

only reprise of this opening pattern appears at the beginning of the second

section.

After the Baroque era

some composers began

to display in their

even complete restatement of the opening thematic manear the end of the movement. Ex. 23-5 demonstrates how a movement that

tions traces of a partial or terial

binary composi-

basically

is

binary integrates

this principle

of a

recapitulation.

380

BINARY FORM

Haydn: Quartet, Op.

23-5.

Ex.

Trio Violin

I

Violin n

Viola

Cellc

B

76, No. 8,

(Trio).

III

yr^-r

m^ mi

^ ^ ^

t?

:v

P

E

3:

a » S

^

^

wm

f

m

p

«

g

^

^^

^ 75

p

/

• \

W^

^/

^ 3J

^

^

fS.

^

#

i?p

o>

i^

=^^ i?P

1^^ f=FT # 80

/'

frr

^ns

^

^

=^

ii^

^ ^

^

.

^B

1^

70

i

*j

ii

^m m

P

i ^f

-^ f^v^^

go

i

i P

i

ft:

s^ g^

I '^

^

^ ^ ^

^

^

1

r

i

PP

3-c

«.

^ ^

85

^

i^ ^J:

-T-

J-

•

^-t

i

fl

-14

^ J

P

BINARY FORM

$

387

^

$

-&-

')

J

{

^

-9-^

^J

3EE

w \

i

P The

first

i^^

^

^3^

ii

i

^

3E£

3^

J3EE

1

f

3^=F

J-> 95

3^

-i 1

^ ^ ^ ^

fr\\^c>V

1

P

*:

^

90

P ^

'

f

i

^ i.

^^

t?

f

^P

^ D.C.

three of the four criteria suggested above apply to this composition.

Significant alterations have been

made, however. The two

sections are not approx-

imately the same length as in the Scarlatti Sonata; the second section here

than four times the length of the

first.

We

also find a restatement of the

is

more

opening

material in measures 93-100, where the mutation of the parallel major key returns to minor. In contrast to

measures 56-64, these^measures are not modulatory but remain solidly in a minor. Another example of tonal instability occurs following the double bar at measure 64. This additional factor contributes to the recognition

of the binary structure. typical example,

The rounded binary

must be viewed

as a

form, of which this composition

hybrid form. Although

the ternary form, notably in the restatement

it

contains,

it

it

is

a

reveals traces of

belongs clearly to the

binary category.

Song Form and

Ex. 23-5

is

Trio

the middle part, or "trio," of the third

movement

of Haydn's

"Em-

movement that illustrates clearly the song form and trio princiThis formal arrangement was used frequently by composers of the Classical period as one of the middle movements in large works such as the symphony. peror" Quartet, a ple.

382

BINARY FORM

String quartet, sonata,

movement

and concerto, and

it

was

cast in the spirit of a

The

dance or

at

and the scherzo and trio are the most frequent names given to these movements which are moments of relaxation in the midst of the weightier and more serious movements that surround least a

of a relatively light nature.

menuet and

trio

them. Actually this formal design incorporates two different small compositions (the so-called "trio"

is

merely a second menuet or scherzo). The

trio

apparently derives

from the Baroque practice of lightening the texture in sections such times even to three voices; hence the name "trio."

as this,

some-

Exercises

For more detailed assignments see Materials and 1.

Structure

of Music

Listen to a recording of Ex. 23-3, noting each formal change

I,

Workbook, Chapter 23.

and comparing

the

two

large sections. Analyze further for the following details:

Examples of

a.

repetition, sequence, imitation, phrase extension, motivic develop-

ment

2.

b.

cadence types

c.

Points of contrapuntal interest

d.

Points of contrapuntal sterility

Play Example 23-5 from the score at the piano. Analyze for the following points:

example exhibit principles of effective counterpoint? b. Analyze for phrase and period construction; analyze and label each cadence jr^ by key, Roman numerals, and cadence type. c. Make a harmonic analysis of measures 76-92. In what ways does

a.

(

Discuss the intervallic structure of the theme in measures

d.

developed

in the

remainder of the

Find examples of

d. 3.

this

stretto

and of

movement

details at

first,

accuracy.

at least twice,

make

— 8 and how

this

is

imitation.

Follow a recording of Beethoven's String Quartet, Op. 18 No. full

1

trio,

a diagram of the form.

5, II.

Try

After listening to the

to incorporate the

broad

then perfect by noting smaller details. Listen once again and check for

Then answer

the following questions:

b.

How closely does the form of this movement correspond to the diagram of Ex. 3. Are there contrasts of homophonic and contrapuntal textures? If so, where do

c.

Are there examples of sequence, melodic inversion, and repetition? Where do

a)

they occur?

they occur?

4.

5.

Where do

main cadences

and what types are represented? Following exercise 3 above, study a score of the movement, taking note once again of the above points. Then make a harmonic analysis of selected passages. d.

the

fall

Write a brief composition for piano that is cast in simple binary form. Make each section no longer than sixteen measures, and retain a simple texture of two voices throughout (prominent top line, accompanimental bass voice).

Secondary

24

Dominants

As we have

may

seen, the presence of chromatic alterations in a passage

indicate one of several things: aherations of decorative tones (non-chord

tones), usual altered tones of the

minor

of music contains accidentals, either

scales, or

flats,

modulation. Practically any page

sharps or natural signs, which indicate

inflections of notes within the diatonic scale system.

from the composer's desire ships, that of

such alterations result

one of music's strongest harmonic relation-

to exploit

Our

"dominant-tonic."

Many

foregoing study of

harmony has shown

the

important role played by this relationship, a role emphasized by frequency of use, as well as structural prominence. It is also possible that composers simply developed a preference for such relations. In any event, a particular practice developed,

namely that of creating "secondary dominant-tonic" will be the basis of

In Ex. 24-1 the

our study

d-naturals that

(leading tone) relation with

Mozart: Symphony

Ex. 24-1.

for the

relationships. This practice

next few chapters.

appear in the seventh measure create a half step

e-flat.

in

E-flat

Major

(K.

543),

II.

Andante :)

1 ^

^i ffi

f

J^

-

^

E»

M

^ f

T^

i^

J-

x

gffia

At:

y

m

0-If )i^ i:**'-d

1 ±3;

p

i

K i^^ (

^

f VS V'/v

SECONDARY DOMINANTS

384

The

d-natural

is

part of a melodic sequence begun in measure 6 that leads to the

dominant of A-flat major. The last chord in measure 7 is 7 chord on b-flat, the V7 of E-flat. Mozart here heightens the effect of the a cadence on the dominant by preceding the dominant with its own "dominant seventh" chord. In other words, he employed a "secondary dominant"^ (more precisely, a "secondary dominant seventh"), the symbol for which is V7/V. It is interesting to conjecture why Mozart used this pattern for the second cafocal point of

e-flat,

the

Mm

dence rather than for the first, or why he used different patterns at all. Probably two different cadence patterns were used for the sake of variety, and the particular order was established to sustain interest.

Had

the order of cadences been reversed,

would have been somewhat anticlimactic, for the point of maximum harmonic tension would have been reached at measure 4 rather than at measure 8.

the result

A further study

of the second cadence in Ex. 24-) reveals other interesting facts.

Notice the third chord from the end. Vf. This chord

and the two following

It

the

is

dominant

— V^/V —V) that —V^ — In both

constitute a progression (V^

resembles one of the most

common

stances the middle chord

the "dominant," which

is

in second inversion, the

cadential patterns, I^ is

in-

I.

preceded by

its

"tonic" in

second inversion, then followed by its "tonic" in root position. The cadence in this example may be designated as follows: V® V^/V V. The cadence could have

— — been accomplished through the use of V^ — V/V — V. The addition of the seventh V/V

which increase the expectation of resolution. Using this example as a point of departure, and from observations made of musical practice, we may generalize about "secondary dominants" as follows: to the triad

creates dissonant elements

1.

Any

2.

Such embellishment

diatonic major or minor triad creates

may

be embellished by

its

own dominant.

harmonic color and strengthens

linear

motion

(leading tone effect), thereby heightening resolution tendency.

sometimes indicated by the appearance of one or more chromatic tones of harmonic significance appearing in music that is basically diatonic. (Remember that chromatic notes may indicate other things as well.)

3.

Their presence

4.

The secondary dominant seventh, because of the added dissonance and the resolution tendency of the members of the tritone, stands in stronger relation to its

5.

is

"tonic" than does the corresponding secondary dominant

triad.

Secondary dominants and secondary dominant sevenths appear

in inversions as

well as in root position. 6.

In four-voice textures the root of the secondary dominant

is

frequently doubled

while the secondary dominant seventh usually appears in complete form;

however, 7.

if

not, the root

is

doubled.

Secondary dominants resolve regularly, (to their "tonics"), deceptively (to a major or minor chord whose root is a step above the root of the secondary dominant), or irregularly (to a variety of other chords).

In

this sense, the

dominant of a key might be regarded

as the

"primary dominant.

SECONDARY DOMINANTS

385

Melodic Significance of the Secondary Dominant In analyzing homophonic music with regard to secondary dominants

melodic significance and

of harmonic structure.

Ex. 24-2 (late

To do

"secondary dominant"

as

g-sharp, a, d,

and

c-sharp,

and

Ex. 24-2.

Gesualdo

t^

to

to ignore

in function.

/-sharp, the

:

Through

the use of the chromatic inflections

composer has heightened the melodic drive

Madrigal, lo pur respiro.

to

Ke)/

i ^ u ^m m^ ^ m JZ

m

-*^

0—0-

f

In

J i*

easy

g, respectively.

^¥ h

it is

regard them as simply another type one very important aspect of their use. so is sixteenth century) contains patterns of harmonic relation identifiable

to overlook their

-

>

;^

mfe

m M-

f*

^^

J3J,J

JJJ I

^

?

'

•<•

H

VI 'Q^/i vi

II

In Ex. 24-3, composed

m

-.

i f

some two

centuries later, chromatic alterations are again

used for line inflection, resulting in a secondary dominant chord function.

Ex. 24-3.

Mozart

:

l\ne

kleine Nachtmusik. K. 525,

Menuetto

m #um ^ m ^ m Allegretto

Violin

I

Violin n

la*

i^

^ f

Viola

Cello

^ G:

^

^

^

^

^

^

^m M ^

t f ^

/

tr

^ pi ? VJ,

V

P P

^

'^

^ ^

^

J3

386

SECONDARY DOMINANTS

At the transient-terminal cadence in measure 4, perform either the viola or cello line as written and compare that result with a performance in which c is substituted for c sharp. Obviously either arrangement is possible; however, it is apparent that the original version drives more unequivocally to d, the dominant. Stressing the transient nature of this interior cadence, the composer immediately cancels out the leading tone effect of the c sharp by the use of c's in the following passage.

Harmonic Significance of the Secondary Dominant

worth noting that second ary dominants are generally used to embellish and emphasize structural chords within a tonal framework. Consequently, their appearance is usually predictable. For example, we can expect to find V7/V used with considerable frequency preceding the V chord in authentic cadences. It

is

Ex. 24-4.

Bach: Chorale, Cantata No. 140, Wachet Auf, Ruff uns Die Stimme.

i

3 r

9^S^

i

331

m ^%

^ ^ 1

di

i 1

g V

4

ot -ozaz

J ii 'rry i i n.

\

"

^ PP I

^

^Af

V4

.

IV6

I

P

^

i r 1

A

--^i

M P^ m t

T

Li

1

E^

I

/7\

-«-

I VV,

IV

s

f

ii7

two are on the dominant. In both instances these important structural points have been emphasized by the use of secondary dominants. In so doing, Bach has stressed the It

is

interesting to observe that of the three cadences in this excerpt,

dominant tonal

area,

and

emphasizing the tonic

in the third phrase he

is

convincing fashion.

He

in a

faced with the necessity of re-

by turning secondary dominant. In other the upper dominant, the lower accomplishes

this

toward the subdominant through the use of its words, in the course of three phrases he stresses dominant (subdominant) and finally at the end of the third phrase arrives

at the

"mid-point," the tonic.

In seeking

to create variety,

tional patterns.

We

composers are not always content

find secondary

dominants used

to follow tradi-

to obscure the tonic tern-

387

SECONDARY DOMINANTS porarily, thus creating

on a

Ex.

Mm^

24-5.

an added element of suspense. For instance, Ex. 24-5 begins

chord with E as root (V^ of IV).

Chopin: Mazurka, Op. 41, No.

2.

^

Andantino

m f.

T

3j

VT

iV

Through hindsight we

are able to hear the harmonic design

the tonal focus of the passage. This

hearing, at least not during the

first

is

and

to establish

not immediately apparent upon a

first

few measures.

Sequential Treatment of Secondary Dominants

Secondary dominants are used frequently in harmonic sequences of nonmodulatory nature. They add tones foreign to the basic key, and they make more cohesive the harmonies of which the sequences are comprised. In Ex. 24-6, the melodic sequence is accompanied with a succession of secondary dominant sevenths. The chord of resolution becomes a secondary dominant seventh that progresses to another, etc.

Ex. 24-6.

Mozart: Symphony

Anda nte

m

f~3~r'

^

^

in

C, K. 551,

cantabile

-

3

4 SSS 4

S F:

Vy

3

W

f

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3

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3

II.

388

SECONDARY DOMINANTS

In Ex. 24-7, the composer doggedly maintains a pattern of sequences so that

harmonies quite foreign

Ex. 24-7.

to the basic

key are introduced.

Chopin: Mazurka, Op. 59, No.

2.

Allegretto

"Jl

B'It

seems

illogical to

regard

the indicated tempo. In

I%1

'/I

this as

a series of fleeting modulations, particularly at

this instance the

simple root relations are

still

apparent,

As the study of harmore complicated chromaticism, the analysis of such an example will become less difficult. For the moment, suffice it to observe the rapid rate of harmonic change, the particular root relations, and the secondary dominants appearing at the points marked, each of which resolves to its respective "tonic" or but the so-called "functional" relationships are not so clear.

mony

progresses through

"tonic substitute."

From

Ex. 24-7

we may

generalize that to^ establish

s eq uences

of secondarv

which each "tonic" successively becomes a "dominan t" of the n ext chord will weaken tonal stability. This is especially true if the sequential pattern is maintained so loi;ig that an overabundance of non-diatonic chords is introduced. This very factor made the harmonic sequence a popular modulatory device, for example, in the Classic period. A pattern of chord motion could be established and maintained until the original tonality had been obscured. Then, upon arrival at the desired new tonal region, a cadence pattern would establish the new tonality.

domin ants

in

Secondary Dominant of the Dominant (V/V

Y'V

In major keys the ap2earance of the

of the raised fourth degree of the scale as a the chord will have as

its

,-

or

VVV) V'/V

member

con tainJTie notes of the diatonic

think of the scale,

and

V/V

in

suggested by the_piesence^

of a chord. In such instances

root the second degree of the scale,

altered note (the sharped fourth degree of the scale will

is

both ways

:

ii

which

chord (with

for the

the third of the chord),

chord. As a matter of

as a major triad built

as a variant of the supertonic

is

and except fact, it

is

helpful to

on the second degree of the its

third raised). (See Ex. 24-

8.)

Iiijnh}2r_ke.y3 the

V/V

or

V"/V

is

created by two chromatic alterations, the

Observe that two alteratioxiS-are rx=. quired to create a major triad or major-minor seventh chord on the second_di of the harmonic minor scale, for the supertonic triad is diminishe d.. (See Ex. 24-8.) raised fourth

and

sixth degrees of the scale.

;

389

SECONDARY DOMINANTS Ex.

24-8.

Secondary dominant of the dominant.

Major

a)

b)

Minor

33=

331 -O-

UI

ini e-

o-

_i

I

W ii6

>V

Approach

Dominant of the Dominant

to the

The V/V

V«/v

or VJ/yjrequently

is.

preceded by a chord that

is

common

both to

which the secondary dominant would be the., V/V is preceded by a chord common to the tonic (vig) and to the dominant keys (iig) in Ex. 24-9b, the V^/V follows a minor triad that is ig in a minor and ivg in e. t he origina l^fcey ^rid to the key in

true dominant. For instance, in Ex. 24-9a the

;

Ex.

24-9.

Approach

to V/V.

b)

a)

Vmi

A.

iffS

"

tfi' If

'f

^K

'^

^•< D •j.Jdtt

**

IT

•

n o

o r» o

r»

Jj

||o

H M

V Jf fyft Vu

t^

A:

Vi6

V^

V

a

E:

iic

V

I

e

tt

^

J

r* o r» o

^5

1

r*

J%" •!•

''

*^ *•

:

16

:

iV6

f» .r

O O

1

**^

1

;t

1

X

o 11

i-i

1

V V7

I

Although the approach to the secondary dominant indicated in Ex. 24-9 may result in a smooth melodic/harmonic progression, such progression is not always desirable or possible. Other cases may necessitate the creation of a chromatic relationship between members of the secondary dominant and the preceding chord one tone of the scale may appear in its natural form in one chord followed by its chromatic alteration

Ex.

in the other.

24-lOa. Secondary dominant.

m

mw^

-e"0~

m

331

-e-

-e-

33=

IV6

V4

V

Vv

390 Ex.

SECONDARY DOMINANTS 24-lOb. Secondary dominant with chromatic alteration.

V

V6/

IV6

In Ex. 24- 10a, note that the g is approached from the g-flat in the same voice. The resuk is an unbroken melodic ascent to the fifth degree of the scale. In Ex. 24- 10b the g-flat appears in one voice

somewhat rougher is

in that

and the g

in another. This cross relation

is

both notes are prominently located, and their relation

exaggerated by the fact that they do not appear in the same voice. Although the

cross relation

not always undesirable,

is

it

is

when

usually avoided

a

less

dis-

jointed result can be obtained, as in Ex. 24- 10a.

In connection with melodic movement in secondary dominant progressions one other observation should be made.

It is

often true that a

note progresses in the direction of the inflection. That

chromat icallY_infl££j.f.d

is,

if

a diatonic note

is

by an accidental the melodic line tends to proceed upward the reverse is true if the note is lowered by an accidental. In Ex. 24-11 this tendency is quite apparent. Note that the /-sharp is followed by a ^; the/ by an e. raised

;

Ex. 24-11. Schein

:

Ge/obef

^U

s

^

1

J

^

seist du, Jesu Christ.

i r 4 ^

^^

This rule of "tendency" corresponds to the functional relations of tones within the major-minor scale systems in that the leading tone (here represented by fsharp) progresses up and the fourth degree (here represented by /) progresses

down. Resolution of the Dominant of the Dominant

The of the

principles of resolution of the

V

and

V. The

usual resolution

V/V and V'/V is

are not different from those

to their "tonic," that

is,

to a

major chord

SECONDARY DOMINANTS

whose root stands

391

in a fifth relation

below.

The

raised fourth degree, the "secondary

leading tone" in the secondary dominant, generally progresses to the

In other words,

it

follows the tendency of the inflection. See Ex. 24- 12a.

when

ception occurs

fifth

a third below, that

degree.

One

ex-

the third of the chord (the inflected tone) proceeds to a note

is,

chord of resolution. This usually occurs in Ex. 24- 12b) in order to provide a full triad for the

to the fifth of the

one of the inner voices

(see

resolution chord.

24-12. Resolution of the V/V.

Ex.

b)

ui:

^m

jQI nsz

§^

a)

i

ijo

1>

"O"

m: F:

V7

K3L.

-*-Tr JOZ

V

V,

f:

yy

'/v

The

331

V'/V usually resolve as do those of the V^. The expands stepwise and the diminished fifth contracts stepwise. One exception to this appears where the third of the V'/V

notes of the tritone in the

augmented fourth (See Ex. 24- 1 3a).

proceeds to the

fifth

of V. (See Ex. 24-13b.) Notice that each of these resolutions

corresponds to the melodic progressions illustrated in Ex. 24- 12a and Ex. 24- 12b.

