Music Analysis

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Music Analysis and Music Perception Music Analysis, 1998, vol 17. No.1 Ian Cross [email protected] Introduction In his article on Analysis in Groves, Ian Bent asserts that "Underlying all aspects of analysis as an activity is the fundamental point of contact between mind and musical sound, namely, musical perception." (Bent 1980). If this assertion is accepted (and it does seem fairly plausible), it appears that consideration of the nature of musical perception should be of central concern to the music-analytic community. However, it seems that only a small number of analysts have devoted much attention to perceptual issues, most analytic and theoretic literature yielding only infrequent and rather diverse references to such topics. Nevertheless, the references that do exist enable something to be inferred about the notion of musical perception as it may appear from the standpoint of the majority of analysts. A common set of assumptions or beliefs seem to run through statements such as: (i) "Only the recognition of an a priori decision to hear certain patterns in a piece can account for the sense of directedness and culmination when those patterns are actually heard" (Smith, 1981, p 157) (ii) "We should try to hear a twelve-tone piece, then, not only in itself but also in reference to its basic set and to the operations of the twelve-tone system" (Hyde, 1993, p 63) and (iii) "The whole question of deciding 'what one hears' is problematical. After all, I can 'hear' the most preposterous analytical relationships if I choose to; it is a question of deciding what I want to hear." (Cook, 1987a, p 57). The commonality here is the idea of musical perception as something that is essentially conscious and volitional, indeed, more-or-less untrammelled by anything other than acts of individual will guided by analytic insight. Harking back to the quote that opens this paper, it should be admitted that it was presented in incomplete form. In full, it reads "Underlying all aspects of analysis as an activity is the fundamental point of contact between mind and musical sound, namely, musical perception (see Psychology of Music)." In other words, the implication is that to provide an adequate account of musical perception, reference must necessarily be made to the empirical and scientific findings of the psychology of music. This immediately poses the question of whether perception as I have construed it to be conceived of by many analysts squares with perception as characterised within the psychology of music. The simple answer is that the two accounts are fundamentally incompatible; far from perception being conscious and volitional, the findings of the psychology of music appear to indicate that perception of aspects of music can be, and often is, more-or-less involuntary or "reflexive", and that it necessarily involves nonconscious processes. What can account for this mismatch ? It could be (as Cook (1994) argues) that perception as studied within music psychology is in fact musicological perception - that the empirical study of the psychology of music is predicated on simple music theoretic notions to an extent that undermines its capacity to explain musical perception. There are at least two reasons for disputing this view. While Cook's criticism of "theorism" (an a priori reliance on music theoretic concepts as constituting or corresponding directly to cognitive categories and concepts) may be levelled at specific studies of music cognition, it is not a charge that can be levelled against all studies of music cognition de natura. At the very least, in providing a framework for discourse about musical phenomena, music theory has an instrumental utility for studies of music cognition in that it may serve as a basis for initial hypotheses about categories of musical experience that are themselves open to empirical evaluation. Moreover, it can scarcely be argued http://www.mus.cam.ac.uk/~ic108/MusicAnalysis/

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that those many experimental studies that employ musically untrained listeners as subjects and require them to make judgments that do not rely on any overt use by them of music-theoretic concepts or labels in their responses fall into the error that Cook condemns. One can instance studies such as those by Sloboda and Parker (1985) and by Oura and Hatano (1988), which examined the nature of recall memory for short pieces of music simply by requiring both musically experienced and inexperienced subjects who had heard the piece to sing or hum it; in addition, a number of recent studies, such as that by Deliège, Mélen, Stammers and Cross (1996), have examined the capacities and strategies used by both musically experienced and inexperienced subjects in musical construction tasks employing purely auditory materials. A "folk psychology" of music One might seek to sidestep this issue by questioning whether the music-analytic idea of perception harmonises with perception as understood within the broader domain of cognitive psychology. Again, the mismatch persists; the idea of perception as involving involuntary and non-conscious processes is common to virtually all psychological domains. Nevertheless, the music-analytic account of perception fails to square with the cognitive-scientific account in a way that is at least definable from the perspective of cognitive science. The "analytical idea" of perception can be thought of as a partial "folk psychology" of music, or of musical analysis, on the analogy of the distinction between cognitivescientific accounts of quotidian behaviour and common-sense accounts of everyday life. A "folk psychology" is, in Jerome Bruner's (1990, p 35) words, "a set of more-or-less normative descriptions about how human beings `tick', what our own and other minds are like, what one can expect situated action to be like, what are possible modes of life, how one commits oneself to them". In this "folk psychology" of musical analysis, the act of perception is subject to purposive volitional intervention, and categories of experience - qualia - may be consciously shaped and re-made in the light of the analyst's enquiries (for the analyst, at least). But if this is a folk