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Schoenberg’s theory of motive, shaped by his understanding of the constraints on musical composition imposed by human cognitive processing (his “laws of the mind”), offers insight into how we organize our understanding of music in ter ms of categories of musical events. Motives were, for Schoenberg, where musical recogni-tion started, and the coherence of musical motives was what made musical com-prehension possible. As we have seen, these two functions are replicated in cognitive categor ies. Our preferred level of categor ization is at a level in the middle of a tax-onomy — the basic level — which, like the motive, strikes a compromise between efficiency and infor mativeness. The categor ies we use most often in everyday life

50. Carl Dahlhaus, Nineteenth-Century Music, trans. J. Bradford Robinson (Berkeley: University of California Press, 1989), 273.

cate g ori zat i on 59 are not defined in ter ms of individually necessar y and jointly sufficient conditions.

Instead, they have variable membership: some member s are more typical of the cat-egory than others, and membership in the categor y is graded rather than an all-or-nothing affair. Musical motives show a similar amount of variation, and it is through developing a notion of what they have in common — a conceptual model for what is typical of the categor y — that we begin to comprehend the musical organization of works like those that f ascinated Schoenberg.

As the analysis of Wagner’s use of the Leidensmotiv shows, Schoenberg’s con-ception of a motive is not adequate for all circumstances (especially in its reliance on rhythmic figuration), nor are composers always content to establish a single model for a motive and stick with it. Indeed, they may vary it constantly (as did Wagner in the case of the Leidensmotiv), or they may combine the models for different motive forms in any number of ways (as Cone’s work on the problem of motivic der ivation shows). Although focusing on motives offers a place to star t, it is on the more gen-eral notion of a musical categor y — free as it is from associations with Beethoven’s compositional process, fascinating as that is — that I want to focus. While a collec-tion of assorted motive forms is a good example of a musical categor y, categor ies can be much more various and str uctured around whatever set of musical relation-ships seems best to account for what is salient about a par ticular repertoire. The rel-evant units may be harmonic (as in a chaconne), involve a repeated bass patter n (as in a passacaglia), or combine the two (as in the linear cadential patter ns that Susan McClary has shown provide a structural framework for music of the sixteenth cen-tury);⁵¹ music of the twentieth centur y suggests an even greater number of possi-bilities. And music (construed as patter ned sound) may be just one of a number of contributing factors: one could also envision musical categor ies infor med by the text being set (of particular importance for liturg ical music) or the affect that is to be summoned (a concer n for some types of dramatic music). In all cases, the choice and structure of the relevant musical categor ies will be guided by the global con-ceptual models relative to which the local models for each categor y are framed.

My proposal, then, is that categor ies are where our conceptualization of music starts.

If to think is to think in ter ms of categories, then to think of music is to think in ter ms of musical categor ies.Viewed this way, categor ies constitute an analogue— or perhaps replacement — for the notion of a group as it has been developed by Fred Lerdahl and Ray Jackendoff. For Lerdahl and Jackendoff, musical under standing begins with the process of segmenting a musical work into contiguous sequences of pitch-events, drum beats, or the like.⁵² Each such segment constitutes a g roup, and groups are arranged into a strict hierarchy that ultimately yields the entire work of music.⁵³ Musical categor ies

51. Susan McClar y, Conventional Wisdom: The Content of Musical Form (Berkeley: University of Cal-ifornia Press, 2000), 14 – 16.

52. Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, Mass.: MIT Press, 1983); the process of grouping is descr ibed on p. 13; the definition of a group is given on p. 37.

53. By “strict hierarchy,” I mean a hierarchy in which the boundar y points at each superordinate level confor m to boundar y points at the level immediately subordinate. Lerdahl and Jackendoff define this sort of organization as “hierarchical”; see Lerdahl and Jackendoff, A Generative Theory of Tonal Music, 13, 37. Conceptions of hierarchy as they are applied to music are discussed in g reater detail in the latter part of chap. 7.

can absorb many of the functions of groups — specifically, the role of the group as the first level of organization for musical phenomena — but do not require absolute con-tiguity or str ict hierarchical organization. As a result, a theor y of musical categor ies can easily account for the multiple strands of polyphonic music in a way that group-ing theory cannot. Each of the overlappgroup-ing entr ies of a work in canon, for instance, could be regarded as a member of a category; this sort of analysis is simply impossi-ble with g rouping theor y, since overlaps between groups are not per mitted.