24-13. Resolution of the V/V.

Ex.

b)

a)

::ii=

t

m

»

-

o

nsz

no i

"cr

^te^ CT

e:

V7

Vv

CT

V

E:

Vl '/v

Use of the Dominant of the Dominant

As previously mentioned, the V/V or V'/V

is

frequently used in transient-terminal

cadences. In such instances the secondary dominant often appears in root position

and progresses

to

V

or V^, which

is

also usually in root position.

—f

—

392

SECONDARY DOMINANTS

Ex. 24-14.

Mozart: Symphony

^w

E-flat

in

Allegretto

^^

^ ^

m^

K. 543,

h

^

0-

i9-

Trm

—

^^ ^^ —

—

f

i

<

^

S

—

l^-d-

^3

:^-

i

I

-d

m

^^

m.

:

n

Vi6

)

i

V

V7 '/v

— —

—

Note the similarity of the cadence pattern (Vig V| V^/V V) to the cadence "formula" previously discussed (iig 14 V^ I). This similarity becomes more apparent when the two possible analyses of this kind of transient-terminal cadence are compared.

— —

Ex. 24-15. Analysis of

P^

cadence pattern of Ex. 24-14.

f

S

fe E^:

V

V6

Vi6

V7

As

illustrated in Ex. 24-15 the

such instances,

this

chord

is

V'/V

I)

is

frequently "prepared" by the V^, and in

often preceded

—V7/V—V pattern may be preceded by comparable —V^ —

V^

to iv

1%

I.

by

I,

vi or vig.

resulting in a

In other contexts the

harmonic progression

——

-

393

SECONDARY DOMINANTS Ex. 24-16.

Beethoven:

Op. 97,

Trio,

II.

Allegro »;

i2.-

i«ig

-9-=

rH

p i.-^y^'ij

r p

1

-^ gf^ »— U— hi

ffffi

-J

M.

crf5c.

—— f

-

-0 -J-

31

3" 5-

>

1

-4

—-

•

•

f

-9

f

-•—

1

'

'

.

-f- •-

>.f-

m

1

-h

•

•

I

V|

V7/^

IV

16

V7

Bi*:

[F:

In the study of

V

and

V we noted that the

4

V I

]

resolution of the chord might be

delayed momentarily by the interpolation of other harmonies, by suspensions and by other means. This is also true of the resolution of the V/V, as will be illustrated

and discussed

in subsequent chapters.

used in the interior of a phrase, V/V or V'/V generally occur in connection with transient-terminal cadences. In such contexts they frequently resolve to an inverted form ofV, thereby contributing to the forward movement of the harmony.

When

Note that

Ex.

24-17.

in Ex. 24-17 the

V/V

is

preceded by

ii,

its

diatonic counterpart.

Wagner: lannhauser, Overture.

Andante maestoso

lLi

^m^ wmm

^ ^

^.>jV

EZKZE

S ' It

.

»g

g

.

zz

T

V/V occur somewhat

nrf

.

-ft^

^ i ^p

d

less

^m

rT ^/V^Jv

The V/V and

f^

r

' '^

'r

r

u f f

^S

frequently in minor. Creating a major

major-minor seventh chord by altering a ii chord involves two chromatic changes, and in this respect the V^/V in minor is more remote from its key than the V^/V of major. It is possible that composers frequently bypassed the V^/V in minor for other sonorities more closely related, or they bypassed the tonic minortriad or

dominant key

relationships for others such as tonic minor-relative major.

—

394

SECONDARY DOMINANTS

When we compare

Ex. 24-18 and Ex, 24-19 with Ex. 24-17

are no major differences in the use of

and followed

as in major.

V/V

In Ex. 24-18,

or

V^/V

precedes

i

in

we

find that there

minor; they are preceded

V/V,

whereas

ig

precedes

V^/V

in Ex. 24-19.

Chopin: Ballade

Ex. 24-18.

Moderate

m

i

{^^

p

V

dolce

^ff^

f

s-

in

G

Minor, Op. 23, No.

P ^TT -SM-

^

P

# P

W^

^ nfTrfr

??

^TTT?

jr

r

M*^

r

V7

^5'v

Ex. 24-19.

^ VTt FfT

(*

iEE£

i

$

^

1.

Chopin: Polonaise, Op. 40, No.

2.

Allegro maestoso

^

lii

^f

i^ i 1*

s

^

J

f

t

^t

jsr

^^

v|

It

is

^^ i6

not unusual to find

in

dominant. In Ex. 24-20 the V'/V

approach

to the

cadence on

V7

^KV

V/V tonic.

minor used is

=^

in conjunction with v, the

minor

preceded by v and followed by V^ in the

SECONDARY DOMINANTS Ex.

24-20. Verdi

:

395

Requiem, Agnus Dei.

Andante J

When

V/V and V'/V

working with

in

minor

in a choral style, care should be

taken to avoid augmented intervals in the melodic lines containing the chromatic

In instrumental performance these melodic intervals are not as

inflections.

to

Inversions of V/V and in complete form.

V/V;

V/V are used with considerable frequency, and

They may be designated by

inversion, first .31 iiiv..iaiuii,

\rTi\7. c_„*

V/V;

first

inversion,

third inversion. inversion,

Ex.

difficult

produce accurately.

V 6/ V VJV;

generally

the following symbols:

second inversions, V^/V.

,

V|/V; second V|/V. VilV.

inversion,

V^/V;

24-21. V/V, V7/V and Inversions.

I* s i

i

^

T 1

r

^s

i fV

^ ^ A^-

/v

r

f:

rV

/v

V6/

/v

^

V5/

i

^ f

i

^ V6 5/v

vv

V4/

f i fV4

3/v

/

V

i

T ^ V6

7v

Pc:

f

P

V6

VV

^

ii

i

:2te:

¥

¥ vv /v

^

V6

/v

3/v

V4

Vv

396

SECONDARY DOMINANTS

As indicated

in the previous chapter, the

V/V and V/V

nection with the transient-terminal cadence. This forms. Inversions character.

make

To some

is

often appear in con-

equally true of the inverted

possible a conjunct bass line that

is

more "melodic"

in

degree, the use of inversions stresses the "temporary" nature

of the transient terminal cadences, since in terminal cadences the penultimate

chord

is

more conclusive cadential effect. cadence pattern V|/V V. The movement to V

usually in root position, thus producing a

—

In Ex. 24-22, IV precedes the

—g — g-flat

a-flat. A smooth connecbetween IV and V|/V is possible because the third and fifth of the IV chord {B-flat and D-flat here) are common to V^/V. In typical fashion, the cadence chord, V, appears on the strong beat and is preceded by V|/V on the previous weak beat. This cadence may be considered as a variant of the simpler pattern, IV V, here modified by the insertion of an intermediate V|/V. The introduction of the chromatic leading tone (here g), and the presence of the dissonant elements in the Mm'' chord {g d-flat and e-flat d-flat) increase the sense of inevitable move-

is

heightened by the chromatic ascent of the bass

tion

—

—

ment

—

to the cadence.

Ex. 24-22.

Schubert

:

Moments Musicaux, Op.

n

^m

^m

94, No. 6.

n

1 iz^

SP

3

is:

Ex. 24-23 contains another treatment of the V^/V. Here the chord appears in

Such an approach is quite smooth, for there are notes in common between the two chords. As in Ex. 24-22, there is an acceleration of harmonic rhythm in the approach to the cadence. Notice also the simple C D E-flat. step progression in the middle pattern, A-flat B-flat second inversion preceded by

vi.

—

Ex.

24-23. Beethoven: Piano Sonata Op. 13,

Adagio cantabile

II.

— — —

—

^

—

—

—

—

397

SECONDARY DOMINANTS

As discussed in the previous chapter, the dominant of the dominant is sometimes used in the minor mode to embellish the minor dominant chord. This is the function of the V|/V in Ex. 24-24, in which the minor dominant is introduced quite unexpectedly as the cadence chord of a passage in which the major dominant has prevailed.

Ex. 24-24.

Beethoven

:

Piano Concerto No.

Op.

c minor,

in

3,

37,

^ ^^

Allegro

^ ^^ ^ i

rm

f

= if

mf

ms

?

2i'\,

rwtmW-

m

j-^,

W— at J

1;^

r

1,;

lu

— ?-

—

r

-^1

y

y Z

-

.

^

KlJ'

_,L^

t_?Z_

*-— -V#-

*-

'f

1

J

^

3-#

4?

t

w

J

—#

#?

?

^^^

^

1

'y

r

V4 Vv

Ex. 24-25 and Ex. 24-26 show inversions of the

Ex. 24-25.

Schumann

:

Albumn

Moderate semplice

^

S

Ex. 24-26.

Brahms

:

Tranquillo

for the Young, No.

^ J

=

V'/V within

phrases.

I.

96

Tragic Overture, Op. 81

,

^

f^

>

398

SECONDARY DOMINANTS 24-26. continued.

Ex.

fc^^^ ^g

i

^8~

§

dim.

m

331 ini

jOZ

In Ex. 24-26 the

and

it

V|/V

occurs on a

weak

ISt

un

beat. It

is

preceded by subdominant,

V. Through the use of double suspensions over the dominant measure 3, the texture maintains linear interest, while prolonging the

resolves to

pedal after

dominant

for six measures.

In Ex. 24-27 the composer has combined two

lines

which imply the progressions

indicated.

Haydn: Symphony No.

Ex. 24-27.

m ^M

Allegretto

85. (La Reine),

m m

p

£

^

iS;

III.

#

,

in the fifth

measure of

?

? this

p

p

V§

Vi6

The V|/V

^m

^

i

V^

s/v

excerpt

is

Vi

ii6

I|

V

I

clearly outlined, having

preceded by a fleeting suggestion of vig and followed by by a succession that cadences on the tonic, B-Jiat.

V.

This in turn

is

been

followed

Dominant of the Subdominant

The dominant As previously

is

frequently the tonal goal of a phrase or larger melodic section.

indicated, the tonal

movement

to this goal

inclusion of secondary dominants, for example,

V/V. This

is

by the turn, can

often intensified

relationship, in

be strengthened by the addition of other secondary dominants which precede the

V/V,

for

example, the

V^IV

and the V^ii.

399

SECONDARY DOMINANTS 24-28. Mozart: Piano Sonata, K. 279,

Ex.

II.

Andante

^m

&7:sj^

p

')Wi\

J^ ji^''^^ ll

1^ I T3—\

^^

\

i

%

^

i V7/

The domi nant ro ot

is

seventh of the

5/v

subdom ina nt (VjIV;

V^/iv)

from minor to major, thereby creating the leading tone of

a rhord whose

iv.

Dominant of the subdominant. b)

a)

i

is

appearance in minor requires a change of the tonic chord

th e tonic. Its

Ex. 24-29.

V

V6/.

IV

^IV

tf

4t

3i:

* ife ^

e-

W W

s

_Q_

Ml

331 -e-

V^/

E:

V6.

^IV

/rIV

ll^

4

c

_Q_

331

-H-o-

:

V4/

VV,

^VlV

7IV

^

T^

/iV

3/i

V4

ViV

/

2/iV

Arr

i^^D

IV as V does

However, a "dominanttonic" relationship is not so evident between the major tonic triad and its subdominant until a minor seventh is added to the former, thus creating an unstable sonority on the tonic. In terms of roots,

Ex.

24-30. Handel

:

m

l t ,i

stands in relation to

I.

^

-tSl-^

r

r^

5

\^

to

Piece for Harpsichord.

^=f^

fct

^

I

^ J

«

^S

J

fi

^ ^i # IV

^'/iIV

-zn

^

^

^#

^ ^

33

^

400

SECONDARY DOMINANTS

In normal resolution the dissonant elements (minor seventh and tritone) are treated as were those of the V'/V.

That

the tritone as an

is,

generally expands stepwise, just as a diminished tions are

made

in order that the

augmented fourth

contracts stepwise. Excep-

fifth

chord of resolution be a complete triad

(see

Ex.

24-3 lb), or because of other considerations, such as a desirable voice doubling

Ex. 24-3 Ic).

(see

of dominant of the subdominont.

Ex. 24-31. Resolution

i

^^(c)

(b)

(a)

-e-

^

:xx:

-o-

$

F^o=

^ ice:

_ti_ >o-

„(d)

L[

|

-o=

o F:

V7/

V7/.

IV

'/iv

^

-e-

o

IV

b:

VO

'^/iv

_Q_

an

m

zee:

i

"-» o

^^

o

(irregular) ti

«^^"^

^=^

ti

3s;

^TT

G: V4/

iV

(f)

EEJI

+4

(irregular)

-»o

(e)

fc-&-

V4

IV

IV6

a:

•^/^

/iV

V4/

iV6

TiV

Uses of the Dominant of the Subdominant

The V'/IV is often used to counterbalance emphasis on the dominant and, in many such instances, appears toward the close of a phrase, period, or section. Ex. 24-32 shows the

last

phrase of the second period of a theme, the

first

period of which

—

ended with a transient terminal cadence, V/V V. Through the use of a V|/IV, the subdominant is emphasized at the climax of the phrase. The augmented fourth (c^f-sharp) expands by step to its typical resolution (B G).

—

Ex. 24-32.

Haydn

Presto

:

Piano Sonata

ma non

in

D Major,

^a

i

y

^m

troppo

t§^

w^

III.

±±

m

ig

m V4

ff IVO

/^

On

the other

hand the V'/IV

^

^±k^-±L^

5 16 4

V

also occurs as in Ex. 24-33, at the beginning of

a section before tonic has been established. Although tonic

is

not readily apparent

—

SECONDARY DOMINANTS at the

beginning of

401

this exerpt,

it

becomes clearly established

in the

ensuing mea-

sures.

Ex. 24-33.

Chopin: Mazurka, Op. 41, No.

2.

Andantino

^^

P

In Ex. 24-34, the subdominant is stressed by the V'/IV, and by the prominent melodic use of the interval d g at the head of the motive appearing in measures and 3. Any tonal ambivalence between d and g which may have arisen by measure 4 is soon dispelled by the cadence pattern, iig I V^ I, in measure 7-8.

—

1

— V—

Ex.

24-34. Bartok: Little Pieces for Children, Vol.

I,

No.

2.

—

Copyright by Edwin

F.

Kolmus.

*

w-m

Reprinted by permission.

Molto sostenuto

^g

*ptt

^

mp

^-^-0-

=iF

u

te^

D

Because of the

common

:

%

V7/

,

pitch shared by

respectively), these chords often

^ ji

i

dole

appear

IV6

I,

mm

IV

F'

Vi

V'/IV and IV

in conjunction

i ft^ iic

V

(root, root

IV6 4

and

I

fifth,

with a tonic pedal. This

402

SECONDARY DOMINANTS

procedure of a

offsets the

weakening of tonality that otherwise can

result

from the use

V^IV.

Chopin

Ex. 24-35.

6,

No.

4.

ma non troppo

Presto

The V^/IV

Mazurka, Op.

:

in Ex. 24-36 appears in conjunction with a shorter tonic pedal, and_

examples gives way

as in the previous

subdominant

to the

Note the smooth introduction of the seventh of the functions as a passing tone between g andf.

Gounod

Ex. 24-36.

Faust, Act

:

II,

"Salut

I

p

^S ?

^

\

*=i

T^

pf^

t>

Yl

/iv

In Ex. 24-37 the V'/IV rearticulated pedal.

of the seventh,

Ex. 24-37.

xt

^^

:

(J

iffi

m

i

IV«

4

is

preceded by tonic in a passage characterized by a

The harmonic movement

Piano Sonata

=

in

E-flat

to

Major,

80)

IV

is

heightened by the addition

>i*^

f

te ^ra=

I.

mS

M.T.

W

it

I

d-flat.

Haydn

Allegro

where

^m ^

^ ^M^ Ul *=*

f

cresc.

in the tenor,

Demeune."

Larghetto

^m^

V/V

in second inversion.

-

^A-

-r4^n

^T^

#

m

j'^

}U}}

403

SECONDARY DOMINANTS

The subdominant

an important

often plays

frequently appears embellished by

Mass

in

G

cadence chord, and

it

secondary dominant. In Ex. 24-38 a transient-

its

terminal cadence on the subdominant

Ex. 24-38. Schubert:

role as a

is

preceded by

Major, No.

2,

its

dominant seventh, V'/IV.

Kyrie.

Andante con moto

m

s

^ i=4

i

i

^ 1

r

r

Ex. 24-39 is

#

illustrat^es

another cadential use, but in

i

^

f J

9^
i^=^

J-

A

i IV

this instance the

n/„

IV

subdominant

The b-flat pedal underlines the first V^/IV appears. The V^/IV links the two forms of

the penultimate' chord of a plagal cadence.

two measures, above which a the same sonority, IVg and IV, which occur at the phrase's high point.

Ex. 24-39. Schubert: Octet,

Op. 166,

II.

Andante un poco mosso

w^w '^m^-^m ms 1

i

WlTf

5

3W

'JU

^^

^VtIV

p=^^ IVC

(ivo)

I

I

h

5

I

s

r=^ V8

Vk

1

\^ 0\>t»\Z

f iveyt,

IV

I

Viv

There are many other uses of this chord; obviously, any appearance of a subdominant could be embellished by its dominant. The standard "blues progression" of jazz cadences on a V^IV at the end of the first four-measure phrase.

404

SECONDARY DOMINANTS 24-40. Arlen-Mercer

Ex.

^

:

Blues

in

the Night. Copyright 1941

by Remick Music Corpora-

Used by Permission.

tion.

Blues tempo 1-3-

r-5-i

iy hni \

xr

h

,

r-3-i

mifm

s

X5~

^

m p^ £

^

pi

^ ^ii

¥

Bt:

Dominant of the Supertonic

The

relation of V/ii

chord in minor

is

tonic." Its^root

is

is

diminished and does not function satisfactorily as a "temporary

d egree of the

first

its

presence

is

suggest ed by _the

scale (leading tone of 2) that usually

Dominant of the supertonic.

Ex. 24-41.

zssz

lOI

I

and

the sixth degree of the scale,

appearance of the raised resolves upward.

fefe

generally limited to the major mode, for the supertonic

il

ni

Vi

—

-e -o

-(»)-

3nr jQ

_Q_

iEi

=8=

-e^

(o)

ii

(ii)

^

_Q_

(£U_

o

^

jol:

n

o

rO3S=

_Q_

-(o^ (ii6)

V4/

^^)

ii

zsc

fo)fo>-

-e-

CT

A:

V7/

V,

/||

II

As indicated

earlier, the

Vf/ VW

V4/

ii

ii

VW

presence of the raised

first

ii8

vii

degree of the scale (leading

tone of 2) suggests the V/ii. In Ex. 24-42, the c sharp in the second measure is the third of an arpeggiated A major triad which moves to D. Similarly, a secondary leading tone

Ex. 24-42.

is

formed

Brahms

:

in the

penultimate measure by the F-sharp.

A German Requiem,

^^

Section 6.

Allegro

3

^

mf C:

fffHtf-

zm

^gf#^ "/«

P

^

^^ - M

XL.

P

f=-

W

ih-t

^

^

V/

/v

•

•

-

V

^m J#

a

405

SECONDARY DOMINANTS Uses of the Dominant of Supertonic

The at

V/ii

is

almost entirely limited to the interior of phrases.

cadence points, except rarely when there

It

seldom appears

a transient-terminal cadence on the

is

supertonic.

Ex. 24-43.

Schubert: Octet, Op. 166,

IV.