psychology, it is being employed within a very restricted domain, very far away from that of everyday life. According to Bruner, we "learn such a folk psychology early, learn it as we learn to use the very language we acquire, and as we learn to conduct the interpersonal transactions required in communal life." The music analysts' folk psychology, however, is being used to articulate and to impart highly particular insights within a community of experts. There are a number of possible grounds for objecting to such a usage. The apparently unexamined nature of such a vernacular account of the processes of perception sits ill with the detailed and deeply contextualised specificity that characterises the act of musical analysis. Moreover, while the employment of an analytical "folk psychology" in discussing the experience of complex musical phenomena may well adequately characterise the analyst's listening processes, the fact that these complex musical phenomena are unlikely to be present in the consciousnesses of ordinary listeners - who may nevertheless enjoy music - makes it difficult to relate the findings of musical analysis to the musical experiences of the "averagely educated" but musically untrained listener (except that one can simply assert that the perceptions of music analysts and the perceptions of such untrained listeners will be different). Further to this last point, some of the empirical findings of the cognitive science in respect of musical perception seem to indicate that little qualitative difference may exist between the perceptions of musically untrained, and highly musically educated, listeners (see, for example, Bigand's (1993) study in which musically trained and untrained listeners are shown to exhibit remarkably similar sensitivities to global tonal-harmonic structure in the course of listening to melodies). So, if this "folk-psychology" of musical perception is partial, unexamined, and potentially in conflict with the findings of "scientific" psychology, perhaps Bent's suggestion should be heeded, and the Psychology of Music should be employed to underpin the structures and methods of analysis. Perhaps, as Erickson (1982) appears to suggest, music analysis might even come to be recognised as a sub-domain of the study of musical cognition. I would imagine that such a view, involving what Cook (1987a, p 223) calls "the deletion of the listener as a free agent", would find little favour within the music-analytic community. Moreover, the hermeneutic and critical dimensions to music analysis that Cook and others such as Treitler (1980), Tomlinson (1984) and Kerman (1985) have insisted upon would seem to render it immune from contamination by "postivistic" or "reductionist" cognitive-scientific explication by locating music analysis firmly in the "mythopoeic" cultural domain. But such a defence appears untenable in the light of contemporary views of scientific enquiry, which stress that it cannot be defined solely in terms of the "positivism" previously held to differentiate it from other modes of investigation, and are disposed to http://www.mus.cam.ac.uk/~ic108/MusicAnalysis/

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view its conduct as the result of the "situated-ness" of that positivism within more general frameworks of thought and behaviour (see Brown, 1977). Feyerabend (1981, p 7) suggests that the distinction between hermeneutic methods of explication (which he terms "historical traditions") and scientific accounts (which he terms "abstract traditions") is, in fact, illusory; he proposes that "abstract [i.e., scientific] traditions are not alternatives of historical traditions; they are special parts of them. The structures they contain, the abstract notions that enter these structures, can be learned, understood, adapted to new cases only because they form parts of an underlying historical medium that supports them, gives them meaning and shows how they can be applied." Even those such as Lakatos (see, e.g., Lakatos 1970) who have no truck with the "conventionalist" notion of science seemingly implicit in Feyerabend's statement would still accord scientific activity a historical dimension that ties it to the time and culture within which it is conducted. Thus the "culturally-situatedness" of music analysis provides no defence against scientific imperialism, and supplies no compelling reasons that would prevent science from playing some role in music-analytic endeavour. While it is difficult to sustain an argument for the subsumption of music analysis by the study of music cognition, it does seem plausible to argue that music analysis should at least be underpinned by scientific accounts of perception, replacing analytical "folk psychological" views of perception with theories that are grounded in cognitive science if these can be shown to be more accurate, more generalisable, and more fruitful. Indeed, the term "folk psychology" was brought into common currency by cognitive scientists such as Stich (1983) and Churchland (1984) who wished to characterise the "everyday conceptual schemes for accounting for our own actions in terms of beliefs, desires, etc." (Greenwood, 1991, p 7) which would be explained away and replaced by the findings of cognitive science. In order to test the proposition that analytical "folk psychology" should be replaced by cognitive science it seems appropriate to review the two most highly developed analytical methods that purport to be based on cognitive premises, those of Lerdahl and Jackendoff, and of Narmour. These methods will be discussed in the context of brief analyses of the first four bars of the second movement of Mozart's Sonata K.311. Lerdahl and Jackendoff - a generative theory At first sight, Lerdahl and Jackendoff's (1983) theory, which is intended to "account for the musical intuitions of a listener experienced in a given idiom" appears to be an amalgamation of psycholinguistic and Schenkerian theory. It seeks to elucidate a number of perceptual characteristics of tonal music segmentation, periodicity, differential degrees of importance being accorded to the components of a musical passage or work, the ebb and flow of tension and relaxation as a work unfolds - by employing four more-or-less distinct analytical levels, each with