If categories are where our conceptualization of music starts, they must be closely linked to concepts themselves. At the r isk of some confusion, I would like to go further and suggest that musical categor ies are concepts. Now, to attempt any definition of a concept is to (at least potentially) embroil myself in a long-standing debate within philosophy and cognitive science.⁵⁴ To skirt this debate, I concentrate on a definition of “concept” that reflects recent work in the mind sciences and the brain sciences, and that can be applied to music. Although I think this definition can inform the larger debate on “concept,” I shall leave the substance of the debate for another time.

The definition of “concept” I develop here is influenced by the work of Gerald Edelman, who has been interested in developing a biological approach to con-sciousness. Edelman’s definition of a concept is developed as a descr iption of the capacities necessar y for the control of complex interactions between an organism and its environment:

An animal capable of concepts is able to identify a par ticular thing or action and con-trol its future behavior on the basis of that identification in a more or less general way.

It must act as if it could make judgments based on recognition of category member-ship or integ rate “particulars” into “universals.” This recognition rests not just on per-ceptual categor ization (although a concept may have a highly sensor y content) but, to some degree, must also be relational. It can connect one perceptual categor ization to an-other even in the absence of the stimuli that tr iggered these categor izations.⁵⁵

Thus to have concepts involves not only the process of categor ization but also rec-ognizing relationships between categor ies.⁵⁶ What is also impor tant is that having concepts is a capacity that is not limited to humans, a point also made by Donald Griffin.⁵⁷ Concepts are thus not necessar ily tied to language.

54. For a recent and stimulating sally in this debate, see Jerry A. Fodor, Concepts: Where Cognitive Sci-ence Went Wrong (Oxford: Clarendon Press, 1998).

55. Gerald M. Edelman, The Remembered Present: A Biological Theory of Consciousness (New York:

Basic Books, 1989), 141.

56. Other works that either make a strong connection between categor ies and concepts or asser t their equivalence include James Hampton and Danièle Dubois, “Psychological Models of Concepts,” in Categories and Concepts: Theoretical Views and Inductive Analysis, ed. Iven van Mechelen, James Hampton, Ryszard S. Michalski, and Peter Theuns, Cognitive Science Ser ies (London: Academic Press, 1993), 11– 33; Barsalou, “Flexibility, Structure, and Linguistic Vagary in Concepts”; Barsalou et al., “Concepts and Meaning”; Smith and Medin, Categories and Concepts; and Gregory L. Murphy and Douglas L.

Medin, “The Role of Theories in Conceptual Coherence,” Psychological Review 92 (1985): 289 – 316.

57. Donald R. Griffin, Animal Minds (Chicago: University of Chicago Press, 1992), chap. 6. A simi-lar approach can be seen in the work of Douglas Hofstadter and his associates, which has resulted in a number of computer programs that deal with relatively compact bundles of information they call “con-cepts”; see Hofstadter and the Fluid Analogies Research Group, Fluid Concepts and Creative Analogies:

Computer Models of the Fundamental Mechanisms of Thought (New York: Basic Books, 1995).

cate g ori zat i on 61 With this perspective in mind, let me propose that a musical concept has three character istics. First, it is a product of the process of categor ization. A musical cat-egory, then, is quite literally where our conceptualization of music begins. Second, a musical concept is an essential par t of the means through which we guide present and future actions. These actions thus constitute a sor t of indirect evidence for a cognitive structure almost as ephemeral as music itself . Third, a musical concept can be related to other concepts, including concepts associated with bodily states (both physical and emotional), perceptual categor ies (including sound, which, after all, is not necessar ily music), and linguistic constr ucts.