U^lU ^ w^ ^^ i,t iJ ^.i m g

IV

tf^

y

i w

?

f

V7

^ "

V>ii

1^

^

y

f

V

I

^^

i

V7

v'/v

tr

^p

Ma f^^ of

ii

as in

^^

yjtl

±

16

sequential root pattern 6

ment

A

1

?

v§

The

i

£? y

i

— 5— 2,

1

frequently involves a dominant embellish-

measures 2 and 3 of Ex. 24-43.

noteworthy exception

to the foregoing principle

appears in Ex. 24-44 in which

the Vjii serves as a climactic cadence chord (measure 4).

Ex.

24-44. Chopin: Prelude,

^

Op.

28, No. 6.

Andantino

^

i i

#^-» i

i

i

i

^^¥^ ^

:2i

ii7

V9

V7

I

M-

nm

¥

406

SECONDARY DOMINANTS

Although the V/ii

is

often preceded

purpose. For instance, vi

is

used in the

by

I,

other chords

Haydn

may

be used

for this

excerpt of Ex. 24-44, and IVg in

Ex. 24-45, in which the secondary dominants are treated sequentially.

Ex. 24-45.

Schumann

:

Symphony No.

3

in

E-flat

Major,

(J^=116)

V4

V4

TVS

,

Viv

An

interesting use of the Vg/ii occurs in Ex. 24-46

where

it

ing chord, again forming the initial part of a sequence (VJii

iis

.

Mi

appears as the open-

—

ii)

that

is

completed

by the pattern Vg/I.

Ex. 24-46.

Mozart: Piano Sonata,

V8/.

It

(V|

is

—

K. 283,

V6

ii

III.

CTIJ

I

not unusual to find the V'/ii used in sequential patterns such I), as

Ex. 24-47.

as, (V|/ii

Mozart: Piano Sonata

Major, K. 333,

B-flat

I.

i #-i»

vrB

,jj'..trr,t7r

—

f»

tt

£^

• *

|

'U p

ii)

exemplified in Ex. 24-47.

Allegro

V-iJ

—

w

p

^3^

^V^

"

m w

21

Vi

^

*

ivg

3

vii°8

407

SECONDARY DOMINANTS

The

V/ii

is

often used to prolong the action of the

ii

chord, as in the beginning

of the second phrase of Ex. 24-48. In this passage the V^/ii appears between successive occurrences of the first

ii

three measures of the

Ex. 24-48.

and iig. This treatment parallels the phrase, where I and Ig are linked by V^.

in the forms of

first

Beethoven: Piano Sonata Op.

10,

ii

No.

3,

Allegro

Similarly, V/ii

is

used to predict the arrival of

progressive cadence occurs

change

is

on

V/ii.

ii.

However,

in this instance a

In such a context, the impression of actual key

sometimes considerably stronger than in the V^/V transient-terminal

cadence.

Ex. 24-49. Schubert: Octet,

m

^

Op. 166,

i

rr

pp

i?

^ ^

f

P '

^ w

w *

Vii

In

many

instances the temporary "tonic" of the V/ii

is

altered, so that

becomes a secondary dominant (V/V). In Ex. 24-50 V|/ii progresses which in turn resolves deceptively.

to

it

too

V'/V,

408

SECONDARY DOMINANTS

^m

Chopin: Nocturne, Op.

Ex. 24-50.

Andante

fe

mP ^C

'^^"i,

2.

P-

O'D^

.

0. ps* »

r^^yt

^fg

cP

Ir

No.

9,

^

£f f^fhfe

i

tP C^ vy

^>v

.

V

vi

'S/i

„

/v

—

# *

„

>fr

-"

-

#

V4/V> V7 M\ /v

Although Ex. 24-51 represents a conventional progression of the V'/ii, it does contain an unusual twist in that the resolution is delayed (triple suspension) until the third beat of the fourth measure.

Mozart: The Magic

Ex. 24-51.

Andante

t

Flute, Act

II,

"March

of the Priests."

^m

i

*

%

f

sotto voce 71

9-

-m-

^V.

The

V^/ii in measure 6 of Ex. 24-52

However, it is followed not by ii followed by V|/ii which resolves

Ex. 24-52. Verdi

:

approached in a conventional manner. but by its own dominant, the V'/vi. This is then

to

is

iig.

Requiem, Requiem and Kyrie.

^

Andante

'^m F

ppp

dolcissimo

i

f

J-.

„

J]

TTTf

^ r

»c;"^ r

^

H^z.

Vi7

VT /v

V7

21

i

—

:

409

SECONDARY DOMINANTS

-^^ 1

—

3 i

M

-o*

T^ W7

Vt

V4 V4

/V

To

the scale. (2) /ii)

( 1 )

The

—

oj^ution

as a

and

I. is

t

he

first

in

many

to supertonic,

it

patterns. (7)

may serve The

is

instances

it

is

some

is

tlie

third of the

(4) Xh.e

chord of a phrase:-

"prolong" the supertonic or appear

V/ii° rarely occurs in the

is

usual les-

to \' l\L (5) In rare instances it

first

(3) It

form, of the basic progression

approached throughj.

but occasionally tO

th e sixth degree of.

degree of the scale be raised chromatically.

cadence chord, or even as the

tr^tments

w

dominant of the supertonic certain

root of the V/ii or V/II

often u sed in phrase interiors in connection with i i

^«-

4

J

'

create the leading tone of supertonic (which

rec[uices..that

V'^

^^

Vii°i

iio

2/-

the previous presentation of the

points should be apparent.

V

=3

331 331 -e-

311

rxsz

From

^^

qg

3;=

(6)

appears

In other typical

in various

sequentiaF"

minor mode, a use that would require

mutation of the supe rtonic chord (thus y/ii). Exercises

For more detailed assignments see Materials and Structure 0/ Music I, Workbook, Chapter 24. 1.

Find examples of the use of secondary dominants

2.

Scan new music rapidly, looking for chromatic inflections as possible indications of secondary dominants.

3.

Indicate the major and minor keys in which a-c-sharp-c-f might appear as a .secondary dominant seventh, and the appropriate identification of each. Practice spelling V/V and V^/V in various major and minor keys. Consider various pitches as root, third, fifth or seventh of V"/\' and spell the chord and

4. 5.

resolve 6. 7.

8.

it

to

music you perform.

V.

Use a V'/V in a transient cadence in a four-part choral texture. Use a V'/V in the interior of a phrase for piano. Compose two phrases of music using Ex. 24-1 as your model. Employ (or (V^/V).

9.

in the

Arrange

for four

at least

one

woodwinds.

Analyze some of the following, indicating keys, chords and non-harmonic tones

Haydn: Piano

Sonata

in

Mozart: Piano Sonata

in

D major. D major.

Beethoven: Piano Sonata, Op. 26, String Quartet,

Op.

18,

III (1-8) III, var. 12, (1-9) II,

No.

(1-8) 5,

IV

(1-12)

Op. 114, IV, (1-8) Chopin: Mazurka, Op. 56, no. 2, (33-38) Wagner: Wach Auf {Die Meistersinger, Act

Schubert:

Quintet,

III) (1-10)

V/V

: :

I

:

SECONDARY DOMINANTS

470

10.

Spell (from the bass up) the following: a.

v6/V,

b. V|/ii,

d.

V4/IV,

E

e.

viii, A-flat

V^/V, . B Find examples of secondary dominants of dominant, subdominant and supertonic c.

11.

G

c

V4/iv, d

f.

2,,

in

the music for your instrument. 12.

What

is

a.

the third of each of the following:

V|/V,

c sharp

b. V|/ii, B-flat c.

13.

e.

V7/V, B V|/IV, D-flat

f.

Vi/ii,

d.

V|/iv, g

Make an SATB

A

setting of the following

I—V|/V—Vg— vig—V/ii|—li— 16—V7— I—V7/IV— IV6— 14.

Using Ex. 24-48 as a model, compose a period (4 part texture, note the sequence) using at least one each of the following

V3/V 15.

16.

17.

V|/IV

V|/ii; arrange for 4 brass.

Using the sequence pattern (V|/ii— ii) (Ve/V—V) (V|— I) (V/IV|— IV) construct a phrase in which motivic treatment is a characteristic feature. Add 2 phrases to those in Ex. 24-49, using dominants of dominant and subdominant. When completed arrange for flute, oboe, clarinet and bassoon. To continue the study of secondary dominants, analyze several of the following works, indicating key chords and non-chord tones

Haydn

:

Mozart:

Symphony No.

6, 111. {\

Piano Sonata, K. 284, Piano Sonata, K. 332, String Quartet,

K. 387,

Beethoven: Piano Sonata, Op.

7, I,

-18) (1-10)

I. I.

I.

(1-12) (1-6)

(59-61)

Op. 18, No. 5, III, (9-16) 7, Op. 21, II, (1-26) Bagatelle No. 3, Op. 33 (1-17) Ich Liebe Dich (song) complete work Octet, Op. 166, II, (1-5) Octet, Op. 166, V, (trio) (1-16) String Quartet,

Symphony No.

Schubert:

Chopin:

Symphony No.

5,

IV, (1-16)

Mazurka, Op.

6,

No. 2 (9-16)

Prelude,

Op. 28, No. 3 (1-34)

Nocturne,

Op.

37, (57-64)

Conclusion

25

,f

Secondary Dominants

Dominant of the Submediant

(V/vi; V/VI)

There are two basic forms of the submediant chord, vi in major and VI in minor, with each having a related secondary dominant whose root is the third degree of the scale. The V/vi (major mode) requires that the fifth of the major scale be chromatically raised. The c-sharp m Ex. 25-1 is the third of a chord whose root is a,

the third degree of the /major scale.

tioning as a leading tone to

d, is

The chromatically inflected note, funcan important member of a major-minor seventh

chord that has a dominant relation to the submediant.

Ex. 25-1.

Dvorak: Symphony No.

7,

in

d Minor,

Op. 70,

II.

Poco adagio

^^

p'

^

?r

^^ i

^m ^^ nig

r^^n^I

f

412

CONCLUSION OF SECONDARY DOMINANTS

There are no new problems of resolution for the V'/vi, because same way as each of the secondary dominants discussed earlier.

it

resolves the

Uses of the Dominant of the Submediant

The V/vi

frequently appears early in a phrase following a dominant or tonic

—

—

When

preceded by the dominant, as in the progression V, Vg/vi vi, the result is an elaboration and chromatic reinforcement of the deceptive progression V, vi through the interpolation of the Vg/vi. chord.

—

V— V7— Vl/vi—

Ex. 25-2a. Progression

vi.

LMi S

* ^^ C:

V

V7 Vg/

Vi

yvi

Ex. 25-2b.

Brahms

:

A German Requiem,

Section 6.

^m^

Allegro

^

I

Pf

J-

4

WAk

p^

p Ie

^^

—

vi in

^

,jTJ

^ f

i

iRl

p

V/ V

Vi

/v

/Vi

A similar chromatic

n

i^

V6V

C:

J

4

connection

{a

—

a-sharp)

is

involved in the progression Vg/vi

Ex. 25-3. Melodic repetition and variation are important features of the

organization of this passage.

Ex. 25-3. Bartok

:

Little

Pieces for Children, Vol.

I,

No.

9.

Copyright by Edwin

F.

Kalmus.

Reprinted by permission.

Poco piu vivo

m p

s D:

>

^ V7

n

m ir

lis ^%i

\i

^'

V7

V7.

yrv

CONCLUSION OF SECONDARY DOMINANTS

^

t

413

4t=i:d

sRIV

The

progression of tonic to submediant

is

common,

particularly at the beginning

of a phrase, and the V|/vi frequently serves as a connecting link between the two.

Ex. 25-4.

Wagner

:

Lohengrin, Overture, Act

Sehr Lebhaft

^ mr nI

i 0-m-

t i=y

r

nf

s

^=^ $

t^

«-

^^ ^ ^m ^ i

i

l>y

J.,

m/^

ij

j

dim.

it

f=f V4/

I

i

EI

^— &

V7

Vi

>V

mode no chromatic

In the minor

*^

i

^^^M *j

,i^=M

V/VI, but the seventh chord (V7/VI)

alterations are required for the triadic

form

necessitates the lowered second degree of the

scale.

Ex. 25-5. V7/VI,

* ^ a:

in

Dominant of the submediant.

ff

331

VI

"'M

VI

In measure 6 of Ex. 25-6, the lishes the

submediant.

b-Jiat

creates the seventh of a chord that embel-

CONCLUSION OF SECONDARY DOMINANTS

414

25-6. Mendelssohn:

Ex.

Andant e

Song Without Words, Op.

2.

es pressivo

^

ti mf

'imn

J

i

fl

i f

f=TT

TfTTl

m ^

P i6

^

T

r i

dim. if-

if-

-^

i

fa^P

Sf^z^

*

r

VI

^Vv,

The dominant by

No.

19,

.

,.rri> iife

S

=g

r

of the submediant in the interior of a phrase

is

often preceded

tonic or dominant, as the previous excerpts have illustrated. In Ex. 25-7 the

Vg/vi

is

approached through the dominant and prepares the way

to the half

cadence.

Ex.

25-7. Verdi: Aida, "Su

Allegro

a^

0-

¥

Except

Nilo," Act

m fmfT

for occasional

I,

Scene

\

m

WTf

j^ p-if

I.

^^

«-^

I

mf 4'

Del

!

> >

n

Phrygian cadences

A

A

A

'^

i in the

major mode,

it

is

unusual to

cadence chord. When used as in the next excerpt the harmonic drive from the progressive cadence on the V/vi result is to the transient-terminal cadence on V. find the V/vi serving as a to strengthen the

415

CONCLUSION OF SECONDARY DOMINANTS Ex.

25-8. Brahms: Liebeslieder Walzer,

^^ ^ Slow waltz

^=^

Op.

No.

52,

^^

si

JJ ')ah>ii

I

r

^

J-J ^

f

ii ill

p^

r

(vocal parts).

8,

p

f^ Vii°6

V

Vi6

ii

In the next quoted passage the submediant chord is prolonged through its repetition and its attendant secondary dominant. The result is the creation of a momentary tonal "cell" on vi prior to the progressive cadence on V.

Ex. 25-9.

Wagner

Siegfried

^ ^m :

Idyll.

Con mote ma mi

Violin

I

Violin n

Viola

Cello

tranquillo

m

U

^

la^ 'r-mi

i

^^ P

W

i

^ ^ P

^ A ^^ §

Ptt

-o-

SI

-iS>

(^

Vi

F

3

V/vi

-e-

cr

331

^

J ii^

it

sm ^^

J

^^ W

V/„. Vi

—

CONCLUSION OF SECONDARY DOMINANTS

416

Frequently the chord to which V/vi resolves

namely the

V/ii.

The

—

is

itself

a secondary dominant,

normal root resolution of degree of the scale. Such progressions

V/ii) represents a

relation (V/vi

the V/vi since the root of the V/ii

is

the sixth

are often found in harmonic sequences.

Ex. 25-10.

Mozart: Symphony

in

C, K. 425,

III.

^^ ^^

Menuetto

i /

^j^i k

^m

sF¥^

^y V7/_. '>iv

mmn m *

4

j^

C3

^

e

IV

^«

r

m-

^^ V6

I

i

^ V7

I

I

In another similar treatment a V|/vi proceeds to V'/ii the effect of the dominant seventh of submediant is enhanced by the accented passing tone d. ;

Ex. 25-11. Verdi:

Requiem, Agnus Dei.

m^

Andante

$

e^

is:

04^u

m

i>P

Sm

ZEE

V7/ /IV

To summarize

IV?

^

¥'l^

^^ —

m

331

«;?

•

Tt

•

V4,

Xi

V7/

/"

V4^

^

116

ii

a

i

^*F

V7

Vi

ill

P V7

I

ii

dominant of submediant has as its root th e third_ degree of the scale. Its presence in major is suggested by the appearanc e of the raised fifth degree of the scale, in minor by the lowered second degree. This secondary dominant frequently appears at the head of or within a phrase, pi briefly, the

417

CONCLUSION OF SECONDARY DOMINANTS

and resolving to vi. It sometimes occ iirs^in the .transient-terminal cadence Vl/yi vi, and as the final chord in a Phrygian cadence pattern, preceded by ii,. It is often involved in sequential passages in wjhuch it sometimes prec edes the V/ii. by

I

or V,

—

Dominant of the Mediant

(V/iii

V/lll)

;

As is true of the submediant chord, the mediant chord usually appears in one of two forms, iii in major and III in minor. Each has a related secondary dominant whose root is the seventh degree of the scale. To introduce a V^/iii (major mode) requires the chromatic alteration of two diatonic tones; the second and fourth scale degrees both must be raised a semitone. In minor, the root of the V'/III is the subtonic of the scale.

Dominant of the mediant,

Ex. 25-12. Vy/iii

b)

a)

i

^

^ a *

rjsi

P5

w

;n= L F:

^&

L.T. I

—

1

(of-

3x: -e-

V7

The

331

Ty

ZSSl

ICC

n

V7/ '^i

III

>fi III

By

-e~D"

mode) the leading tone of iii is created. degree permits a perfect fifth between the root and fifth of

raising the second scale degree (major

raised fourth scale

the chord (see Ex. 25-12).

Ex. 25-1 3 contains a passage in which V'/iii follows Vg. Notice that this particular

form of the progression uses the

common

tone between the two chords as a kind

of pedal bass.

Ex. 25-13.

Brahms: A German Requiem, Section

4.

418

CONCLUSION OF SECONDARY DOMINANTS

Uses of the Dominant of the Mediant

As exemplified

and Ex. 25-14, the V^iii frequently appears in the interior of a phrase, generally resolving to iii and frequently being preceded by V or I. In Ex. 25-14 the step motion up to the dominant climax in the top voice is given added thrust by the chromatic alterations that yield the a-sharp as a fifth in Ex. 25-13

of the VViii.

Ex. 25-14. Schubert:

Symphony

in

B Minor,

Andante con moto

^ ^

1 ^m

*-M

^m ^m **

^^

m

V4

f

m^

E

III

3/..

The

inverted forms frequently occur in the course of a phrase and thus minimize

the strong root progression. In Ex. 25-15 the V^/iii

used in a short sequential

is

pattern, measures 3-4 being a melodic-harmonic sequence of 1-2.

Ex.

25-15. Beethoven: Quartet, Op. 18, No.

1,

III.

Allegro molto

1

s

Pt

zc,

p

^

m^

¥=*

V i-

B 7^

')\

r

i

>

III

One

~w-

of the

V/ii

§.

v^i

^ n

^ V7'/y

^X;

common

^

1r

i ^E^

functions of a secondary

cadential patterns. Such a use of the V'/iii

may

dominant

IS

=!»

^

"iAi

#

PS

9-

is

m P

III

^ f fV

£E£

to reinforce various

be found in Ex. 25-16 and Ex. 25-

r

CONCLUSION OF SECONDARY DOMINANTS 17.

419

In each instance the period closes with a transient-terminal cadence on

followed by an immediate return to tonic

pare the treatment of the

first

upon the

Com-

repetition of the period.

and second phrases of both examples. Also note that

examples the V/iii appears more decisive cadence on the iii chord. in both of these

Ex.

iii,

in root position, thereby creating a

25-16. Beethoven: Quartet, Op. 18, No. 3,

Allegro

iiis

Ex.

25-17.

Haydn: Symphony No.

^

t

iii

V^y...

iii

88, IV.

—

~»

m

i

If^^

# P V^/..

Hi

III

The

cadence of Ex. 25-17, a transient-terminal cadence on iii, implies a convincing modulation to b minor. However, upon the immediate return to G major final

that occurs, the tonal organization

strengthen the

iii

becomes quite

clear: the V/iii has

been used

to

chord.

Through an extension of the process, the "tonic" of a secondary dominant may become a secondary dominant in its own right. If this happens after V/iii, the chord of resolution is V/vi or V^/vi rather than iii. In Ex. 25-18 a dominant of mediant is

used as the head of the second phrase.

— Vg/vi

It

appears in the progression V/vi

(measures 6-7), a relation that parallels the progression

sures 1-2) of the initial phrase.