its own more-or-less formal analytical principles, or production rules. These production rules, or Well-Formedness rules, specify which analytical structures may be formed - which analytical structures are possible - in each of the four analytical domains on the basis of a given musical score. Each domain also has a set of Preference Rules, which select between the possible analytical structures so as to achieve a single "preferred" analysis within each domain. The four domains - Metrical, Grouping, Time-Span and Prolongational - are conceived of as partially interdependent and at the same time as modelling different aspects of a listener's musical intuitions. Thus structure within the domain of Grouping is largely predicated on events at the level of the musical surface, the Metrical domain is based on principles of binary and ternary hierarchy (though strictly limited in terms of the levels to which the hierarchy might extend), the Time-Span domain is predicated partially on the Grouping and Metrical structures but partially on principles of tonal-harmonic referentiality, while the Prolongational domain is based largely on the dynamics of tonal-harmonic relations and partially on the Time-Span structure. Hence the Grouping and Metrical domains are largely derived from the musical surface, their Well-Formedness rules ostensibly modelling the principles that might apply in the "raw" perception of immediate relations between musical events, while the TimeSpan and Prolongational domains, though taking the products of the other two domains into account, are modelling the application of stylistic and "musico-semantic" knowledge that occurs as part of the perceptual cycle.

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The application of their theory to the first four bars of the second movement of Mozart's K.311 seems uncomplicated. The Metrical analysis (shown in the dots below the piece in Figure 1a) appears selfevident, deriving from Well-Formedness Rules such as those stating that "Every attack point must be associated with a beat at the smallest metrical level present at that point in the piece" (although the lowest, semiquaver, level is not shown in the figure), "At each metrical level, strong beats are spaced either two or three beats apart", etc. These Well-Formedness rules are supplemented by Preference rules, that suggest preference should be given to e.g., "metrical structures in which the strongest beat in a group appears relatively early in the group", "metrical structures in which strong beats coincide with pitch events", etc. The Grouping structure (shown in the brackets above the piece in Figure 1a) appears similarly selfevident, being based on seemingly truistic Well-Formedness rules such as "A piece constitutes a group", "If a group contains a smaller group it must contain all of that smaller group" (thus ensuring a strictly nested hierarchy), etc. Preference rules here specify such matters as the criteria for determining group boundaries (which should occur at points of disjunction in the domains of pitch and time), conditions for inferring repetition in the grouping structure, etc. Thus a group boundary is formed between the end of bar two and the beginning of bar three both in order to ensure the symmetrical subdivision of the first four bars (themselves specifiable as a group in part because of the repetition of the opening of bar one in bar five) and because the pitch disjunction occurring between the G and the C is the largest pitch interval that has occurred in the upper voice of the piece up to that moment. Perhaps the only point of interest in the Grouping analysis is the boundary between the third quaver of bar three and the last semiquaver of that bar, brought about by the temporal interval between the two events (again, the largest that has occurred in the piece up to that moment). Here, the Grouping structure and the Metrical structure are not congruent, pointing-up a moment of tension at the level of the musical surface that is only resolved by the start of the next group at bar five. The Time-Span analysis (tree-structure above the piece in Figure 1a) is intended to depict the relative http://www.mus.cam.ac.uk/~ic108/MusicAnalysis/

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salience or importance of events within and across groups. The Grouping structure serves as the substrate for the Time-Span analysis, the Well-Formedness rules in this domain being largely concerned with formalising the relations between Groups and Time-Spans. The Preference rules suggest that metrically and harmonically stable events should be selected as the "heads" of Time-Spans, employment of these criteria resulting in the straightforward structure shown in the Figure. This shows clearly the shift in metrical position of the most significant event in each Group or Time-Span, from downbeat in bar one to upbeat crotchet in bars two and three to upbeat quaver in bar four. A similar structure is evident in the Prolongational analysis (Figure 1b), which illustrates the building-up and release of tension as a tonal piece unfolds. The Prolongational analysis derives in part from the Time-Span analysis, but is primarily predicated on harmonic relations, which the Well-Formedness and Preference rules specify as either prolongations (tension-producing or maintaining) or progressions (tension-releasing). The Prolongational analysis that results for this passage appears to emphasise those features and structures that might result from a Schenkerian analysis of the passage (see, for example, that by Salzer, 1962), betraying perhaps some of the parentage of the theory. Lerdahl and Jackendoff's theory is a competence theory in the strong sense of the word, that is, a theory that is intended to make explicit the rules and processes that underlie a listener's experience of tonal musical works. As such the theory exhibits several lacunae, some of which the authors themselves acknowledge while others have been identified by reviewers of their work, notably by Peel and Slawson (1984), Rosner (1984) and Clarke (1986). Among the lacunae that Lerdahl and by Jackendoff have themselves identified and addressed (separately) in subsequent work are those concerned with the theory's lack of a detailed, formal