From the perspective provided by this definition, language — in the sense of nat-ural language — is not required in order to have musical concepts. I have, of course, used language to character ize musical categor ies, as well as the conceptual models around which musical categor ies are organized. But we could imag ine a listener — perhaps a particularly astute listener, but perhaps one no more skilled than Proust’s M. Swann — who develops a musical categor y without recourse to language.While language is still nearly indispensable for communicating features of musical concepts and for developing such concepts in r icher contexts, it is not required.⁵⁸ The notion of concepts independent of language is more than a little provocative, and with con-sequences that extend beyond music and the general debate on “concept” noted above. Where some author s have excluded music from the conceptual realm (because, by their definition, concepts require language),⁵⁹ music can join dance, the visual arts, and any of the other nonlinguistic modes of human expression as a prop-erly conceptual activity.

This perspective on musical under standing also offers a new way to think about musical syntax. Music theor y has traditionally (if not explicitly) character ized syn-tax in ter ms of relationships between categor ies of musical objects or events. For instance, a perfect authentic cadence, as it is usually defined, consists (in par t) of a dominant chord followed by a tonic chord, with bass motion from ₅ to ₁, and with the soprano concluding an octave above the bass. The definition involves categor ies like scale step (₅ and ₁), harmonic function (dominant and tonic), voice (bass and soprano), and interval (the octave). Members of these categor ies, when placed in specific relationships (succession and “above”), produce a component of musical syntax (the perfect authentic cadence).⁶⁰ Musical syntax can also be conceived of

58. The idea that language was not required for musical analysis was one of the ideas behind Hans Keller’s wordless analyses. See Keller, “Wordless Functional Analysis no. 1: Mozart, K. 421,” The Score and I.M.A. Magazine 22 (1958): 56 – 64; idem, “The Musical Analysis of Music,” in Essays on Music, ed.

Christopher Wintle (Cambr idge: Cambridge University Press, 1994), 126 – 28; idem, “Functional Analy-sis no. 9a: Mozart’s Piano Sonata in A Minor, K. 310,” in Essays on Music, ed. Christopher Wintle (Cam-bridge: Cambridge University Press, 1994), 129 – 38.

59. Ray Jackendoff, Consciousness and the Computational Mind (Cambridge, Mass.: MIT Press, 1987);

Mark DeBellis, Music and Conceptualization (Cambridge: Cambridge University Press, 1995).

60. It is worth noting that Type 2 categor ies are chiefly involved in this definition: within a given context, something either is or is not an example of 5; something either is or is not a dominant chord;

and so on. Such categor ies are typical of the sorts of taxonomies established by formal music theor y.

However, note that at least one categor y (for voice) is less explicitly defined and functions more like a Type 1 categor y. For instance, the soprano is, by convention, the highest sounding voice within a mul-tivoice texture, but in instr umental works it may actually sound well below the range of human sopra-nos (and thus be a somewhat atypical example of a soprano voice).

as an emergent property of sequences of musical events. Wagner’s treatment of the Leidensmotiv offers one example of this, but the same can be said of most of the musical works that interest us: it is through the development of local levels of syn-tax that musical works become distinctive, and it is the multivalence of this synsyn-tax that makes repeated listening to the same work a rewarding exper ience. Of course, syntactic structure that is shared between musical works is also impor tant, and in most music there is a dialogue between the two analogous to the dialogue between the local and global models relative to which musical categor ies are framed.⁶¹ Elab-orating this approach to musical syntax is the main goal of chapter 4. There we will see how composers rely on syntactic conventions to provide a framework for the development of more local patter ns of syntax specific to individual works.

Before we can more fully investigate the role musical concepts play in under-standing and the way musical syntax comes about, we need to consider two impor-tant issues. First, there is the issue of how relationships between concepts are estab-lished. This will be taken up in chapter 2, which explores how conceptual domains such as music and language are cor related through the process of cross-domain mapping. This process allows structure from one conceptual domain to be brought to bear on another and for relationships among concepts to be established. Second, there is the issue of where conceptual models come from and how they are used to guide reasoning. Chapter 3 shows how concepts and conceptual relationships are combined into conceptual models and how conceptual models are connected together to create theor ies of music.

61. My perspective on musical syntax owes a debt to Eugene Nar mour’s construal of musical style.

Narmour distinguishes between intraopus style (which is specific to a g iven work) and extraopus style (which can be seen across a number of works). See Narmour, The Analysis and Cognition of Basic Melodic Structures; and idem, The Analysis and Cognition of Melodic Complexity: The Implication-Realization Model (Chicago: University of Chicago Press, 1992).