I

—V —

—

Ig

V/iii

(mea-

420

CONCLUSION OF SECONDARY DOMINANTS

Ex. 25-18.

Beethoven: Piano Concerto No.

4,

Op.

58,

I.

Allegro moderate

^

fc

^ 1=J

P?re

'W~w

f=i

£

k

:s

f=«

•-•-•-^

S

21

^

is:

^t#

^-4-»

% % % %

f

i^iiiii

pp m~0-

^

\1S

r

^.y.

V/

V/..

V/.. /ii

Vv, Vi

^^^t^ /vi

/ill

^/1i

^'/v

i

IS

"XT

pp

e/':

i

J-

-e-

IE

^

za.

In a different context the dominant of the mediant might occur in connection with a transient cadence on (major) III, again exemplifying the mutation of "tonic." In Ex. 25-19 the III does not function as a secondary dominant, for progresses to Ig rather than to

Ex. 25-19.

Beethoven:

Trio,

its it

vi.

Op. 70, No.

5,

III.

5^S IV

V|^,

®

m

16

As previously mentioned, the root of the V/III in the minor mode is the subtonic scale degree, hence a conventional fifth relationship exists between the roots of V^III and III.

CONCLUSION OF SECONDARY DOMINANTS

421

25-20. Chopin: Nocturne, Op. 55, No.

Ex.

^

1.

Andante "^

—r^

^^

ft^

'H\?<''

F

'ij>

f-T p

t

\

"

^Vm In Ex. 25-21 the V'/III

is

so

^

VS

prominent that

its

role in this transient-terminal

cadence on III becomes that of supporting dominant in a more structural sense. The pattern of harmonic movement introduced in the first measure is interrupted

by a two-measure appearance of V^/III, followed by III, which persists for four beats. It is the extension of the phrase its fifth measure that accommodates the

—

harmonic assurance that V" chord ably impresses fifth

Ex.

C

not, after

is

this

upon

—

to

all,

be regarded as a new tonic.

the listener during the final two beats of this

measure.

25-21. Schubert: Moss

in

G

Major, No.

2,

m^m

Voice

Chri

-

ste

e

Kyrie.

r

^ lei

-

son

nri

Piano

^ lei

-

a:

J

m

Vg

i6

i

^^Im

m

""'A

zpi

^

son

Chri-ste

t t t t t

'^^>

The

y

^

U^

i iit i i

M

'

^ttt

^fe^ ^=ff=^ P

W

Vi

V^

I

-^

P^P ste

e

422

CONCLUSION OF SECONDARY DOMINANTS

The V'/III

in Ex. 25-22 is used in the approach to the transient-terminal caon III, dence measure 4. If the subsequent phrase continued in G, the entire first phrase would represent the modulatory pattern that first establishes the new key.

Ex.

25-22. Beethoven

m s

a

ty

n

if

-=

P=^

e:

Piano Concerto No.

:

4,

m

:$

r

iaI V

V42

K

i

V6.

i6

m1 ^

I

f*=F

V?/

IV

5X,, ^/iv

V7

HI

i

iV

ii6

:

J

i6

V7

4

/TTr

\

fi

Because the \"'III in minor is identical to the V" of the relative major, it frequently is used to exploit this "duality." In Ex. 25-23 the V^/III supports a tran-

on III at the end of measure 4. The harmonic resources of ^ minor have been expanded here by this vacillation between these two closely related keys, each tonic is in turn supported by its own dominant. Since the passage does begin and end in g minor, the fleeting focus on B-Jiat as temporary tonic is best regarded as more a prolongation of the mediant than a true change of tonic. sient-terminal cadence

Ex. 25-23.

Beethoven

:

Andante ^fcji

t

9—t i^3

^

Piano Sonata, Op. 79,

^ ^

m

?

? f-^'

•

'

O

• '

^

V 4-^

S

s

^

—0-

-0

-0—0-

-0—0-

-^z^

-»-^ ni

"'/w

J'r

-^-^

m

^gr

p

r

g.ij^^

m d

-it iis

V7

CONCLUSION OF SECONDARY DOMINANTS

423

dominants are introduced quite unobtrusively, but tlie opposite is true of Ex. 25-24 which follows a progressive cadence on the dominant. Here the \7iII makes an abrupt appearance following the dominant (chi'omatic thiid relation). The resolution and the subsequent progression to tonic inaiu' instances secondai)'

III

accomplished

is

which

Ex.

in a

stress the III

smooth, conventional fashion, as

chord as a temporary

25-24. Schubert: Impromptu, Op. 90, No.

previous examples

in the

major key.

shift to the relative

1.

Moderate

in

Vtin

A number mediant.

of important points have been

It is

a chord whose root

is

ii°B^iV7)

made about

tions are required for the pitches of the \

foi^rhe V'/TII.

a semitone.

The chord

No

is

V4

i'J

the

"

ui: the

major,

second

alterations olihc ualLUcd

used most

two

io

4

3

V7

i

dominant of the

the seventh degree of the scale

of the majo r mode, subtonir of the minor mode. Tn

n^ml be raised

V

—leading tone

rhrnmafi<;;. altera-

an,dL-fQucLh..scale d£gre.es_

minor

l\iiically in the interior

scale are required

of phrases preceded

and followed by mediant; to reinforce the transient-terminal cadence on the mediant in minoi", the progressive qadence (or so-called '"Phrygian Caderue""; in major; in progressions in which the mediant chord itself is altered to become a secondary dominant (\'/vij or to exploit the inherent duality betw een \'" (relative major mode). t he V"/III (tonic minor mode) and the by

\

or

I

;

Dominant of the Subtonic This survey of secondary dominants would not be complete without brief mention of the

V/VII

in minor. Since the leading-tone

therefore never functions as a temporary tonic,

However, a major

its

chord

(vii°) is

diminished and

secondary dominant

is

not used.

on the seventh degree of the natural minor scale (subtonic) may be embellished by its dominant, the V^/VII. In Ex. 25-25 note that the V^/VII is used in a sequential pattern that begins in measure 3 and terminates in measure 6. Observe also the jolting effect of the root relation (tritone) in the progression V^/l>n V'/V, in measures 6-7, in spite of the very smooth motion o^ g-flat g-natural in the melodic line.

—

triad (VII) built

—

.

424

CONCLUSION OF SECONDARY DOMINANTS 25-25. Chopin

Ex.

:

Mazurka, Op. 67, No. 2

Cantabile

^m

Irregular Resolutions of

Thus

An

/S.VI

/''III

/v

Secondary Dominants

our discussion of secondary dominants has been concerned primarily with "regular" resolutions. By definition, a secondary dominant stands in a fixed far,

harmonic relationship fourth

up or

to

"secondary tonic," a root relationship of a perfect

its

down; and

perfect fifth

realization of this relationship

its

by

(i.e.,

the case but the chord of resolution

harmonic function

determined by the

is

When

regular resolution).

its

is still

be identified as a secondary dominant. Progressions of

as irregular resolutions.

Ex. 25-26.

^

F: VJ

^ I«

r

V«,

In Ex. 25-26 the

iii»

V|/V

is

not

member sonority may

this

kind are regarded

such examples are shown in Ex. 25-26.

Irregular resolutions

P m3 f:

Two

is

diatonic or a clearly related

thereof (another secondary dominant, for example), the embellishing still

such

of secondary dominants.

f

i it

i

f

vi

10

V

&

1

S *

s f T^ I V4

16

Yl

f

r

^ V6/

Vi

m k ^ 16

V

resolved "deceptively," to chords whose roots are a step

above that of the secondary dominant. In

(a) the

chord of resolution

is iii^,

and

in

425

CONCLUSION OF SECONDARY DOMINANTS (b), V*/vi, the root

of each being the third scale degree. This

but one type of

is

irregular resolution; others will be discussed later in this chapter.

Deceptive Resolution

No

particularly

new problems

doubling and voice progression

arise in regard to

secondary dominants; the principles established

in deceptive resolutions of

for the

deceptive resolution of the dominant chord are applicable. Recall that the of the secondary dominant of resolution frequently fifths

is

is

fifth

sometimes omitted, and that the third of the chord

doubled. In addition, care must be exercised

and/or octaves are to be avoided.

The

if

parallel

dissonant elements are treated as they

are in regular resolution: the tritone, (between the chord's third and seventh)

an augmented fourth, contracts if a diminished fifth. Thus the chromatic "leading tone" moves to its "tonic," even though this "tonic" is no longer usually expands

if

the root of the chord of resolution.

Ex. 25-27. Deceptive resolution of

(a)

«»=^

t

I

m D:

J

J

^

J-

-e"

^

^^ I

i^

y. V

g:

i ^

ZSSl

V6/.. 5/111

I"

IV

fei

-o-

i

^8^

^

1

P iir

vy^

i

m

i

V4

(d)

i

T>^:

-&-e-

T=^

v;iv

(c)

i^

-e-

^

^ I

J

secondary dominants.

V

i frf

e

w_o_

:

I

^^V|^ Ft V6

iV6

ii°6

-e-

—

—

426

CONCLUSION OF SECONDARY DOMINANTS

In Ex. 25-28 the

Ex.

V/V resolves deceptively.

25-28. Mendelssohn:

St.

"O Great

Paul,

the Depth," Voice Parts.

Is

^ Wm ^ ^ ^ Poco

poco piu animate

a

J

r rr 4

F:

As

Vi/^

is

is

25-29 the V'/IV (root

^

"'«

#

v;.^

may

i ¥^ i^

14

(

d) progresses to

"In

ii

resolve deceptively. In such cases the

(root

e).

Splendor Bright."

P

P i

-

')^>ic

Vi

I

31

—>»

P

F5^ zaz

Z££L

VV

D:

V7/ /iv

IV

The

« V

T

V7

'«

Andante

„

f^

usually a form of the supertonic. In measures 3-4 of Ex.

Haydn: The Creation,

25-29.

i.

r

p

true of the \"/\', the \''/I\' also

chord of resolution

Ex.

i^P

..

IV

seldom resolves deceptively, particularly to a diminished triad on 7. However, it is found occasionally preceding ''\T I, a major chord built on the subtonic of the major scale. In Ex. 25-30 the chromatically raised first degree of \'/ii

the scale (E-natural) follows tonic pitch.

The

its

"leading tone" tendency and resolves to the super-

effect of the deceptive progression to ''VII,

and the attendant

disturbance of the tonality caused by the extended duration of''VTI lified

by a clear return to E-flat.

The

effect

is

is

later nul-

that of a brief '"region" based

on a

tonic of D-flat.

Ex.

Haydn

25-30.

:

Piano Sonata No.

3,

1.

Allegro

^ ^

hi

dim.

Vi

^

P

.

I ?VII

^^m

i

^

427

CONCLUSION OF SECONDARY DOMINANTS

ft »F3t»

i

mI

m^ A to to

i

deceptive relationship

is

dim

^^

vJ^Jj^Jj^

j

m &-^3 s

H |P

li

#^

^^

found between the V/vi and

its

p

irregular resolution

V. As in Ex. 25-31. this progression frequently creates the effect of an approach the diatonic chord (IVg in this instance) by a chromatic leaning tone chord

built a

semitone below (B major—*

Ex. 25-31.

C

major).

Beethoven: Piano Sonata, Op. 49, No.

^^jp

r i[Xr

i

\

2,

II.

^& ^^ ^m

m^

^

m

::zi

p:iS»

WW

mm

*^

£

j=±

^

VB/.IV6

The V'/VI

which is an interesting example of a contrapuntal texture (above a bass theme) in which imitation plays a promis

treated deceptively in Ex. 25-32,

inent role.

Ex. 25-32.

—— 1

17,

Bach

:

C Minor.

in

1 ^j=j.

M » F

it

Passacaglia

r

i^"^

.

^ff

P"^^

^S ii.^ ^

^ ?

^ ^^

fl

>''ii-v'j

I

f

##

^

r V7/_

im

XJ % P

£^S*yF"

;v

'/vi

Ex. 25-33

is

particularly interesting because

it

illustrates the use of simple

chords

complex relationships. Note particularly the deceptive resolutions of the secondary dominants, V^vi IV and V'/iii I in measures 3-4 and 7-8, respectively. in

—

—

CONCLUSION OF SECONDARY DOMINANTS

428

The harmonic treatment root Hne

d— — c

is

in measures

1

and

2

a progression of major triads whose

is

and whose two-voice frame

b

organized mainly in contrary

is

motion.

Ex. 25-33. Prokofiev: Classical

Symphony,

III.

by

permission

of

Reprinted

que.

Copyright 1926 by Edition Russe de Musi-

Boosey &

Hawkes

Inc.,

Assignees of the

Copyright.

Gavotte

mw

I fet /

^

^m

^

m m ^

=-*

^i

^^

i

Vi

fP

p

p'f

f jff?

i

U

f

/

fe^

'

j

V? V",. V7/ vy

IV

Y^f /Vi

n f

m

i

$

^

*

ijca gjjp ip^rlr\ ^

vy..

iii

common

9

t

V7V /Vi

Fir

mf

m

t

which the chord of resolution is itself a secondary dominant. In such progressions the secondary dominant still resolves to a chord whose root is a step above, but the chord of resolution is Another

type of deceptive resolution

is

that in

a non-diatonic chord.

25-34. Deceptive resolutions to secondary dominants,

Ex.

m

^

J

LA

G:

If

I

m b)

a)

^^ V!

Yy

V9

i r 4

J

^^ I

I

rvi

two complete seventh chords are used

i "T^ r=^ T A 4 Li i 4 i

p

^Kr

^>^vi

^'

V'

I

in such a succession, they are generally

inverted in a conventional resolution of the dissonance (see Ex. 25-34a) Otherwise, if in root position, one or the other is usually incomplete (see Ex. 25-34b). .

Frequently,

when two secondary dominant

sevenths are inyolyed_in_jJ^decep-

429

CONCLUSION OF SECONDARY DOMINANTS tive" pr ogression, usua

from one chord clioid

may

found

in

rtOt

l

voice loading prorrdurrs arc ignored

to the other in parallel

motion. Although the seventh of the

resolve in a conventional sense, the note of resolution

in Ex.

is

first

usually

25-35 resolves deceptively to V|/vi (measure 8) in the

begun

transposition of a two-measure sequence

move

25-35.

Gounod:

to

measure

first

Observe that the the other, each "line" moving

in

5.

from one seventh chord to the corresponding note of the next chord.

in parallel

up a major second

Ex.

ypi£es.rT).Qye

another voice of the chord of resolution.

The V|/V voices

and the

Faust, Act

III,

"Faites-Lui

Mes Aveux."

Allegro agitato

^^

Voice

i2=^

mm mn

Piano

a:43:

fff

11111

^^ P 2==t ^ i

i

y

I

wm

mill rffff

—V

yw i

y

C:

-

pp

(j

j^pirr

^S/v

A

-''

i

^ PnO

p

P

i

i

O

y

i^

2==:t

^

^k

similar progression involving a V|/iv appears in the second phrase of Ex. 25-

Here the chord of resolution is V|/V whose root previous chord. The accompanying texture moves in 36.

is

a step above that of the

parallel motion, in opposi-

tion to the descending pattern of the melodic line.

Ex.

25-36. Debussy et

Cie.,

Calme

e't

:

Preludes,

Book

Paris, copyright

No. 8. Permission for reprint granted by Durond owners, and Elkon-Vogel Co., Inc., Philadelphia agents. I,

doucement expressif

(J

=

66)

Viv

Vv

CONCLUSION OF SECONDARY DOMINANTS

430 Other Irregular Resolutions

The number and

variety of irregular resolutions

able variation regarding frequency of use. to the

most common

this practice will

and there

great,

is

is

consider-

The subsequent discussion will be

limited

more thorough knowledge of

types with the assumption that

be acquired through continued observation of the works of various

composers.

As a point of departure, consider the various irregular chord (root

c)

resolutions of the

Mm"

appearing in Ex. 25-37. Keep in mind that any one of the progres-

might represent the resolution of a secondary dominant seventh chord in one V|/VI in f tonality context or another. For example, (a) might represent

sions

minor, or

Ex.

25-37.

\'"/iii

Some

—V|

in D-flat major, etc.

irregular resolutions of a

M 6i TT (b)

W^ rr The

V—

(c)

ft

^

m

(d)

Mm7

chord.

(e)

(f)

fr

(h)

(g)

:#S

TT

11

T

^ w f^

irregular resolutions indicated as (a),

Of these three, (b) and two common tones between

(b)

and

(c)

m 11 ^

(i)

Tf

exemplify chromatic

third relations.

(c)

permit the simplest connection because

there are

the

first

chord and

its

chord of resolution.

Note the conventional resolution of the seventh in (a) and (b) in which the roots move down a third, while in (c) (in which the root moves us a third) the seventh is retained in the same voice. In each of the three, the other member of the tritone (the "leading tone") is not resolved in the usual manner, either being held over as in (b) or resolved downward by step as in (a) and (c). It is apparent that such resolutions create various chromatic relationships, and as a general rule, cross relations between voices are avoided. In progression (d)

movement down a fourth) the seventh B-flat ascends as does the "leading tone" E. The resolution by root movement down a second (examples (e) and (f )) (root

permits a conventional treatment of the leading tone

;

however, the seventh

is

retained as the root of the next chord. If the

move

chord of resolution in such a succession

is

a

Mm'

chord,

all

voices

may

motion as in (g), and the "leading tone" usually appears in an inner voice, possibly to minimize the effect of the irregular treatment. The root relation of the tritone (h) and (i), though rare, permits conjunct voice motion because there are two notes in common (one enharmonic relation). The members of the tritone remain unresolved, but there is an enharmonic change in one voice in parallel

or the other.

In Ex. 25-38, Ex. 25-39, and Ex. 25-40, various secondary dominants appear as

.

431

CONCLUSION OF SECONDARY DOMINANTS

important structural units because they are the final chords of transient-terminal cadences. The subsequent chord of each is one whose root is a third below that of the secondary dominant.

25-38. Schubert: Mass

Ex.

^m

G

in

Major, No.

2,

Credo (Voice

Allegro moderato

$

J

3

J

^^

oo

J

J-

=ni

IV

^/1i

and subsequently Chapter 1 1

Phrygian, as discussed in

25-39. Beethoven

:

m T rr 1^

eI-:

^

f

^ ^^ £j

V4/

rvi

Vi

IV

to V'/vi.

The

cadence,

ivg

I

upon

—V/vi

is

IV.

lie

FT rr

^ W

f

i^

r

#^

V/vi which progresses to

r-

I

n''i,l

_CL.

m m ^m ^s

Allegro con variazioni

i

Op. 74,

String Quartet,

is

J

A

f

the repetition of the phrase,

£

J

i

In the Beethoven excerpt the cadence chord

Ex.

Ud ^^ w^ i

J-

zsn

i

J-.

w

i

# JJ

f

zaz

r^rr

G:

j^^ i

m

^—

JJ

J

s

Parts).

^

ri ^ j>p

^J

^ V /Vi

^

^

j=^ ^=^

^

a V7/

/vi

8^4?

/ji

W

/V

P V7

I

CONCLUSION OF SECONDARY DOMINANTS

432

Ex. 25-40 contains an effective cadence on V/vi which

then followed by I. This use of V/vi as a transient-terminal cadence chord emphasizes the close relation

between a major tonic key and

Ex. 25-40.

its

relative minor.

Faure: Requiem, "Pie Jesu."

Adagio

& i

^

S

iA

i

iH^-m-d

f*ff

^

^ i^

'|^%i

V4

Vi6

7Vi

to

seventh of the latter supplies the former with is

its

its

own secondary dominant,

the

"leading tone" resolution. As a

followed immediately by a return to the

secondary dominant, in a basic scheme such as

first

^i

i ^ ^M

I

one secondary dominant resolves

general rule, the chord of resolution

i

rrr

r *=^

^/V/..