account of tonal-harmonic relations and its neglect of the temporality of musical experience. Lerdahl (1988) outlines a theory of tonal-harmonic pitch relations which has much in common with the harmony-space proposed by Krumhansl (1990) (itself related to Schoenberg's (1954/1969) "charts of key regions"). This he further develops in the context of an analysis of the beginning of Mozart's Sonata K.282 in Lerdahl (1996). Jackendoff has been more concerned with describing the nature of ongoing musical experience. In Jackendoff (1987) he examines the nature of musical experience in time in the context of the development of a theory of consciousness that privileges what he calls the "phonological" level (that level of cognitive representation that is directly tied to the "surface" of stimuli), with only indirect links to schematic representations of more complex structures (such as tonal-harmonic relations, semantic networks, etc.). In Jackendoff (1991) he proposes a parallel, multiple-analysis model of musical parsing which relies strongly on multiple non-consciously accessible parsing mechanisms of which only the selective and integrated output is available in the form of conscious experience. Jackendoff does no more than sketch out his parallel multiple-analysis parsing model; it constitutes an untested and preliminary description of the experience of music in time. Moreover, neither Lerdahl nor Jackendoff have sought to extend their theories so as to provide an account of the experience of truly contrapuntal musical textures. Nevertheless, until recently their theory constituted the only comprehensive attempt to relate current understandings of music perception to music analysis; Eugene Narmour has now provided an even more comprehensive theory that takes as its premise the need to account for the experience of music in time and does so by focusing specifically on the perception of melodic line. Narmour - cognition and analysis Narmour's theory appears to be more formal and explicit than Lerdahl and Jackendoff's; however, Narmour differentiates far more sharply than they do between the analytic consequences of styledependent factors and those of the operation of "cognitive primitives" (see Narmour, 1989: 1992), and the formal nature (if not the explicitness) of his theory is mostly to be found the latter domain. He conceives of these cognitive primitives, which are intended to reflect the operation of biologically "hardwired, innate" cognitive principles (after Fodor, 1983) and whose operation is largely derived from Gestalt thinking, as the main determinants of musical structure in cognition. His theory starts by close examination of note-to-note relations, which he typologises according to the degree to which these relations are similar or different, and hence anticipatable or unexpected. The structures that his theory describes are thus intended to map the unfolding of the musical surface in the course of the listening experience. Narmour is much more overtly aware of the difficulty of characterising the listener than Lerdahl and Jackendoff appear to be; although his theory can again be described as a competence theory, it is constructed modularly so as to be ostensibly capable of mirroring the differences between listeners with different degrees of stylistic knowledge, though he conceives of the primitives of his theory as functioning even in the absence of any such knowledge. http://www.mus.cam.ac.uk/~ic108/MusicAnalysis/

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While it is impossible to give even a sketchy account of Narmour's complex theory here, I shall try to provide at least a flavour of it. Very approximately, relations within pairs of consecutive intervals can be classified as exemplifying either Process (if they are similar) or Reversal (if they are different), with small intervals giving rise to implications of continuation or process, and large intervals giving rise to implications of reversal, or differentiation. Similarity or difference can be found both in the domain of interval size and in the domain of registral direction (ascent versus descent). Questions of similarity or difference are determined by the application of quantitative measures (Narmour's "syntactic scales"), so that, e.g., two consecutive intervals that differ by a major third or greater are different, although the definition of difference that is employed is sensitive to context (e.g., when registral direction is reversed in a pair of consecutive intervals, they are adjudged different when they differ by a minor third or greater). These basic terms provide means of classifying groups of consecutive notes, so an ascending passage such as c´-d´-e´-f´ would constitute a Process (symbolised as P), an ascending-descending fragment going from a large interval to a small one such as c´-g´-f´ would constitute a Reversal (R), a figure such as c´-e´-c´ would constitute an Intervallic Duplication (ID) etc. More complex types of classification arise when the implications of the initial interval are controverted by its successor, hence an ascendingdescending fragment such as c´-d´-b would constitute an Intervallic Process (IP), while an ascendingdescending figure such as b-f#´-g would constitute a Registral Reversal (VR), etc. Rhythmic, metrical, harmonic and stylistic factors can be brought to bear on these classifications of consecutive interval structures so as to suppress either the "non-closural" (implicative) or the "closural" (non-implicative) qualities that patterns may bear, thus leading to patterns at the level of the musical surface combining or chaining with their predecessors and successors or being separated from them. The terminal elements of individual or combined patterns are deemed to function at a higher hierarchical level, enabling Narmour's theory to depict relations between non-adjacent notes and on that basis to construct a multi-levelled representation of musical ongoingness. It should be noted that the construal of pattern is not always prospective in Narmour's theory; it is possible for local contextual ambiguity to operate so that the identity of a pattern only emerges retrospectively (represented in his analytic notation by parenthesising the symbols for such retrospective patterns).

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Bearing all this in mind, let us turn to Narmour's analysis of the first four bars of the second movement of K.311. Letters (IP, P, etc.) within the "grouping" brackets identify the patterns involved, while the b's and d's in parentheses above the top system indicate the influence of, respectively, metre and duration. Most notable at first, perhaps, are the separate and independent analyses provided for each voice and the fact that scale-step function is not privileged within the analysis (being regarded as a variable stylistic factor). The three systems show the progressive "transformation" of pitches to higher hierarchical levels, and it should be noted that the steps involved do not produce a neatly nested hierarchy of the sort that Lerdahl and Jackendoff's theory provides. This could be said to arise from the fact that Narmour's "single-domain" analysis conflates the operation of factors that would function in independent domains in Lerdahl and Jackendoff's theory. A major point of divergence between the two analyses is the omission of any event within the last beat of bar two from the highest level; the melodic semiquavers B and G - both possible candidates - are subsumed into the "Intervallic Duplication-Process-Retrospective Registral Reversal" chain, neither functioning as a terminal pattern element and hence remaining at the lowest level. Narmour's analysis has here suffered one tiny addition; the parenthesised letters "fm" have been added above the semiquaver B of bar two to indicate something permitted within Narmour's theory but not present in his analysis, the possibility that a note may act "formationally" as opposed to "transformationally", that is, may portend a transformation to a higher hierarchical level but not in fact achieve this. http://www.mus.cam.ac.uk/~ic108/MusicAnalysis/

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Narmour's analysis thus construes the passage not as a progression from tonic to dominant (as the analysis by Salzer (1962) has it) but as a I-IV-V structure. As he states (Narmour, 1992, p221), "Salzer's analysis" [which he takes to be archetypally Schenkerian] "shows the phrase as one more instantiation and confirmation of tonality, whereas the implication-realisation model shows it as an example where melodic, metric and durational weakening of prolongation of the tonic occurs." In point of fact the terminal level of Narmour's analysis is not so different from the Prolongational structure derived from the application of Lerdahl and Jackendoff's theory (with the exception of their theory's postulating a weak tonic prolongation in bar two). Folk psychology versus scientific psychology Having briefly reviewed the operation of these two theories, we are in a better position to judge whether the ostensible replacement of a music-analytic "folk psychology" by specific and scientific accounts of perception has conferred any advantages. Considered from the analytic perspective, the result is debatable. Both theories are explicit about the bases for their analytic decisions, and can account for aspects of structure that do not seem quite so coherently articulable within more "conventional" approaches. Against this, both theories may appear crude in the accounts that they provide of tonalharmonic relations or of the complexities of musical texture, in part because of that very explicitness; even Lerdahl's development of a sophisticated and formal theory of tonal-harmonic relations can be criticised on the grounds that its "ahistorical" account of harmony renders it unsuitable for sensitive analytic application (a criticism that Cook (1987b) makes of the very similar model proposed by Krumhansl). Moreover, the whole approach to analysis that these theories exemplify is itself likely to seem unacceptable to many analysts. As Cumming (1992) suggests in her review of Narmour's second book, cognitively-based approaches appear to replace the "listening I" with the "cognising brain", almost "factoring out" the analyst as an agent in the act of analysis. Although Narmour, in particular, is explicit about leaving space for the exercise of analytic judgment, it can seem that such cognitively-based theories offer what Nagel (1986) calls "views from nowhere". From the analytic perspective the verdict on the success of these two theories seems at best "not proven". Perhaps that perspective is not the most appropriate from which to judge the merits or otherwise of these theories; it might be more relevant to consider them as instances of the application of cognitive science to music that are intended to explain the listening experience rather than as analytic methods first and foremost. However, even from this perspective the achievements of both theories can be disputed on the grounds that what they are based on are not "veridical" accounts of the experience of listening to music, but more-or-less formal theories about that experience that are predicated on contestable views about the nature of perception and require to be empirically tested (as Clarke (1989) has suggested in respect of Lerdahl and Jackendoff). Their explicitness is perhaps the most