When

is

V/V — V^/ii — V^/V.

This

represents the embellishment of an already chromatic secondary dominant.

Ex. 25-41. Verdi:

Requiem "Libera me."

Andante _Q_

te

»

^i

± vn p £

^A

-e-

^FW?

Bk

~n~

J=J=J=J

^ ^^

sc :2=

n.

V7/. '>ii

V/

Vv

V7

W

IV

iV

/iv

Although other possibilities of voice leading exist in the resolution of one secondary dominant seventh to another (root movement by step down, for example), we frequently find all voices moving in parallel motion. Obviously such practice precludes the regular resolution of the dissonant elements. In Ex. 25-42 this treat-

ment

is

made

obvious by the use of the block chords and by the repetition of the

irregular pattern (V^/ii

—V^).

—

—

CONCLUSION OF SECONDARY DOMINANTS Ex.

433

25-42. Beethoven: String Quartet, Op. 59, No.

^Mmr

Allegro

^ ^

m

I.

#

^

Iff f

;2 =3

LU

^ r'it

4r

te

sl^rn::t

ife

V7

V7/

1/:

li

9

I

a

r

V7 >^ii

lA

J-^

J •

—tn — -M

1

9

^

^—

-A 1

many ways

— ——

e

11

may

m

f

Q

u

summation of the practice of irregular resolution, at least in regard to the harmonic materials thus far presented. Contained therein are six irregular progressions: (V^ — vi) deceptive; (V^/vi V) root movement up a third; (V vig), and (V'/V root moveivg), (V'/iii Ig) ment down a second (Vg/V V'/iii) root movement down a third. An important In

Ex. 25-43

—

;

serve as

—

—

—

—

— —

—

is the contrary motion between the outer lines in the long measures 1-5. Through the use of secondary dominants the

organizational feature

melodic descent

in

harmonic potential

Ex.

25-43.

Wagner

:

is

increased, particularly through the irregular resolutions.

Lohengrin, Prelude, Act

I.

Lento

*t

m

M w

h

^

I

^^

i^

#•

t=f:

o _

p^« p'

»•

rr iV6

VMi

434 Ex.

CONCLUSION Of SECONDARY DOMINANTS 25-43. continued.

4t

^P rof

k

-rw

FfFtp

/)ZMi>

^ ^^

9^^

Vy

Vi6

16

^

r f

^

IV

^ f m

^P

il

"'

^ii

Sequential Use

Secondary dominants frequendy appear in sequential passages. This procedure may be employed in modulatory sequences or in sequences in which the tonic remains unchanged. In Ex. 25-44 the beginning and end of the passage focus upon the same tonic, yet the composer runs the sequential gamut through the use of a two-note pattern beginning with progressing without interruption through /HI to the I, cadence on tonic. Since each Mm" chord resolves to its "tonic," regular voice

V—

leading

Ex.

is

maintained.

25-44. Beethoven

Piii

V

:

String Quartet

59, No. 2, IV.

presto

^m

3

^

^

i

i r

^^

1=^ i f

e:

Op.

I

,V7

Passages such as these

I

^^ J

^

m

E

''^

Jl

^ V>'iii

may

or

may

^^ '

P "'

J

not be modulatory in

r

,^v'\

L

effect,

-^^ ,^v

but they do

unsettle the tonality to a degree, thus allowing the option of returning to the

original key or proceeding to a

new

one.

The powerful

unity of the sequential

435

CONCLUSION OF SECONDARY DOMINANTS

pattern sets up a propulsive force that continues to an appropriate cadence, either

new

in the original or in a

key.

In Ex. 25-45 a modulation from e to a takes place. The original key is clearly established (measures 1-4) and an imitative pattern begun which continues past measure 8 (where the key of C is reaffirmed) to measure 14 where it becomes part

dominant sevenths (exception, V in measure 5) This sequence is maintained to measure 8 where the pattern is interrupted in preparation for the cadence on the dominant of A. From measure 8 the key is a minor. However, the presence of the chain of secondary dominants creates an ambiguity that is unresolved until the arrival at the cadence on the dominant. Test this fact by substituting the optional cadence (No. 2) prepared by the author of a sequence of consecutive secondary 1

1

.

to effect a return to

C

major.

Beethoven: String Quartet, Op.

Ex. 25-45.

18,

No.

IV.

5,

Allegro

^ ¥-

MVMf

'

r

r

'^

IV

V7 W'

^

I

5pf^

m#^ t^

^±

'

fp? %

^

f aoz

^^m

^

^m Vi

W ^

»?fi — ^ — z=z: ^*^ mm

^^

J=U a i^

in

a:

Pff^ ^

^

W^ \f^~~~.

^m

f f^

^^

u^ ^Ljpj^

T

—

436

CONCLUSION OF SECONDARY DOMINANTS 25-45. continued.

Ex.

f£fi^'^

<

r

ia^ %

F^

r

r f

r

VI4

VI

"'AVI

f

^ pd^ r

i

i

r-

^'/m

V" '

i

Although the secondary dominant concept generally provides a explanation of the function of

many

satisfactory

non-diatonic M-mseventh chords,

this

is

not

always true. Consider Ex. 25-46 which contains a progression of tertian chords (predominantly M-m seventh chords) and consider the possible validity of the attendant analysis.

Chopin: Nodturne, Op. 55, No.

Ex. 25-46.

1,

Andante

^ 'y,

\

,

.

U,

y

^^^

f7\

^ ii

i

i,

£^^I

-^r

1

'^

^

^I'tn

^^w

T 16

^^im

^>|vi

r

vy

i

^i f

f V7

True, there are some familiar root relationships as indicated by the symbols

(V/^V— V^) and (V^— III-VV— VI and (V'/vi analysis

—

ig),

;

as well as a tritone relation

may appear on

(V|/II— V7III) As logical as such

also, there are third relations

(V/VII

Vj — III).

paper, the question arises as to the information imparted

harmonic materials. The rigid application of the secondary dominant classification to any and all M-m seventh chords can sometimes lead to naught, and the resultant symbolic representation may contribute little or even impede the understanding of the

by such an assortment of symbols,

as they pertain to the unfolding of the

musical relationships involved. Generally speaking, the application of

this

should be limited to those relationships in which the chord of resolution

ognized

member

is

it

entirely, or treat

from those of previous composers. Its sound, as an isolated too reminiscent of major-minor music, and its implication of a simple

ways

chord,

a rec-

seventh chord, once used frequently as a secondary dominant,

has fallen into disuse. Contemporary composers usually avoid in

is

of the diatonic family, or one clearly related.

The major-minor it

concept

different

437

CONCLUSION OF SECONDARY DOMINANTS tonal resolution

too compelling to enable

is

to

it

more chromatic

into the

fit

textures

that have prevailed in music since the turn of the century.

Exercises

For more detailed assignments see Materials and 1.

Spell the indicated chords

E

h. V^/iii,

Vg/bVII,

c.

2.

of Music

Workbook, Chapter 25.

I,

from the bass up:

A

V^/vi,

a.

Structure

c

d.

V6/Vi,

e.

V7/III, d

b-Jiat

V^/vi, D-Jlat

f.

Devise a phrase featuring a sequence employing the following secondary dominants: of supertonic, of mediant, of subdominant, of dominant, and of submediant. Use

V

root position and/or the various inverted forms. 3.

4.

Consider various pitches as root, third, fifth or seventh of dominant of submediant chords. Spell and chord from the bass up, indicate the key and function and the chord of resolution. Do the same for the dominant of mediant.

Using the following harmonic progressions as models, create two different settings of the other SATB. Use different harmonic rhythms, textures and keys for the two settings.

each, one for piano,

5.

6.

7.

a.

I

b.

i

V

iig

V|/vi

VI

\'|/VI

vi

ivg

V*/m

ii

V

V^/III III

Symphony No. 85 (La Reine),

Brahms

V^

i6

i

II.

(1-8)

Op. 21, I. (1-21) on a Theme by Haydn, Op. 569 (1-10)

jVo. /,

Variations

:

Schubert

Der Erlkonig (87-96)

:

Schumann

Symphony No.

:

2, .'\dagio

( 1

-9)

Chopin:

Mazurka, Op. 67, No. 2 (1-16)

Liszt:

Les Preludes (70-80)

Practice resolving various forms of the secondary dominants of at the in a

10.

Illg

Arrange the whole for solo clarinet, violin, viola and cello. Seek out examples in which V/vi and V/iii appear. Pay particular attention to the approach and resolution and their significance in regard to context. Analyze a number of the following, indicating keys, chords and non-chord tones. Beethoven: Symphony

9.

V|/IV

Compose a phrase to follow that of Ex. 25-19, maintaining the same general texture. Employ at least one secondary dominant (other than V/III) and cadence on tonic.

Haydn:

8.

iiig

V5/VII VII

mediant and submediant

keyboard. Establish a key and introduce and resolve the embellishing harmony

smooth

fashion.

.Assuming that each of the following secondary dominants spell the chord of resolution of each from the bass up. a.

V|/V,

d.

V|

E-Jiat

vi, Z)

h.

is

V|/iv, b

c.

to

be resolved deceptively,

V^/III,

c

f.V*/lV,B

e.V^/V,e

Considering the root relation indicated, spell the chord of resolution (from the bass up) for each of the following: (The chord of resolution must be a diatonic triad in the key indicated.)

Third down a.

V'/iv, c

b.

V^/iv, d

d.

V^/ii,

f

V*/III, g

Third up c.

V'/vi, .A-flat

F

Second down e.

V/ii,

E

: :

:

:

438 11.

CONCLUSION OF SECONDARY DOMINANTS Construct short progressions using different forms of the dominants of dominant, supertonic, mediant and submediant, and resolve them deceptively and irregularly (up a third,

12.

down

a third, tritone, etc.).

Write an instrumental and choral setting of each of the following progressions. Use ferent textures 3..

I X

b.

i

and harmonic rhythms

dif-

for each.

V'/V iii vig V|/ii V6 V7/V V Vg V4/VI ive ii° V V> VI V^/III vig Vi.e

V

V7

i

^

13.

Construct an example in 4-part texture employing a sequence of secondary dominants in which tonic remains unchanged.

14.

Using a three-part texture similar to that in measures 4-12 of Ex. 25-45, develop an example employing imitation of short motives, using secondary dominants in deceptive progressions or in other types of irregular resolutions. Arrange for oboe, clarinet and bassoon.

15.

Analyze a number of the following indicating keys, chords and non-chord tones. String Quartet, Op. 18, No. 3, III (63-74) Beethoven String Quartet, Op. 59, No. 1, IV (1-18) String Quartet, Op. 59, No. 2, IV (179-209) Schubert

String Quintet in

C

major,

Op.

163, III (11-17)

Mendelssohn Nocturne (Midsummer Nights Dream) (91-100) Chopin Mazurka, Op. 56, no. 2 (33-44) Mazurka, Op. 59, no. 1 (38-42) Act III (1-16)

Wagner

Lohengrin, Prelude,

Verdi:

Requiem,

Requiem and Kyrie

(8-11)

Tonality

26

Changes

we

an important aspect of tonal organization, the change of tonic. This expression refers to a shift of tonal focus, and it may be used in connection with most musical styles. Modulation, on the other hand, In this chapter

shall consider

a particular process through which a change of tonic can be effected.

is

Modulation

To tonic

modulate, a composer must establish two different tonal centers

and a new one. This relationship may be created

exists at the point of actual tonal

it

there

is

number

initial

of ways, but

change, a point usually established by a single

mutually identifiable in both keys. A modulation takes place a change from one tonality to another, the second of which is estab-

pitch or chord that

when

in a

— the

lished cadentially

is

and confirmed by a subsequent phrase beginning

in the

new

key.

Tonality change

may

be accomplished in a smooth, almost imperceptable

way, concealing the actual In

this

of tonic, or

it

may

from an abrupt

result

modulation

shift.

may

or

may

not be indicated by a

be recognized visually as the result of a new sense "signal" the change of key.

A

new key

signature^, but

set of accidentals

modulation from

c

minor

which

to A-flat

Modulations within short sections are seldom indicated by a change of key signature.

439

it

may

in a real

occurs in Ex. 26-1.

^

shift.

book, the former will be described as a modulation, while the latter will be

described as a tonal

A

shift

major

#

TONALITY CHANCES

440 Ex. 26-1. Schubert: Ersfarrung.

^^

Voice

^Aj . =^

^

S^

;

Piano

%'A^J^J^P

—-Tw—

vw

—

-:

^E

^

*

W V am V* ^

i?P

?=^ xz=

»f'

C^CiJCJ^CXJ

^

pr

f

principal key of the song

modulation

p

m m pi

-"TW

'^'^•^^^6} cJcXJ^c^ The

^

I

r

9#

.F]nn

1^\^[S^\J^

minor, and the change of key that occurs

is c

to the submediant of

CJ-JC^CiJC^

A-flat.

c,

is

a

Schubert might have changed the key

signature at measure 5; that he did not emphasizes the subsidiary relationship of A-flat, the new key, to c minor. The note d-flat occurs as an accidental, and b-flais

replace the

b'

naturals

which were the leading tones

in the original key of

c.

Melodic Modulation

The same melodic factors that establish an initial tonic usually function in the establishment of a new one. For example, melodic motion from leading tone to tonic (7-8), tonic triad outlining,

dominant

to tonic skips, repetitions of tonic

and

the treatment of tonic as the beginning and/or closing pitch of a phrase or larger section typify the estabUshment of a point of focus in melody. These factors (or

some of them) are usually evident modulations.

in

both

initial

key affirmations and subsequent

441

TONALITY CHANGES

D

major is firmly Several of the considerations just noted are found in Ex. 26-2. established in the opening two phrases of the minuet, and the notes of the

D

major triad frame the melodic activity of measures 1-4. In the subsequent phrase, however, d becomes an unstable pitch, because of its tritone relationship with g sharp. The tonality is unstable through measures 5-8, although we anticipate the confirmation of /I in a cadence. A is confirmed in measure 10 by the melodic

motion 7-8

{g-skarp to a).

A

convincingly reaffirmed as a

is

ginning of the next phrase in measure (the

dominant key of D) has been

Mozart: Symphony No.

Ex. 26-2.

1

Thus

1.

D

to

A major

effected.

7,

III,

Minuet.

i

ffrf-fiP'rcnr

^ important

tonic at the be-

a modulation from

oEf/irrr

It is

new

W

PS 3^

tf^LL/

a dual capacity in Ex. 26-2.

to note that a serves in

i

The

repeat

sign in measure 10 indicates a return to the beginning and, therefore, to the key of/).

The importance

of

A

as a

new key

is

lessened, since

quickly erased with

it is

the return to D. In the light of these broader structural considerations,

we need

product of a modulation, but rather as the point of arrival of a transient-terminal cadence on the dominant of D, which momentarily diverts attention from tonic. However, with the repetition of the section, a is cast in an entirely different not regard

A

as the

opening of the next section is clearly in A, and establishes it as a new point of focus. The note a has been heard in a dual capacity: first, as a strongly emphasized dominant in D; and second, as the tonic of a new key that supercedes light, for the

the previous one.

dominant key of D. The emphasized at the cadence (measure

Ex. 26-3 contains a clear modulation from

change

to

D

is

established in measure

second phrase, where the

5.

D

is

D major

G

to

triad

is

a transient-terminal cadence on the dominant of

G

4) of the

affirmation of D,

Ex. 26-3.

Bach

:

it is

solidly

Chorale, A//e$

confirmed as a new

ist

ist

heard as the cadential chord of major. With the subsequent re-

key.

an Gottes Segen.

m

^ ^s i ¥ rn n m iiij iiA UU ^ ^p r Wm Alles

its

an Gottes Segen

s

^^^ rrrr

^m r

v:;

^

o

m r

442

TONALITY CHANGES

The changes

and Ex. 26-3 were introduced cadentially and confirmed by the subsequent phrases. Although modulations achieved through such a process are those most clearly and strongly perceived, changes of key often occur entirely within individual phrases. Three changes of key, each contained within a separate phrase, may be found in Ex. 26-4. In contrast with the more subtly effected modulations shown earlier in Ex. 26-2 and Ex. 26-3, these more of key in Ex. 26-2

.

abrupt key changes, contained entirely within one phrase, are called

transitory

modulations.^

Ex. 26-4.

Hans Leo Hassler

Infrada.

:

^

Slow

^

.

I

«=*S

g min.-

^

g

mm.

p

The modulations shown

-e-

P W

^

-o-

2

W^

ipz

£

d min.

r^

i

I

o

-g min.

in Ex. 26-4 are considerably

discussed earlier. In each case the change of tonality

cadential duration of a newly perceived tonic,

Id

ii^rrr

more abrupt than

those

emphasized by the long which has occupied an entire is

phrase.

Since the main key (in this case beginning and ending key)

is

g, it is

easy to see

and d minor represent only brief departures from tonic to the relative major and dominant minor keys. Note also that these three tonics (g, b-flat and d) comprise the notes of the tonic triad of^ minor. An abrupt shift of tonic from B-Jlat to D occurs in conjunction with the repetithat the changes to 5-flat

tion of a characteristic melodic motive in Ex. 26-5.

or d occurs, nor

No

melodic cadence

to either

approached by a leading tone the change of tonal center (and key) is purely a product of the repetition of a figure based on major triads. Each tonic is heard as the root of an arpeggiated chord. Shifts of key such as this are found most often in developmental sections of compositions where sudden shifts of tonality and passages of tonal uncertainty are common. b-flat

Ex. 26-5.

Beethoven

:

is

either pitch

Symphony No.

6,

;

I.

»cj^rj c^Oir!^C; r!£/c;i^^-E/Cri^Jg i

i

D: '

For a

fuller description see

Book

II,

and the

discussion of

Tonal Regions.

—

TONALITY CHANGES

443

should be clear from the preceding discussion and illustrations that changes

It

of key, either smoothly introduced or abruptly efrected,

However,

single strands of melody.

the tonality of a single line interpreted as tonic. In the

whereas

Ex.

c is

as

we

i "—e—e—

o-

discovered in our earlier study of melody,

may be ambiguous, and more than one pitch may be opening of Ex. 26-5, g may easily be perceived as tonic,

Ave Maria Motet (melody).

:

jet

:«=

^

M

o

o

l

|

The ambiguity

-o

HBJ-

ti

—e—

-e-=

n

M

e-

=rn

:»:

^

iBp

of the melody of Ex. 26-6 can be attributed partially to the

absence of a structural half-step relation in the is

be established by

apparently confirmed as tonic in the third and fourth phrases.

26-6. Josquin des Pres

that

may

dispelled in the fourth phrase

by the

b

—

three phrases, an ambiguity

first c

(leading tone

—

tonic) cadential

figure.

The

tonal ambiguity of a single melodic line usually disappears

related to other parts of a texture.

As we know, the

are often organized through chord patterns;

chords to a tonic and the melodic activity of tonality

To

becomes most

pursue

actually a

shown

Ex.

this point,

work

all

it

we

through the relationships of

is

the parts that the realization of a

by Josquin des

shall reconsider Ex. 26-6

for four voices.

The soprano

line

of Ex. 26-7

which is the melody

Pres,

is

in Ex. 26-6.

-e

Alto

S —e -e

Tenor

:

—e—o-

Soprano

l-^ 8

s

«•

is

clear.

26-7. Josquin des Pres

Bass

it

when

different parts of a composition

&-

"

"

«-

-e-

Ave Maria Motet

ini

=W:

#

ZEE-

voices).

(all

j

o

TV

101

M

-e

HeK-

-o

^e^

ZSJZ

itt:

HBh

HBh

o-

i

:XC

—e—e-

—e—on

n

&-&»

» qct

TONALITY CHANGES

444 26-7. continued.

Ex.

^ ^ m

-&-

Heh

33=

iW:

tr

=PC

33=

Hei-

-e-

3S:

:is:

5r

=Q=

T%

TV

mi

He(-

HBh

»

det

=n=

=|DC

=&

=n=

:W=

33=

w

I

^

zz

_Q_!

* 5

M

P

o

-o-

33=

HEK-

-e

Hei-

=n=

-e- =0=

2Z

HSh

?2=^=CC

-e-

=ee:

33=

-e-

Ha-

TT"

:W=

-o-

HB(-

—a-

_Q_

n =£3=

Hei-

=a=

o

Ut:

M :W:

A

study of the

forms the

fifth

first

of a

phrase shows that the beginning pitch

C major

triad,

and

it

recurs in the

same

(g^) in the

soprano

role at the close of the

same phrase. After hearing the whole texture

bihty of interpreting g as tonic

is

we no

longer sense any ambiguity; the possi-

erased by the establishment of

c

as the root of

both the beginning and ending chords. Further emphasis on c results from the melodic activity of both the alto and tenor voices the leading tone-to-tonic half step occurs cadentially in the alto, and c^ is clearly heard as the focal point of the :

tenor

line.

The chords

sion I — IV — V — I.

that are heard on successive strong beats create the progres-

It is interesting

that in this composition,

in texture, a canonic relationship at the fifth exists

which

is

quite chordal

between the soprano and tenor

parts.

There

is

nothing that suggests modulation in

established the fact that while a single will

become

definitely

melody may

determined only

this excerpt.

We

have simply

clearly define a tonic, tonality

after considering

both the melodic and

harmonic elements. The melody shown in Ex. 26-7 unfolds entirely within A. Aside from the progressive cadence on the dominant that occurs in the final measure, there is very Httle activity that could induce one to hear any other pitch than a as a point of tonal focus. Leaps from e to a (measures 11-12 and 16-17) continue to affirm a as tonic. Sing the

line.

445

TONALITY CHANGES

Ex.

26-8.

Telemann

ft iiyp

f

i'

;

.

^

I

Lied Melody.

:

P'PP ^^'p PPP^ l

,

i

jj

I

V'p

IP'PP

i

I

p^'p

W^

ppp p'^pij'i^^^

j

i

Performed without its accompaniment, the Telemann melody is tonally deceptive. With the addition of the accompaniment (Ex. 26-9), an entirely different picture of tonality is gained. A modulation has taken place between measures 8 and 9, and the melodic patterns that seemed oriented to A are cast in an altogether diflerent

framework. The pitch a^ which seemed

stable,

is

now heard

an un-

as

subdominant, forming a tritone with the new leading tone of d-sharp. A change of key, not perceptible in the melody alone, has been effected through harmonic means. The new leading tone in £ major [d-sharp) is absent in the melodic

stable

line. It

is

present,

however,

accompaniment

in the

as the third of

V

in E, replacing

the initial g-sharp as leading-tone.

Ex.

26-9.

Telemann

p

ftf

ftll*

i

fti

PP

I

^^

^p

I

MJ T^Tj)

'

^

Ip-

f%^ W'

ft"

Lied (with accompaniment).

ft iipp

Voice

Piano

:

PPP

Mp

1^

i

p

i

p p

I

J'^P

P'PP

I

m

tt

r»-=

—1*-(*

^m ^ «==*

^ ^m

'p p

I

p

i

^ ^ I

'

m

^

0-

«^^P i

W

^m

^

f

p^'p

/3

p

t

m nr-1

^m I

J,

j)

^

J^ I

J^

^

n^^

nz-^

1

m

-

•

g

m

r

:

||

446

TONALITY CHANGES

Relationships of Keys

In subsequent chapters

we

shall deal in detail

with

many

techniques associated with modulations. For the present

we

developing a more generalized picture of some of the most

and concentrate on

of the processes shall

common key

relation-

ships that have been used to create tonal variety in Western music.

The most

frequently encountered key relationship consists of a change to a near

Near

whose signatures diffeii^y_jiQ_jnore than o ne sharpe r onejiat. For example, the modulation in Ex. 26-9 occurred between near related keys, since the two involved {A major and E major) are one sharp removed. That is, the signature of A major contains three sharps, while the key of E related key.

related keys a re those

contains four sharps.

Modulations from an initial key to the key of the dominant constitute the most type of near related key change. This seems logical and consistent when

common we

consider the strong relationship between tonic and dominant tones.

Near relationship exists between major tonic and major dominant keys, and minor tonic and minor dominant keys. It does not exist between a minor tonic and a major dominant key, because of the lack of common pitches shared by the two keys. The foregoing discussion can be clarified by a study of Ex. 26-10. Ex.

26-10. Tonic and Dominant Keys.

Near

C

Near

related

G

major

major

(#)

c

minor

related

g minor

{\)^\j)

{[,'>)

Distant relationship c

G

minor (b''b)

major (#)

above to any major key, we can see several possibilities for creating near related modulations from an initial key. Using C major as a point of reference, modulations to G and F major and a, d or e minor would represent changes to near related keys. The tonic chord of each of the new keys is a diatonic chord of the key of C. The same procedure can be applied to modulations from a minor key. Considering c minor as a key of reference, E-Jiat major, g minor, A-flat major, / minor and B-flat major are near related keys. It is important to notice that the keys which form near relationships to an initial tonic key ar^ lot always near related

Applying the

to

criteria described

each other. For example, d minor and

e

minor are near related

to

C major,

but

not to one another.

Near related does not imply

close intervallic distance;

tionship of keys, a relationship that results from keys.

common

it

merely denotes a rela-

tones shared by different

1

447

TONALITY CHANGES

Several illustrations of near related modulations follow. Play through Ex. 26-1

and study the changes of key.

Ex. 26-11. Frauenholz

Violins

m

Der Herr gedenki an

:

f

P^

b m^o or

Organ

^

p=^=if

s.

uns, for Voices, Strings

$

«

jS

E

r=r

U ^

^

j

i

nfJP

i

s.

s Voices

T.

omxlL

and Organ.

E

tt

Ji

^^^

p^^ J

JlTl

i

JlTTP

i

J

p^r?^ J

J

J

.'^''1 1

r

r

r

J

J

J

J

TO j

J

^1-f^f^H^tf

r

r

i

^

—

«

»

448

TONALITY CHANGES 26-12. Chopin: \1

Ex.

4v

i

.

^

4

»

b

-t — rr

Mazurka

B-flat.

in

Ul^l 1 i 1

—— ^'

p

»

—

>

-..^'r

^

»

—

1

•<

fj^f

^^

f

\

1-

f

P^ s

^

m.

F

•4-

ft

—

^^p^

»

i

——

a

ni

10

•

^^3

—4

]t i

p^

M

gf

t

.

1

»

—— •

—*^--i

Lj

t

j^''

--^

-,^

«|

p

»

P

P

f=¥

^^y-;f"

yjp

^

4

Ex.

26-13. Beethoven: Sonata for Piano, Op. 110,

Ex.

26-14. Beethoven: Mass

in

C Major.

II.

Am t=t i=i J^ s es M f rr rr ^^t,m

s

^jg^ rfff

^ s

ZEE

i4 r^ ^^

i

i ffit

? 35

30

1 331

si

Jj JJJJ J

IE

^

Jf

u.

^

^ J f

rr rrfT

i

-e-

rr^

449

TONALITY CHANGES

t>Tn

I

J

.

.1

.1

i J

J-

g ?^ Ex.

11

^

40 331

-ozsn

1 J

i

26-15. Bach: Three part Invention No.

.^b

P

/y/«.u 1^

^

7

J^

5.

^

??

1=T

^

^

i^ .U

^

e

^

^JOT

ic:

i

K jn.A,^^

W^

y

rvrfrr J

^^ Ex. 26-16.

Violin

J)

i

J>

J.

.

>i'

£

^

J.

f

Handel: Concerto Grosso, Op.

6.

fe^ JaJ ^i'^*

f^^

^ ^ 5

-#-^»-

Cello

ilf^^i=f

» !

I

Violin n

Viola

V

fe^

^

—— —

:

450

TONALITY CHANGES 26-16. continued.

Ex.

^

^^r^L£^^

^ cr»r

i^'

f

^ » 1

tt

j #

*

#

J

^m

le

»

»

#=^=g

^

p

K

S ^^

f

—

^ f

iitf

££r/ [!r E^J^ C;

.ttJt

')-;'

m.

i^ ^ ^

N

i ^ L/r

^53

^p

[ID

^^

^

?

1^

^

w

^

^^

This group of excerpts, which constitutes a variety of textures and

styles,

contains

modulations of the following characteristics Example

Keys Established

no.

11

D

12

5-flat

major

F major

13

^-flat

major

—/minor

C major

minor G-flat major d minor minor minor c g

14

15

•2,

16

Less

A major

major

Common Key

a

Modulatory Scheme

Modulation Modulation Modulation Modulation Modulation Modulation

to the

Dominant Dominant

to the

submediant

to the

submediant

to the

mediant subdominant

to the

to the

Relations

Composers have by no means limited their choices of keys to near relations, since virtually any combination or sequence of keys may be found. Compositions written after the eighteenth century sometimes use relationships which bring into play

many

or

all

of the

members

of more distant key relations

is

of the chromatic scale. Consistent with the use

the lessening of key stability and reduction of key

Sudden shifts of key, in contrast to the more gradual process of modulacreate an aura of tonal uncertainty that both broadens the tonal perspective

duration. tion,

and weakens the

listener's feeling of principal tonic.

Third relationship describes a more distant key change involving two keys whose

—

451

70NAt/ry CHANGES

one or no common tones and whose tonic chords are a major or minor third apart. For example, C major and E major form a third relationship. Their tonic chords possess one common tone, e, and a change from C to E (or E to C) is often described as a third related key change. Actually, the change to a third related key is usually felt as a sudden shift, rather than as a gradual change. In Ex. 26-17 a third relation is introduced between D major and F major. Beethoven has employed the pitch a as a common link between the tonic chords

scales contain

of the two keys.

Ex. 26-17.

Beethoven: Symphony No.

^ t

33

8,

III.

^

.9 3

^

mE§.

—

#

$

^

5

3

3

\

(»

3

fe^iS #^^^

^^s

Major and minor keys a half step apart constitute the key relation in Ex. 26-18 in which a new key is introduced on the leading tone of the original key. Ex. 26-18.

Wolf: Spanish Songbook, .;i)

Voice

ji^^

I,

No.

4.

\0T

^^

Hv« MFmPmPmF.\> 0^¥^ ^V(^

pfpr^rp py^

Piano

^^ ±t

^J ^»

1

m

^^M^ rrCT^gTlJ

i

452

TONALITY CHANGES 26-18. continued.

Ex.

* :^ ;>

^

^

t*

M

i vrFfiiFrFrFrFriii^^j^

ii'

«^

f^=^=^

i^^

i

^ ^^^^=;

^FF

1^

«.

-^

is:

^

Other Aspects of Tonality Change All of the modulations discussed in the previous sections of this chapter have at least

one significant feature

in

common

;

in

each case the new key was established

and then affirmed by a cadence. Cadences which confirm principal tonics are, as we know, called terminal cadences, and most modulations are confirmed by terminal cadences.

In contrast to the terminal cadence, both the cadences function differently in regard gressive cadence clearly suggests that

the previously established tonic.

A

to the

progressive

and

transient-terminal

confirmation of tonality.

more music

is

to follow that will

progressive cadence to the

The

pro-

reemphasize

dominant occurs

measure 4 of Ex. 26-19.

Ex.

26-19.

Haydn: Piano Sonata

in

D Major,

I.

Allegro con brio tr^

^hi'^lr

r

r

^^^^^

r7 Tr

p—p-

^

ti-

F=^

/

t d t i

r^$=i

r nnnn

mi

i^

^

in

453

TONALITY CHANGES

The shown

between progressive and transient-terminal cadences can be by rewriting measure 4 of the Haydn sonata, as shown in Ex. 26-20.

contrast easily

Ex. 26-20. (revision

The

now

of Ex. 26-19.).

more attention

than when heard as the root of a progressive cadence chord. Leading tones (g-sharp) and root movement to a by a descending fifth {e -a) point to a as a potential new tonic, but note a

attracts considerably

as a point of focus

—

its

existance in such a role

is

short-lived,

and

centering around a to erase the polarity of

it

remains

for

a continuation of music

d.

Both terminal and transient-terminal cadences occur in Ex. 26-21. The excerpt begins in the principal key of/ minor with a sustained statement on tonic, followed

by a transient-terminal cadence on the dominant. The subsequent phrase establishes a modulation to c minor, and the original key of/ minor is reestablished with a terminal cadence at measure 9.

Ex. 26-21.

Beethoven: Egmont Overture, Op. 84 (piano reduction).

-

®

U-^ — r^

"3

5"

y

-^

^

4i -9—9-

^

^i'

^f

fiJ

^

HJ

ww

—g

1

—

454

TONALITY CHANGES

Ex. 26-21. continued.

7

^

t±=n p^z

^

^^

ra=^ i

r rrr

UJU

i

331

— 33

g ICG

^ -e^

«

—«

~T5~'

^7

Z)

^

^ •

-d

15

12

©

nr rfW

m

^e

i

ft»#

r^

-e^

-

- Jzz^ 5

ffi

We

^^

^-^

f)

-

I

rp

^^^

"modulation" denotes a change of key. Since the system of "keys" is most prevalent in music written between the seventeenth and the beginning of the twentieth centuries (music with which we are most familiar), it is natural that we begin the study of tonality changes with this music. However, to form a more comprehensive picture of tonality change, we must examine some music in which "key" is replaced by other means of tonal organization. Two phrases from a composition by Landini, a fourteenth century composer, recall that the expression

are

shown

Ex.

26-22. Landini: 2 Voice Ballata.

s

in Ex. 26-22.

f

ii

s

f

i

^

Z3Z

—

{fiF=F^^rf^ -^ r

~~"-~~~-|

5

=^^1

1

1

1

The

fff

Jt^ r

a

— r

— p-=

•

—f^

measures of the second establish the mode of ^ dorian (f-sharp occurs as a cadential leading tone alteration). The second phrase (the final phrase of the piece) asserts the principal tonal center of the work, first

phrase and the

initial three

455

TONALITY CHANGES

The mode

d.

of the close of the composition

to create a leading tone

in the 7

is

d dorian, with a c-sharp introduced

— 8 cadence pattern.

The change

of tonic

is

not

felt

would have been if d until the final measure, and therefore had had more preparation. However, as the last pitch heard, d can hardly be discounted as a point of focus, and a definite change of tonic from^ to d is perceived. We are reminded, by glancing at Ex. 26-22 and Ex. 26-23, that alterations are common to compositions employing modal bases, just as they are to pieces written in major or minor keys. The designation of a specific mode is made on the basis of the most consistently recurring pitch material. Unlike most works in major or minor keys, many modal compositions begin and close on different tonics. In such is

examples, the closing tonic

is

not so strong as

it

usually considered to be the principal tonality of

the work.

prevailing pitch material of Ex. 26-23 forms a natural minor (Aeo-

lian)

a.

Ex.

The mode on

26-23. Palestrina

:

Motet, Adjuro vos

r^a^ t rr C

ai

^^a

filiae

Jerusalem.

^^ ^ WTT r^rr r ffT? ^^ ^m ^^ ^^ i

rr

^^ SM T Roots

^

W J.

i r

P c

rnrr

^

^^ nr r-

M^ J=^

^

r

r

ii

^

lAdJ

P

T

^ rrrrff

i

^^^f

^ ^^ ^

''

r

-o-

iU

J

J

3^

C

(Roots)

y

n

i

#

^

r

I

f

^r

J

r

TONALITY CHANGES

456 Ex. 26-23. continued.

10

^=^ i

tr

^ff rrr

^

-#

ii

^

m

«—

'

p ^J

i

^

J'

(C: V/v)

(Roots)

P

^^

HI

15

«

^

st^ ^^ rrr

rr

^ If

^f

f#

g^ ^^ ^^ r ^^^ ^ m -J

FfT

^ ^ ^F^

J f

-e-

J

-

rrr

rr

i^i

^

^•-^Jj

s

r

;

J

(V

i r

I)

(Roots)

^

r

I

r

J

f^

In Ex. 26-23 tonal variety is created by a series of shifts from a to C, and the tonal plan of the example can be understood by singing the second bass part, measures 1-10.

An

analysis of the other parts will reveal that the notes a

as terminal points for the various successive imitative entries

overlap.

At no point

c

serve

which continuously

can all five voices be found in of pitch emphasis are not affirmed by

until the close of the excerpt

cadential agreement, and the subtle shifts

strong cadences.

and

The cadences

are

weak because they occur only

staggered locations, rather than simultaneously in

all

the voices.

in rhythmically

The

subtlety of

tonal shifts in the excerpt must be related to the texture of the composition, which is quite contrapuntal, since strong tonality-defining cadences are avoided in favor of continuous motion in each part.

Our

perception of a and

c

as points of focus in this passage

is

dependent upon

three factors: (1) pitch repetition, (2) cadential leading tone patterns (i.e., g sharp I or viig I chord progressions at cadences. C is not a and b c) and (3)

—

—

V—

—

a strongly defined tonality, but as a study of the root relations (accompanying the

r^jvii

—

457

TONALITY CHANGES

example)

will

show, any description of

its

tonal organization

would be incomplete

without some mention of c as a subsidiary point of focus. It is heard in a transitory relationship to a, a point of momentary polarity, but its duration as a tonic is such should be viewed as part of a continuously unfolding tonal pattern comprised of a c a, which creates unity and variety within the principal tonality of a. Vacillation between tonal focal points is a significant aspect of much music. that

it

The

—

principal tonic

(a)

of the Palestrina Motet ]ust discussed

the

is

same

as that

of the passage in Ex. 26-24. Despite the similarity of tonic and prevailing minor mode, the two examples present a striking contrast of tonal material and organiza-

But since both examples

tion.

more

illustrate shifting points of tonal polarity,

alike in basic tonal design

Wagner

Ex. 26-24.

Lento

e

:

Tristan

and

than they would appear to be.

Isolde, prelude, Act

languido s

^

F^r^

I.

^^

F=T

r

i

yi

^P*r

^

^^ ^£

i^ ^^^ fi^^

10

±=^

^

*r

^

they are

I

p

^^^

j^;jj fp=^

^

i ra:

j^m

15

iJ^^~^

458

TONALITY CHANCES

^

Ex.

26-24. continued.

m

r=if^^^*^3

riT

^

p=^J i-

r

jj-^j

r^rrs' J'

bi^5' i£^-jj ^

r— pr-

l

'^^^Tf

±^

^

F^

3^

tp

The

tonality of the \Vagner excerpt

tonic (or

what we regard

dynamic aspect of

might be described

as points of focus)

is

as

IP^

"dynamic" because

continuously shifting. Contrast this

tonality with the stability of solidly established diatonic keys.

This fluctuation of tonic can be related to several of strong, clear terminal cadences; (3) the

s

(2)

common

factors

:

( 1 )

the absence

the predominance of root relations in seconds;

streams of chromatic inflections which by their abundance tend to minimize

the "key effect" of leading tone relations; (4) the absence of pitch repetition in

and (5) the short duration (in context) of each area in which we may perceive an "implied" or an anticipated tonic. It is common to speak of sections such as this as involving "continuous modulafavor of pitch variety;

But since wejiave_de fined modulation as a clearly established change from one diatonic key to another, confirmed by a terminal cadence^ "continuous modulation" would seem to be a contiadiction of what we hear in such an example. If tion."

on the other hand we admit that

all

twelve available pitches

may

comprise the

and that any of the twelve tonic, then a more suitable

tonal material of a composition with one principal tonic,

may occur as a briefly established distinction may be made by the expression pitches

or implied

implied modulation.