positive feature of the theories from the viewpoint of cognitive science. What they provide are not so much fully-formed systems that facilitate the processes of analysis by grounding these in accurate accounts of perception, but arrays of questions, fairly explicit hypotheses about the elements of musical perception and how these might impinge on the processes of analysis that lay themselves open to experimental investigation and perhaps refutation. Indeed, Narmour's theory has been extensively empirically tested by Schellenberg (1996), who finds that a simplified version of Narmour's theory provides a better fit to his results. While the judgment from cognitive science is more positive, it too appears inconclusive. Clues as to why this might be the case can be derived from aspects of both theories which, while not overtly evident in the analyses that they propose, nevertheless strongly influence features of those analyses. In Narmour's theory a strict differentiation is drawn between those aspects of the listening process that are governed by "inescapable", biologically hard-wired, innate perceptual processes, and those aspects that are subject to cultural factors, to knowledge of or to simple exposure to, particular styles. The basis for this differentiation would seem to be a sort of "biological determinism", in terms of which the "facts" of perception can be explained in terms of, and reduced to, an account of the facts of neurophysiology. On this reading, only the workings of hard-wired and innate perceptual processes would be amenable to scientific investigation, that mode of enquiry being unable to account for culturally-determined characteristics of perception. While the same biological determinism is not evident in Lerdahl and Jackendoff's theory, that theory in many places aspires to a level of generality - for instance, in postulating that the majority of their Well-Formedness and Preference rules have universal applicability - that is difficult to reconcile with the idea of science - particularly cognitive science - as culturallysituated (see also Clarke, 1986). Both of these positions are at odds with the rationale adduced earlier for science having some explanatory power in respect of hermeneutic activities, the idea that science is itself a "special part" of the historical tradition that enfolds and derives from culture. http://www.mus.cam.ac.uk/~ic108/MusicAnalysis/

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This contradiction can be resolved by jettisoning the biological determinism, and the claims to universal applicability, in the light of the idea that the functioning and the structure of cognition is determined at least as much by culture as by biology, and, accepting that postulate, that any claims for the universality of cognitive-scientific theories of music must be circumscribed. While many writers have sought to account for mind in terms of neurobiology - or rather, in terms of computational theories of neural structure and function (see, e.g., Churchland, 1986) - some recent theories have proposed that while biology is an evident constraint, the primary determinant of the nature of cognition is culture. Bruner (1990, p 20) states that "the biological substrate...is not a cause of action but, at most, a constraint upon it or a condition for it.", and goes on (p 34) to suggest that: "It is culture, not biology, that shapes human life and the human mind, that gives meaning to action by situating its underlying intentional states in an interpretive system. It does this by imposing the patterns inherent in the culture's symbolic systems - its language and discourse modes, the forms of logical and narrative explication, and patterns of mutually dependent communal life.". In the domain of music and of musical perception, the determinant power of cultural forces is borne out by those few cross-cultural studies that have been conducted (for example, Castellano, Bharucha and Krumhansl, 1984; Arom, 1991; Stobart and Cross, 1994). These indicate that the nature of music and of the experience of music within a given culture are likely to be determined primarily by factors specific to the dynamics of that culture while remaining constrained by general cognitive principles. Thus the uniformitarian principle that would enable universally applicable theories of musical perception to be postulated cannot be confidently upheld, that postulate of uniformitarianism - that past events can only be explained in terms of presently acting and observable causes - constituting one of the most fundamental tenets of science and perhaps the one that confers most explanatory power. And if Bruner is even halfway correct, and mind is formed primarily in the matrix of culture, neither will biological determinism suffice to provide us with generalisable and immutable theories of musical perception. So the issue of whether a scientific account of music perception can replace the analytical folk psychology of music perception remains unresolved, but now open to question. It is perhaps more relevant to enquire whether a scientific account of musical perception should replace a folk psychological account. When the question is redirected in this way, the answer would appear to be that it should not; just as there are no compelling reasons for science not to play a role in the elucidation of hermeneutic activity, it seems that there are no compelling reasons to expect cognitive scientific accounts as currently understood to replace elements of analytic or hermeneutic accounts. It seems more feasible to expect that the cognitive science of music should seek to explain the analytic "folk psychology" of musical perception rather than to replace it. After all, the analysts' "folk psychology" might accurately reflect their own perceptions and intuitions; alternatively, its use might simply constitute the most appropriate strategy for the analyst to adopt in order to "empathically" confront the object of the analysis or even the act of analysis. It could be that a "folk psychology" of musical perception belongs in the same category as the other interpretive tools that the analyst chooses to employ in engaging with the music. This is not to suggest that the entire array of tools is fictive, but simply that their efficacy cannot necessarily be assessed by the same criteria as might be used to assess the adequacy of a scientific method; despite the situatedness of science within culture, its focus on general causes and generalisable procedures is aimed at providing a level of replicability and predictive power that differentiates its procedures from those of the individual analytic act. Nothing in the foregoing is intended as an argument against any efficacy of cognitive science in respect of music perception. Indeed, there are aspect of music perception that appear impervious to all but cognitive scientific method and theory. In particular, the perceptions of those listeners for whom the analysts' "folk psychological" account of perception seems inapplicable - those who are musically untrained - require exploration, and the methods of cognitive science, which are directed towards making explicit the factors that mediate between our experiences and the frameworks of action, discourse and interaction in terms of which those experiences achieve meaning, would seem to provide the most appropriate mode of inquiry. Moreover, the capacity of cognitive science to articulate the unintuitable means that it is likely to have some capacity to be explanatory in respect of the perceptions of even music analysts, in that cognitive-scientific method, if appropriately applied, can be capable of unveiling those aspects of the perceptual process that are not amenable to conscious introspection.

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The cognitive science of music, then, should not be directed towards replacing the folk psychologies that might be used in pursuit of the articulation of analytic insight. If it has any value for understanding music, it should lie in its capacity to bridge the gap between what music feels like - its experiential texture - and the language that is used to describe it and to teach it. To be more specific, the application of cognitive science to music should help traverse the disjunction that exists between the ways that music is experienced by listeners and by practising musicians and the rational frameworks of discourse that are conventionally used to describe and to define music and musical experience. Its "research programme" (see Lakatos, 1970) should proceed by seeking to provide accounts of musical experience that are consonant with the constraints and particularities of embodiment and the concepts of computational logic (see Johnson-Laird, 1983) and with empirically-derived evidence about musical perception, performance and creation. At the same time, its practice must be informed by an intimate awareness of the cultural context within which it is conducted, of the meanings that can be borne by its materials, methods and data. Conclusions In this paper I have postulated the existence of a music-analytic "folk psychology" of musical perception. I have proposed that such a "folk psychology" should be replaced by a scientific psychology, a cognitive-scientific account of perception. I have reviewed two recent theories of musical analysis that appear to be intended to carry out just such a project. I have concluded that neither system can be said to fulfil comprehensively the project of replacing the music-analytic "folk psychology" of musical perception with a scientifically-founded one, and suggested that such a project might be misconceived, one task of the cognitive science of music being not to replace folk-psychological accounts of musical perception but to explain them. In conclusion, it has to be said that it appears to be up to the individual analyst to choose to employ either a folk-psychological theory of musical perception or a cognitive scientific one. The only inference that seems clear from the issues considered in this paper is that the analyst should be aware of which type of theory is being used. For folk psychologies are not immutable; even though cognitive science may not aim to replace them, they are subject to change, and elements of cognitive science may come to infiltrate into our future folk psychologies. I fear that these