Implied modulations are frequently the structural basis of passages of prolonged instabilitv. We are, in a sense, unsure of tonic or key, but we infer tonic on the basis of short passages which only allude to particular keys. Sections or entire works containing implied modulations are by no means limited to any specific period of music (although they abound in works of the late nineteenth and early twentieth

can be seen from a comparison of Ex. 26-24 and Ex. 26-25. Implied modulations may be shown in analysis by indicating the implied key or tonic in brackets, e.g., [C] or [a]. The impUed keys of the Wagner excerpt have been centuries) as

shown

in Ex. 26-24.

Study the implied keys in Ex. 26-25.

459

TONALITY CHANGES

Ex. 26-25.

P

*

s

ICC

*

Giovanni Macque (sixteenth century)

^

W

^^ i^

$

^

M r^

^-j

ii

-e-

J.

fro-

rr F

^^^ ^ F=T r e^d^ Py^^

^ r

f

more recent music. As we

significant in the structure of many

§=

i

In the concluding chapters of volume two the materials of

i

^

^^

TT

Much

Organ Study.

:

we

shall deal extensively

shall see,

contemporary works

with some of

changes of tonality are as as in

music of past periods.

twentieth century music has a strong affinity for tonal relationships that are

typical of

much

earlier music. In Ex. 26-26, tonic

stitute the principal

Ex. 26-26.

Hindemith

&

:

means of delineating the

Ludis Tonalis, Interludium

in

and dominant

E-flat

(The March). (C) 1943 by Schott

Co., Ltd., London. Reprinted by permission.

March (J=66)

relations con-

tonality of the opening phrases.

.

:

460

TONALITY CHANGES

Ex. 26-26. continued

Exercises

Additional materials are contained Materials and Structure of Music 1

Study Ex. 26-26 using

as a guide the

list

Describe the "key" of the example.

b.

In what

c.

d. e. f.

g.

h.

What What What What

tonic

Workbook, Chapter 26.

of considerations that follows

a.

way do

I,

and dominant

relationships organize the passage?

are the prevailing root relations? types of contrapuntal relationships occur?

are the most characteristic

rhythm patterns used?

types of decorative activity are found?

Where do changes of tonality occur? In what way do changes of dynamics

contribute to the organization of the

excerpt? i.

j.

2.

Name

all

Where do harmonic or melodic

tritones occur

and how are they treated?

Contrast the harmonic language of the excerpt with that of Ex. 26-25. the near related keys to

A

major,

c

minor, D-flat major and

b

minor.

3.

Invent an eight measure piano composition which fluctuates tonally between and e minor. Begin in G and close in e.

4.

Sight sing Ex. 26-23.

5.

G

major

Transpose the soprano line of Ex. 26-3 to B-flat major and make a four-voice setting of the melody which contains a near related modulation.

^

Procedures

27


Tonality

Change

Modulation

is

a principle of organization that constantly confronts

we have seen, key change is a common ingredient in compositions. Our objective in this chapter is to study how,

the composer. As

all

shortest

aside from

melodic procedures, the change in pitch focus than observation of musical

produce these

to

results;

we must

is

but the

accomplished. This involves more

delve into the musical techniques used

results.

Modulation by Pivot Chord

One

of the most frequent modulation procedures establishes the relationship

between the two keys by means of a specific chord that they possess in common. The agent of modulation, then, is a chord that can be interpreted in both the old key and the new key. This process capitalizes on the potential ambiguity of chords, i.e., the fact that a single chord can possess a logical identity in more than one key.

Ex. 27-1 illustrates concisely the pivot chord modulation technique, in this case involving two distantly related keys, which

is

not

uncommon

in nineteenth cen-

tury music.

Ex.

27-1. Schubert: (W/nferre/se), Muth.

Ziemlich geschwind, Kraftig Voice

Piano

^ /

^ W & s

5b£ ^— f

ZT

r^

=

m

*^ -f—^

P

^^^

o

PROCEDURES OF TONALITY CHANGE

A61 Ex.

—

27-1. continued.

a

10

f=g-85r

fE^r it

* *^

It*:*

^

I

ft

:

^i=^

iV

'_j

in a in

I

—

p"^f*i

•

u ^

^^':! ';;;:> S*=i^

/I r

[_r

i

E

minor has been measure 9 of this excerpt the change of key has taken place replaced by E major. From measure 8 the tonality is clearly E major; therefore we must look immediately before this location to see the actual point of shift. The major triad on E in measure 7 is clearly \" in .-I minor, if we were to look no further. In retrospect, however, we see that it can also be interpreted as I in £" major. This triad is thus the pivot chord between these two keys; it is analyzed as shown on B\'

;

.-1

the example.

We

can perceive

this

type of modulation only by looking back from the point at

which the new key has been irrevocably established. Since any chord is capable of a number of interpretations in any number of possible keys, we \\ ould remain in a constant state of coiifusion if we were always conjuring up the many possibilities of each chord we hear. Fortunately, although we do make guesses as to the possible outcome of a musical situation, we guess only on the basis of the evidence at hand

we

in other w-ords, this key clearly

Once

interpret each chord only in the light of the current key, until

has been abandoned.

change has taken place, however, it is possible to identify the dual role of the pivot chord. Each modulation generally contains a signal or simple "clue" that the old key is no longer in effect. This is usually an accidental foreign to the old key but diatonic to the new key (often a new leading tone). Occasionally, though, the change of key occurs without additional accidentals, in which case other factors must be considered. Once this "clue" has been spotted, the pivot chord is this

easy to locate;

it is

usually the previous chord.

In Ex. 27-2 no accidental signals the advent of the new key. Instead, the Mm" chord in measure 6 (not a diatonic member of A minor but, as it turns out, clearly

V^

in

D

major)

pivot chord

is

first

indicates that b

thus the previous chord

minor

—

i

in b

no longer the prevailing key. The minor becomes vi in D major.

is

.

463

PROCEDURES OF TONALITY CHANGE

Ex. 27-2.

Haydn: Quartet, Op.

^^ ^ ^

Menuetto

m m

Allegretto

Violin

I

Violin H

=fe^

Cello

^ f m & p.

/

'/

i^

M w^ ^m

Viola

64, No. 2, Menuetto.

—6

«-

y

^—

rF=f=^ f

^

0-

m

fe

J

tt

^

^

i^

m:

^Fm

—

f

Ideally any chord tion

may

chord

result in

/

^/

f

^P ^^

^

£

^ fs

i

m

^

Be

m

m mm ^ ^ —

i

^-#

f I

P

W

^m f it /

in

^

^

^

—diatonic or chromatic — can act

which a chromatic chord

^

^

^

and a situathe old key becomes a diatonic as a pivot chord,

new key or vice versa. The Vg/ii chord in D major, for instance, can Vg in E minor or major. Usiially, however, the pivot chord is diatonic keys. The diatonic pivot chord possibilities are easily determined by pairing

in the

function as to

bo th

two keys involved, as in Ex. 27-3. If, the dominant major key, the V will pair with

off the appropriate chords in the case, the ii,

and

A

to

I, vi

with

Modulation by pivot chord.

ff

mig

Major:

[11 iii

14

i

is

so forth.

Ex. 27-3.

fD

modulation

as in this

U Major: IV

ilti§

,i|i§

IV

^^ Vi

^

Vii*

§ Vi

ff I

H Vii"

f=% III

»1W

—

464

PROCEDURES OF TONALITY CHANGE

We

can rule out several of these chord pairs ii (a minor triad) will not serve as the chord equivalent of V (although V/V will) IV and vii° are likewise incompatible, as are vii° and iii. Four pairs remain I and IV, iii and vi, V and I, vi and ii :

;

:

all

equally possibly.

obvious that the primary^ criteriqnjs jdentity of chord

It is

quality.

Different pairs of keys display widely differing pivot chord potentials. In certain key relationships, as illustrated in Ex. 27-4, the possibilities are more limited than in Ex. 27-3.

Ex. 27-4. Relationships

:^^

D

Minor

^^^%

Major:

'^'

This process of

m

iV

i{

(ii)§

^^

f^»

^^

(i>)8^

VI

m\

IV

iri

ii

H

l\\

i

k

I C

m

of pivot chords.

Vii°

§

Vi

(ii

)^

Vii°

common

chord modulation does not require a harmonic texture of block chords. Ex. 27-5 is clear in its modulatory implications: F major is confirmed (although briefly) in measure 7 I becomes IV in the previous measure. ;

Ex.

27-5. Beethoven: Trio,

Op. 97, ("Archduke"), Scherzo.

Viola

m

Cello

W¥^ ^ W

mm

^w

#^

^

Ex. 27-6 contains a clear pivot chord modulation between two keys that are not closely related.

The

process

immediately before the major in measure 17.

Ex.

27-6. Schubert:

first

Symphony

Allegro vivace

more complex, though. The pivot chord occurs departure from C major IV in C becomes V in B-jiat is

not

—

in

C Major, Scherzo. 5

m #

465

PROCEDURES OF TONALITY CHANGE

±±€:^^±

m

^^

iM

J.

-J.

p.'

i

3t

^

^t

8va -

» p »— r

W

\*-

a^

p

m

a=a:

»

^^ 8va

m$^

•

^=ii ^

^m

V

^

I

it

*

25 7l9H

--# I #

—#

fC: IV Ib'':

^ ^20

m^

sf

'

«L^*V

m

•

•

•

f=TT

^m iff

* f

*=:*

Oa7m

7=rT=if=^^

•

4

?

ffiffi

Pivot Tone Modulation

common

between the two keys is a single tone. Ex. 27-8 contains a pivot tone modulation between the relatively distant keys of F major and D-Jlat major; the sustained tone F (introduced in measure 5) acts as a link between the two keys. Note that the harmonic motion is from the tonic of the original key to the tonic of the new key. Pivot tone modulation became more frequent in the nineteenth century than formerly, often as a link between In some modulations the sole

link

distant related keys.

Ex.

27-7. Beethoven: Trio,

Violin

Cello

Op.

j^''U1||,)"^

I,

No.

3,

Finale.

^

If^

^

s

gffi^

^^

Piano

^pi \

^i

o

i 33C

331

^

^

^^

^

zai

466 Ex.

PROCEDURES OF TONAl/rV CHANGE 27-7. continued.

This principle

G in

is

equally apparent in Ex. 27-8.

the viola part;

its

role

that of mediant in E-flat shift

Ex.

changes from that of tonic in g minor (in measure 8) to major. Here the change is better described as a tonal

than as modulation because of its abruptness.

27-8. Shostakovitch sion of

MCA

:

Quartet, Op. 49,

Inc.,

New

I.

(C)

^ft ^ m ,

r

m

Used by permission of

MCA

Music, a divi-

York, N.Y. All rights reserved.

; jj j:7?^

^ r

m i nm r ^ f-

zc

:$

m

i ^?^^ ^

The pivot tone here is the reiterated

^

}^. ^

^

1

^^^^

common

melodic inflection

r f^

gliss.

Modulation by Chromatic In another

g

P3EEE

ppf ^J

^^f

yb in y

Inflection

by voices than move) up or down a minor

process the relationship between two keys

— a voice that moves

(or

second, leading smoothly to a diatonic pitch in the

new

is

established

key. In this relationship,

PROCEDURES OF TONALITY CHANGE

467

of course, there are no diatonic elements in fore the

connection

is

common between

the two keys. There-

through the stepwise melodic action of one of the

lines.

Ex. 27-9 contains a modulation by chromatic inflection in the fourth and

fifth

measures.

Ex.

27-9. Mendelssohn

:

Symphony No.

3 (Scotch),

I.

rj:^

The

Mm^

chord on

F

fl^.

measure 4 no more suggests G major than does the same chord type on D suggest the F major of the preceding section. The agents of modulation are the bass line, moving chromatically from tonic of the old key to the leading tone of the new key, and the movement from tonic F through E-Jlat to D, the fifth of the new key.

An Ex.

in

extension of this technique

27-10. Bartok

Violin

Orchestra

may

be seen in Ex. 27-10,

in

which the two

Concerto for Violin No. 2, I. Copyright 1946 by (London) Ltd. Reprinted by permission of Boosey & Hawkes :

Hawkes Inc.

tonics

& Son

468

PROCEDURES OF TONALITY CHANGE

Ex. 27-10. continued.

poco

rallent.

^

a tempo

125 h©-

p

PP

^W

I II

p-e-

^

^

i^

i

f I

espr.

^

-^^^if

^

f5/)r.

331

3i:

(F and C) are connected by the chord in measure 126. Although this D-flat minor triad is foreign to both keys, its use as a connecting link is obvious and relates it to the

technique described above.

Modulations by chromatic inflection frequently involve^ the dominant _as_at l east one of theT chjQttifi. Composers often have modulated to the supertonic or sub-

mediant keys by this procedure. For example, the raised tonic pitch of a key becomes the leading tone of ii; the raised dominant becomes the leading tone of vi. Ex. 27-1

1

contains a further example of this type of modulation, in this case

involving a chord that

is

not diatonic to either old or

new

key.

The upward

chromatic inflection in the bass at measure 6 leads our attention from to \'|/\' in c

Ex.

minor.

27-11. Purcell

:

Dido and Aeneas, Prelude, Act

-9-,

//(^

'i^

^

-

-a-

f

EE

*

P

I,

Scene

fe

2.

m

i

in/minor

469

PROCEDURES OF TONALITY CHANGE

i-

^Jm

fefe

^ ^^

t-

i

t &

'J' lI'

i fr

3-

I"

I'

i

w

1^

i

Descending chromatic inflection establishes the modulation in Ex. 27-12, again in the bass line, in measures 2 and 3. It is interesting to note that the two tonics in this excerpt

Ex. 27-12.

lie

a tritone apart,

A

—

they are distant relations.

E-jlat;

Hindemith: Sonata for Organ,

I.

(C)

1937 by

B.

Schott's Soehne, Mainz.

Re-

printed by permission.

Enharmonic Modulation

Composers occasionally have found it necessary to relate the two keys of a modulation through enharmonic spelling. This does not necessarily imply a remote modulation, however, since the enharmonic spelling is often used merely for the performer's convenience. The keys F-sharp major and D-flat major seem distantly related at first glance, but they are in fact no more distant than C major and G major. It is as natural, when in F-sharp major, to modulate to the dominant as when in C major, and most people would find D-flal major easier to read than C-sharp major, because of the notational complications of the latter.

The modulation

in Ex. 27-13

is

not between keys as closely related as f-sharp

and

D-Jiat, but it does demonstrate that convenience of spelling can take precedence over a more notationally consistent indication of key relationships. Measures 5 and 6 of this excerpt are actually notated in F-flat major, although the accompaniment

appears in the enharmonic key of interesting, for

it is

E

major.

The

pivot chord

not diatonic. In the last half of measure

4,

is

also unusually

V

in A-flat

major

becomes V/iii in F-flat major and resolves deceptively to the tonic of this new key. However, a more musical interpretation of this modulatory relationship would recognize the common pitch bond between the two keys; A-flat (tonic) of the initial key becomes mediant of the

new

key.

470 Ex. 27-13.

PROCEDURES OF TONALITY CHANGE

Schumann: Frauen/zeben und Leben,

j''i>'-j

Voice

}n

S'

\

}

Helft mir,

m-

^

:--;^^ii.

ihr

Schwestern.

^' i

\

\

r

p^'e^'^

;.^^}

\

Piano

rit.

a

tempo

Chordal texture is absent from the enharmonic modulation in Ex. 27-14 from E-flat minor to b minor; the change of key is brought about solely by the change 5 in b minor). in function of the pivot tone: G-flat F-sharp (3 in e-JIat minor Schubert has cleverly expedited the modulation by the running chromatic scale j

—

in the piano, effectively blurring the recollection of the previous key.

PROCEDURES OF TONALITY CHANGE Ex. 27-14.

Schubert

P I

Violin

Cello

Piano

Trio

=

ttT-^

^ ^ ^

r

in

E-flat

^

\^

r

471 Major, Op. 100,

I'T

I.

g^

#i»»»#i^»i»»»'»^»»^-#»^»'»^i^.»*-*i^^»»^i^^*»»»«^**»

£ cresc.

Wi3?pJ^J^^'''

»<^»*>#N^^^^ > ^ ^^•^^^^^ ^^^S» ^^.

i»^ »^<»^^<#'^ ^

(T

^7

fcb

il

^^^^^•^^^^'^^^^^^•^^^^^•^^^^•^'^^^^^^'^^'^^•^^-^•^^^•^i^ » ^^^»^>^^ »»»>

^»»0#>^-»*^»'#N#'#'^^'»^ ^ »»^>^>»^l^.^^'^<^S»^i^i^^>»<»^.^ »
771"

p5 eSeiT^l*

vv^k^fei^^ilMl j^^'i^

cresc. I

i

^

•»»»»^^»^»^»»i»^^##i»»*'« #>^0#l»»»i#ll#N»^l*>^»»»^»*.

''^

r

Gt major

^^ ^^•^^^ ^^^ ^^-^s^ ^l<>^^ »

^n

^;^ ^ici^

^

*!£*

?p.>»»lf

f

f

» *»^ ^ »i»^^ > ^»^^ ^^^^^ ^^^ * ^^K^ ^»i^» ^^••^^'^^ ^ ^^.^^•^^

i^

-•—•-

^ »»»*>»^ * #» ^^^^•^•^^1^ ^^^^^'^'^^^^^'^^^•^^^^^•^i^^^'^^ »^>^S#*»i^i

m m m

y

B minor

472

PROCEDURES OF TONALITY CHANGE

More Abrupt

Tonality

Changes

Disguising a change of tonic through a subtle relating of two keys has not always

been the composer's goal. A sudden shift of key can produce a stunning effect, one that many composers have obviously considered desirable at times. We will not dwell on the manifold effects of this procedure except to note that this lays bare the relationship between the two keys, emphasizing their contrast, particularly when they are not near related. First, however, we should observe that modulation between closely related keys occurs frequently near the beginning of a phrase. In this event

it

is

pointless to

single out a pivot chord; the break in musical continuity caused

by the previous cadence and the start of the subsequent phrase helps to emphasize rather than soften the difference in key. In Ex. 27-15 the first phrase cadences in/ minor, and the second resumes with A-flat major clearly established. Because of their close relationship, however, the effect of shift

Ex. 27-15.

Mozart: Piano Sonata,

^m^ ^^^^

K.

'Hh

"M-

barely noticeable.

280, Adagio.

^^m i mf

M

is

^ 1^^i mm Wm ^^^ p

f.

m^

^

J-

'i.

P

^ P ^ P

Measure

11

of Ex. 27-16 contains a cadence on

V

of

c

M

P ^

J

minor, but measure 12

begins with the tonic triad in E-jial major. Despite the cross-relation created by this succession

of chords {BjB-flat), the effect

accommodate possesses a logical and well-defined able to

system. There

is

only mildly abrupt.

We

are well

seemingly unrelated juxtaposed sounds as long as each

is

are near related.

tonal identity in a clearly-established tonal

no appreciable abruptness about

this

key change because the two

PROCEDURES OF TONALITY CHANGE Ex.

27-16.

Violin

Haydn: Quartet, Op.

473 64, No. 6,

lhi;fff}H

I

Violin n >j'''''''J

^J''

I.

?;

^s^^ ^^

Viola

m

Cello

if cresc.

^^ ^ £/•

6

*

Q

?-e-

cresc.

331

sf 33:

^E p

ffi

^^

? ^-

te

cresc.

ICE 5;^

cresc.