inconclusive conclusions may seem highly expedient in that they wriggle out of any obligation to provide answers and throw the onus of considering the issues raised in this paper back on to music analysts. However, from a scientific perspective, this seems a wholly acceptable outcome; after all, as Einstein put it (quoted in Feyerabend, 1981, p 83) "The external conditions which are set for [the scientist]...do not permit him to let himself be too much restricted, in the construction of his conceptual world, by the adherence to an epistemological system. He therefore must appear to the systematic epistemologist as a type of unscrupulous opportunist..." References Arom, S. (1991). African polyphony and polyrhythm. C.U.P., Cambridge. Bent, I. (1980). Analysis. In S. Sadie (Ed.), Grove's Dictionary of Music. Macmillan, London. Bigand, E. (1993). The influence of implicit harmony, rhythm, and musical training on the abstraction of "tension-relaxation" schemas in a tonal phrase. Contemporary Music Review, 9, 128-139. Brown, H. I. (1977). Perception, theory and commitment. University of Chicago Press, Chicago. Bruner, J. (1990). Acts of meaning. Harvard University Press, London. Castellano, M.A., Bharucha, J.J. & Krumhansl, C.L (1984). Tonal hierarchies in the music of North India. Journal of Experimental Psychology: General, 113, 394-412. Churchland, P. M. (1984). Matter and consciousness. M.I.T. Press, Cambridge, Mass. Churchland, P. S. (1986). Neurophilosophy. M.I.T. Press, Cambridge, Mass. Clarke, E. F. (1986). Theory, analysis and the psychology of music: a critical evaluation of Lerdahl, F. and Jackendoff, R., A Generative Theory of Tonal Music. Psychology of Music, 14(1), 3-17. http://www.mus.cam.ac.uk/~ic108/MusicAnalysis/

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Clarke, E. F. (1989). Mind the gap: formal structures and psychological processes in music. Contemporary Music Review, 3 (1), 1-14. Cook, N. (1987a). A Guide to Music Analysis. Dent, London. Cook, N. (1987b). Review of first two volumes of Diana Deutsch (ed.) Music Perception. Music Analysis, 6, 169-179. Cook, N. (1994). Perception: a perspective from music theory. In R. Aiello with J. Sloboda (Eds.), Musical Perceptions. O.U.P., Oxford. Cumming, N. (1992). Eugene Narmour's theory of melody. Music Analysis, 11 (2-3), 354-374. Deliège, I., Mélen, M., Stammers, D., & Cross, I. (1996). Musical schemata in real time listening to a piece of music. Music Perception, 14 (2), 117-160. Erickson, R. (1982). New music and psychology. In D. Deutsch (Ed.), The psychology of music. Academic Press, London. Feyerabend, P. (1981). Problems of empiricism, Vol 2. C.U.P., Cambridge. Fodor, J. (1983). The modularity of mind. M.I.T. Press, Cambridge, Mass. Greenwood, J. D. (1991). The future of folk psychology. C.U.P., Cambridge. Hyde, M. (1993). Dodecaphony: Schoenberg. In J. Dunsby (Ed.), Early 20th Century Music. Blackwell, Oxford. Johnson-Laird, P. N. (1983). Mental models. C.U.P., Cambridge. Jackendoff, R. (1987) Consciousness and the computational mind. M.I.T. Press, Cambridge: Mass. Kerman, J. (1985). Musicology. Fontana, London. Lakatos, I. (1970). Falsification and the methodology of scientific research programmes. In I. Lakatos and A Musgrave (Eds), Criticism and the growth of knowledge. C.U.P., Cambridge. Lerdahl, F and Jackendoff, R. (1983). A Generative Theory of Tonal Music. M.I.T. Press, Cambridge: Mass. Nagel, T. (1986). The view from nowhere. O.U.P, Oxford. Narmour, E. (1989). The Analysis and Cognition of Basic Melodic Structures. University of Chicago Press, Chicago. Narmour, E. (1992). The Analysis and Cognition of Melodic Complexity. University of Chicago Press, Chicago. Oura, Y. and Hatano, G. (1988). Memory for melodies among subjects differing in age and experience in music. Psychology of Music, 16(2), 91-109. Peel, J. and Slawson, W. (1984). Review of A Generative Theory of Tonal Music. Journal of Music Theory, 28(2), 271-294. Rosner, B. (1984). Review of A Generative Theory of Tonal Music. Music Perception, 2(2), 275-290. Salzer, F. (1962). Structural Hearing. Dover, New York. Schellenberg, E. G. (1996). Expectancy in melody: tests of the implication-realization model. Cognition, 58, 75-125. Sloboda, J. A. and Parker, D. H. H. (1985). Immediate recall of melodies. In P. Howell, I. Cross and R. http://www.mus.cam.ac.uk/~ic108/MusicAnalysis/

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West (Eds) Musical structure and cognition. Academic Press, London. Smith, C.R. (1981). Prolongations and progressions as musical syntax. In R. Browne (Ed.), Music Theory: Special Topics. Academic Press, London. Stich, S. P. (1983). From folk psychology to cognitive science: the case against belief. M.I.T. Press, Cambridge, Mass. Stobart, H. and Cross, I. (1994). Aspects of Rhythmic Structure and Perception in the Music of Northern Potosí, Bolivia. In Proceedings of the 3rd ICMPC, Liège, Belgium. Tomlinson, G. (1984). The Web of Culture. Nineteenth Century Music, 8, 350-362 Treitler, L. (1980). History, Criticism and Beethoven's Ninth Symphony, Nineteenth Century Music, 3, 193-210. Go back to Ian Cross - Publications

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