U /

{/•

ia

^ S ^

»/

»-

J

^/

if

Y

5^

i/

if

^^ ^ M P

f

ttrrf-iT^ /

V

# sf

^f

^f

^

10

t

^

if

a

^fg

m-M-m-

:a dtrjtcif

9^^

/

-/

^

?=i^ f^

f=^=^

^^

^^

^

rJ

90

=Z2I

^^ F^^

^

—

474

PROCEDURES OF TONALITY CHANGE

Ex. 27-17 and Ex. 27-18, however, contain

shifts

of tonal center that are not

only abrupt but, at times, of distant relations. In the Beethoven, for example, the rapid tempo contributes to the effect of merely sliding the tonic down a minor

second

—from /-sharp

excerpt

Ex.

is

no

less

F

major.

Symphony No.

8,

i

P

^ Ex. 27-18.

to

The

succession of keys in the

Brahms

unusual.

27-17. Beethoven:

^ El

minor

fc#

^ ^e

Brahms: Symphony No.

Finale.

p

i ^»

4

g

tel

p^

m i

fe#

4,

Allegro giocoso

Although

its

harmonic

style

is

less

accessible than in the previous examples,

C

measure 3 to E-flat in the next measure. The two sections are related thematically through the sequence of perfect fourths in the bass, the first note of which forms a step-progression of^ -f e-flat. But there is an unmistakable change of tonal center after the Ex. 27-19 contains a similar abrupt

—

double bar.

shift

of tonal center from

in

475

PROCEDURES OF TONALITY CHANGE

Symphony of Psalms, III. Copyright 1941 by Russischer Musikverlog Renewed 1958. Copyright & Renewal assigned to Boosey & Hawkes Inc. Revised Version Copyright 1948 by Boosey & Hawkes Inc. Reprinted by

27-19. Stravinsky:

Ex.

;

permission.

^

-

Soprano

-^

i

i

m

/

=te

*

^ a

s

t

Alto

iS: Tenor i'

^-

('

f

'i

^P

8

^

/

Bass

P^wr

Molto meno mosso

p J

'V\.

^ i

.

>

jfgg

p

p

=|:

±=21

—^.—5:

ffi

2

s'

J2:

-a

> J

=

^

72

^ -I I

^

i

^

ZZL

r

r

subito

3:

g

^

^

cresc.

JQ_

f

ll

^i

subito

g

^

J

^^^^

p

g

J

/

—n

subito

_P

± g

^

subito

f.

4

^^

Orchestra"

^

> I

^

I

r

i

476

PROCEDURES OF TONALITY CHANGE

Ex. 27-20 contains a succession of tonal centers too brief to classify as full-fledged modulations, since none is established by a cadence and subsequently confirmed.

In their succession, however, the sequence of tonal areas on C, E, G, B, and again C is organized by the chromatically ascending bass line. Each transitory tonic serves as a

momentary point

of focus in an unstable, constantly shifting tonal

context.

Ex. 27-20.

Schumann

:

Symphony No.

\ft

1|^

^

m =«

^

lA

f

i

2,

Adagio.

^|t^j^-l>^^

f f

4p

^

Ex. 27-21 represents the ultimate in abrupt tonal E-flat, D-flat,

and

C majors,

^^

shifts.

f

it

i^

i

The

^

t

keys in this excerpt,

succeed one another through the successive descents

of the major triads that act as their tonics.

477

PROCEDURES Of TONALITY CHANGE Ex. 27-21.

Beethoven: Symphony No.

("Eroico"),

3,

I.

Flute

Oboes

Clarinetti in Bk

Bassoons

Horns in

Ek

Trumpets in

Kli

Violin

I

Violin n

Viola

Cello

Contrabass

Harmonic sequences are

often involved in the process of modulation.

As

in Ex.

27-22, the sequence can be a stabilizing factor, the repeated pattern sustaining

the ear through a series of distantly related, transitory keys.

Ex.

27-22.

Wagner

:

Die Walkiire, Act

Sehr langsahm

I

A7^ Ex.

PROCEDURES OF TONAL/T/ CHANGE 27-22. continued.

Mutation

We

recall that

of tonal center.

modulation, as defined in Chapter 26, requires an actual change

The

process of mutation

— a change

in mode

—retains the same tonic

and should not be confused with modulation. Although many aspects of one key are changed through mutation (e.g. the quahty of most of the diatonic triads, the roots of several diatonic chords notably mediant and submediant), the most important factor, the tonic pitch, remains unchanged. Mutation's primary effect is a change in the "color" of the key from predominantly major to minor, or vice versa. Such a passage occurs in Ex. 27-23. pitch

—

Ex.

27-23. Brahms: Intermezzo, Op. 118, No.

2.

piu lento

tre

corda

Vjt^

VB^

}

479

PROCEDURES OF TONALITY CHANGE

Although not modulating

to

the tonic triad

made

in itself

modulatory, mutation often serves as an easy vehicle

more remote is

keys.

The

following diagram demonstrates that,

altered through mutation, a variety of

new near

for

when

related keys are

readily available.

(original key)

E

e (mutation)

In Ex. 27-24 Schubert twice uses this technique to accomplish relatively remote modulations: A modulating to F major through a minor, and later F modulating

major through/minor. In each case the second form of the chord undergoing the mutation is the pivot chord, i in the old key becoming iii in the new. to D-Jlat

Ex.

27-24. Schubert

Sehnsuchf.

:

pk)

Voice

^

Piano

I

rH; i

J^

P

J

^

y

y y

^m ^m-'''fn CP 4t i

'

ai

yijf-

P

y

^

vT- '^

l^ '

m ly-

ft

Tr p ^-^M

u-

Uj

-^f-^-

f

-f

;

p

^

^

mijL

-M-t tt

f

1

r^—-p

y 1

c>

^

^ m r^r'i ^

J

*

~ ^ T^¥-P

^

480 Ex.

PROCEDURES OF TONALITY CHANCE 27-24. continued.

j¥

r>

yj

i,j)7ri

J'

ll

P^

^M^I

— pr

p

p

r

Exercises

For more detailed assignments see Materials and 1.

Explore the diatonic pivot chord E-Jlat

A major and

c.

d. 2.

major and

a.

b.

F minor F sharp

and and

its

its

Structure

of Music

C

E

supertonic

subdominant minor submediant major pivot tones between the following

its

its

Roman

pairs of keys? Write a

melody

C major

D

major

A-flat

major

major and

major and

of keys:

mediant minor

sharp minor and

b. A-flat c.

Workbook, Chapter 27.

possibilities of the following pairs

What are some possible containing such a modulation. a.

I,

to a near related key. Imharmonic pattern. Such a melody could be a simple arpeggiated version of the chords, or a more complex line. 4. Choose a simple melody and effect a modulation 1 to 2 measures long that leads to a ^restatement of the same melody a major third higher (or lower). f 5. jUsing the following harmonic scheme, construct a number of 3- or 4-part textures and \ 'arrange the best for some instrumental combination. „ L~m-.^J 3.

Using

numerals plot a modulation from a major key

provise at the keyboard, or vocally, a

melody

that

fits

this

'

,,'

,

F:

6.

I

V-/1V

Find other examples chapter.

IV3

V,/vi

/vi^ :(r^)

'S-«'^ VI V7

illustrating the various types of tonality

'J.WlttoU«/

V

ill

changes illustrated in

this

Ind ex

harmonic, 148-161, 152-154, 203, 207 melodic,

dynamic, 4 metric, 2, 4, 96, 97, 110 Accidentals: 77-/5

55,58-61, 67

progressive, 50-53, 55, 76, 157-159, 340, 346,

Anacrusis: 90-99 Anticipation: 109, 111, 186-187, 248-250, 268 Appoggiatura: see Leaning tone

Approach

50ff,

modal. 152-1 5-1 Phrygian, 291-292, 414, 431, 432 plagal, 290

Accent:

interval: see Interval,

approach

Arpeggiation of chord: see Chord, prolonged

Augmentation: S3, 186 Augmentation Dot: 8

414, 452/ supertonic plagal, 335 terminal, 50-55, 55, 70, 76, 154-157, 288, 290. 325, 346. 458 tonic-dominant, see Half cadence

transient-terminal,

56-88,

159,

396, 400, 403, 407, 419, 421,

386,

391/,

422, 452,

453 Cadential consonance: see Consonance, cadential

Basic associate:

100,

101, 275

Basic consonance: see Consonance, basic

Basic duration: 2, 4, 200/ rest equivalents, 7

beaming, 6 in

compound

subdivision

meter, 10

dominant, 219^, 276, 279-281

Basic melody: 87-99, 244

Basic pitch: 101, 105, 107, 121, 122, 124, 133/7, 163, 164, 168, 170, 178, 187, 190^, 194

Beam: 5-6 1,

2

Cadence: authentic. 288-290, 294, 362. 386 deceptive. 158, 340-343, 362

dominant-tonic, 120, 122, 154-157. 179, 288290 {see also Authentic) half, /5.V. 285. 291-292. 326. 339 •

Canon: 183 Changing tone: 182, 247 Chorale prelude: 200 Chord: 205, 214-219 diatonic, 217

of. 12

Beat (as rhythmic pulse): Bichord: 274 Binary form: 370-381 rounded, 379-381

Cadential tonic six-four: 282/, 309-312 Caesura: 52

dominant seventh, 286-288 doubling, see Doubling embellishing, see Embellishing chord fundamental position, 223 inversion, see In\ersion leading tone, 301-303, 365 major minor seventh (Mm;), 286-288, 384, 387. 396, 430 mediant, 343-349 mutated, 281/, 359-364 neighbor, see Neighbor chord passing, see Passing chord pivot, 461-465 prolonged. 229-230, 278, 314, 407 relationship, 351-352 secondary dominant, 383-437 of dominant. 388-398 of mediant. 417-423

Note: Italic type indicates pages on vvhich the definition of a subject appears.

481

482

INDEX of subdominant, 398-404

in leading tone chord, 302

of submediant, 411-417

in

of subtonic, 423-424

in three voices, 238-240

of supertonic, 404-408

submediant chord, 342

in tonic six-four chord, 310-311

subdominant, 236, 276, 281-285 submediant, 337-343

Dyad: see Diad

Dynamic

accent: see Accent,

dynamic

supertonic. 326-336 tonic, 219j^, 236, 276-279, 303, 345

succession, see

Harmonic

succession

Circle of fifths: 43 Clef:

Echappee: see Escape tone

alto, 14/ri

Elision: 80, 360 Embellishing chord: 314-315, 386

bass, 13 c,

13-14

•Escape tone: 105, 107, 111, 189, 248-250, 267 Extension:

movable, 13-14 tenor, 14/n

by interpolation, 79 by variation, 83

treble, 12

Closed score: 253 Codetta: 150. 157 Common tone relations: 328^, 351^, 401j^ Consonance: 127-129, 181, 214 basic, 127-129 cadential. 127-129, 139, 157, 207, 238

decorative, 127-129 157, 238, 278 Contrary- motion: 137-138, 139, 140, 142, 151,

cadential, 78

False relation: see Cross relation

Fauxbourdon: 207 Fifth of chord: 223-224

156. 164, 179, 329, 333, 344, 368

Figured bass symbols: 224-227

Contrast: 80-81, 185, 320

Flag: 5-6

Contrasting phrase structure, 69 "Corelli clash": 273 Counterpoint: 113 Cross relation: 792-195, 390

Form: binary, 370-381

harmonic rhythm and, 307 key relations and, 378-379

D.C. (da capo): 324 D.S. (dal segno): 324

Deceptive cadence: see Cadence, deceptive Decorative chords: see Types under chord. e.g.. Chord, passing Decorative consonance: see Consonance, dec-

melodv and. 62^ phrase structure and, 66^ song form and trio, 381-382 ternar^, 320-326 texture and, 325 through-composed, 353-359 tonality and, 29 Free tone: 274 Function, tonal: 219, see also Root relations Fundamental pitch: 26

orative

Decorative pitch: 100-\\\, 133^, 190^, 240-244, 266-270,

383.

{see

also

Specific

types,

escape tone) Density: 215 Diad: 227 Diatonic scale: see scale Diminution: 83, 186 Direct fifth: 152, 263 Direct octave: 152, 156. 263 Dissonance: 127-129, 181. 214 e.g.,

Dominant: chord, see Chord, dominant scale degree. 39. 56. 71. 89. 90. 219, 271

Dominant-tonic cadence, see Cadence, Dominant-tonic

Doubling: in

augmented mediant chord, 349

in four voices, 253-255

Gamut:

13

H Half cadence: see Cadence, half

Harmonic Harmonic

parallelism: 207. 300, 367. 369 progression: see Harmonic succes-

sion

Harmonic rhythm: 237, 505-308, 338. 344 Harmonic sequence: see Sequence, harmonic Harmonic series: 25, 232 Harmonic succession: 154/, 219-223, 260-262, 339 283

basic,

483

INDEX

Harmony:

Chord

see

Heterogeneous spacing: see Spacing Homogeneous spacing: see Spacing llomoplionic: 113, 1%, 235-237, 2:)1 1^53

Homophony:

Leading tone: 39-40, 1;')7, 219 Leaning tone: 105-106, 111. 187-189, 248-250, 267

196

Ledger

lines: 13

M Imitation: 164-165, 168, 183-186, 198-199, 280 Imperfect terminal cadence: 55

Major-minor seventh (Mmy): see Chord

Intensity:

Mediant: 40,

1

Meter:

Interval:

57, 89,

approach, 150

compound,

cadential, 150/

simple, 4

classification of, 128-129

hannonic.

16, 119,

liarmonic succession melodic, 16 scale and, 23 stable,

signature.

208-209 of,

N3

table of, 17

ultimate, 150 unstable, 144-147, 181, 190, 214

4.

10

10

Metric accent: see Accent, metric Metric rhythm: 3 Modal cadence: see Cadence, modal

Mode:

134.214

90

2, 3

35, 125

change of, 45 Modulation: 45-47, 85, 160, 161. 435. 439-459 chromatic inflection, 466-469 enharmonic, 469-471 implied, 458-459 pivot chord, 461-465 pivot tone, 465-466

vertical, 119, 208-209

Inversion:

chord, 224-227 first, 225-227

transitory, 48, 442

dominant, 279-281

Monophonic: 113

dominant seventh, 293-301

Motive: 54, 63-66, 165-166, 186, 187, 376 Mutated chords: 359-364 Mutation: 45-47, 84, 194, 323, 359-364, 381, 478-480

interval, 27

leading tone, 301-303 mediant, 347-351 melodic, 84 secondary dominant, 395-396 subdominant, 281-285 submediant, 347-351 supertonic, 330-336 tonic, 277-279 second, 225-227

dominant, 312-314

dominant seventh,

293, 297-298

parallel, 317-318

secondary dominant, 395-396 subdominant, 314-315 tonic, 309-314, 315 triads, 309-318

N Neighbor chord: 243, 273, 296, 324, 339 Neighbor group: 108-109, 111, 136137 Neighbor tone: 103-104, 111, 136-137,

177.

241-244, 267, 273-275 Non-chord tone: 266-267, 273-275, 286/, 321, 383, (see also Decorative pitch)

simultaneous, 273-275

Note head: Note stem:

5

5

third, 293, 298-301

dominant seventh, 298-301 secondary dominant, 395-397

Oblique motion: 137-138, Octave segment: 14

140, 151. 333

Osrinato: 206, 368, 379

Overtone

series: see

Harmonic

series

Key: 32 distant related, 465, 469, 474

near related, 446-450 parallel. 43

relation, 445-452 relative, 43

signature, 40-44

Parallel motion:

137-138,

142,

263, 326, 368

Parallel phrase construction, 68

151, 233, 262-

1

484

INDEX

Partials: 25 Passing chord: 243, 297, 302, 305, 312-314 Passing tone: 102, 104, 111, 134-136, 137, 241244, 267, 273-275

Pedal: 190, 206, 270-273, 306, 402 Perfect terminal cadence: 55 Period: 55/n, 70, 400

double, 71 Phrase: 54, 62-63, 66-74 asymmetrical, 69 symmetrical, 69 truncated, 80 Pitch:

1,

key signature

of,

44

parallel, 43 relative, 43 Sequence: harmonic, 344-345, 349-351. 364-366, 387-388, 406, 434-437, 477-478 melodic, 77, 79, 101, 122, 166-168, 187, 384 Similar motion: 137-138, 140-141, 142, 263, 328 Sixth chords (parallel): 207. 300, see

12-14

151,

also

Slur: 8

Song form and

Pitch spectrum: 14

Sonority: 27^-219, 238, 317 Spacing:

Polyphonic: 113 Prime: 226, 301,302,328 Progressi\e cadence: see Cadence, progressive Prolongation: see Chord, prolonged in

349,

Fauxbourdon

Pitch association: 119-124,205-209

Pulse:

368,

close,

trio:

381-382

256-258

four voices, 255-260

heterogeneous, 212, 257-258

homogeneous, 212, 256-258, 259

1

compound

meter,

open, 256-258

1

three voices, 209-213, 232-235

two

voices, 130-132

Staff: 12, 13

Statement: 320 Step-progression: 93, 95, 96-105, 121, 163, 178,

Range, voice: 130,211,253 Recapitulation: 379 Repetition: 76-80, 97, 165-166, 186, 320, 323 Resolution: change of bass, 178-180, 245-246 deceptive, 425-429 irregular, 424, 430-434 ornamental. 176-178, 247-248 Restatement: 320, 326, 381

40, 57, 157

Subject: 183 40, 57 Subtonic: 39-40 Supertonic: 40 lowered. 193 Suspension: 109-110, 111. 170-182, 187. 188, 269-270, 287, see also Resolution 2-3, 173, 176, 181, 244-248, 245, 248. 269-

Retardation: 180 1

accent, see Accent, metric

phrase structure and, 66-67

270

Rhvthm:

4-3, 173-174, 181, 245. 248. 269-270

metric, 3

Rhythmic Rhvthmic Rhvthmic

Sub-division: 12

Subdominant: Submediant:

Rests: 7-8

Rhvthm:

474 Structural interval: 137^ Structural pitch: 104, 134/, 205

6-5. 173-175.

association: 113-119, 196-200, 233 diversity: 115^, 206

7-6, 173. 177,

181,248.269-270 181,248, 269-270

9-8, 173-175, 181-182, 244-245. 248, 269-

unitv: 200-204

270 Syncopation: 3-4, 170-172, 181, 186, 187, 203

Root: 2V, 26 chord, 223, 284, 337/, 399/ doubled, 238 interval, 27, 157

position, relations.

225-227, 276# 154-159, 161,

276^, 279,

333^,

336. 338, 344

Tempo:

1

Terminal cadence:

see Cadence, terminal

imperfect: 55 perfect: 55 Ternary form: 320-326, 379

Texture: 113, 118/, 200, 205, 206-207, 235-237. 251-253.280,325, 378

Scale:

chromatic, 44 degree, see Separate supertonic, etc. diatonic, 32-39

Theme: entries,

e.g.,

tonic,

376/

Third of chord: 223-224 Third relation: chromatic and diatonic,

361ff, 436, 450-451

485

INDEX major. 216-217 minor, 216-217

Through-composed form: 353-359 Ties: 8

Timbre: Tonal function: see Function, tonal Tonal shift: 439; 442/, 450/, 472^ 1

Tonality: 79,29-30, 122. 219 change of, 161,439-459 form and, S5j

1

ritone:

resolution

of, 145-146. 263.

287. 294, 297

Truncation: 80 Two-voice framework: 119-124

Tonality framework: 21-24, 87-88, 92, 94, 98,

U

119-124, 126

Tonic: 20, 24, 26, 28, 39, 45, 87, 90, 125. 193, 219, 271. 276, 285, 354 Transient-terminal cadence: see Cadence, transient- terminal Transitory moiiulation: see modulation, transitory

Transpose: 33/n Triad: 215, 218 augmented, 217 diminished, 217 fundamental, 224

Ultimate interval: see Interval, ultimate

Variation: 81-85, 186 Vertical framework: 205

Voice: crossing of, 235 leading, 262-265 overlapping, 264

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