Sketch of a Foundation for Music Theory Today
This article was originally delivered as part of a unified group of papers entitled Music Theory: The Art, the Profession, and the Future, which was read at a plenary session of the national conferences of The College Music Society and the American Musicological Society, in Washington, D.C., on November 6, 1976. The other papers read in the session were:
If We Are All Theorists, Why Aren't We All Theorists?, by Richmond Browne
Music Theory's Negativisms, Fallacies, Divisions, and Needs, by Vernon Kliewer
What Theorists Do, by Peter Westergaard
Diversity and the Decline of Literacy in Music Theory, by Carl E. Schachter
Music Theory in Re-Transition: Centripetal Signs, by Allen Forte
(These papers were also included in SYMPOSIUM Volume 17#1.)
As my title indicates, my intention in this brief paper is to sketch one possible current foundation for the making of music theory. In presenting such a sketch, it is axiomatic for me that musical culture—as an instance of which I would view the musical culture of Europe and its extension to the Americas—be regarded as a kind of "linguistic universe" and that a piece of music be regarded as a "linguistic world" within that universe.
What being "linguistic" entails, for me, is to be a system of communication of which the signs, symbols, and expressions are subject to pragmatic, semantic, and syntactic analysis. What being a "world" entails is to exhibit a multiplicity of structural aspects and surface features which make such a world unique with respect to any other world.1 (In terms of music, I am speaking here of what is sometimes called "contextuality"—that is, the idea that each piece of music is in a fundamental sense a working out of certain compositional premises unique to itself.)
I take music theory, then, to be the branch of knowledge devoted to the study of the structural aspects and surface features of existing or possible worlds, or pieces, within the musical universe, and, by extension, the study of that universe as an entity.
The study of existing pieces within the musical universe I shall call "post-dictive" theory; the study of possible pieces I shall call "pre-scriptive" theory.
A crucial question with regard to any theory is whether or not there can be said to be an "empirical test" of it that will or will not confirm its validity. The most proper test, it seems to me, of the validity of a post-dictive theory of music should be the re-cognition of an existing piece as an interpretation of the theory; conversely, the proper test of a pre-scriptive theory should be the generation of a new piece as an interpretation of the theory. In this connection, it is important to note that post-dictive theory—that is, theory based upon the analysis of existing pieces—has traditionally come to assume a prescriptive function—that is, to serve as a basis for the composition of new pieces.
Such questions as the one I have just raised—namely, the question of an "empirical test" for a theory of music—lead inevitably into the realm of metatheory, the branch of knowledge devoted to the study of theories. The study of music theory as theory, then, is an instance of a metatheoretical study. The functions of metatheory, as it applies to a given theory, are, first of all, to determine the universal domain of the theory and define its limits; and, secondly, to establish the theoretical foundations for the study of any object within that universal domain.
As applied to music theory, these metatheoretical functions suggest two music-theoretical categories: first, an "all-music" theory, which I shall informally term "Theory A," the function of which is to determine the domain of the term "music" itself and to define its limits; and, secondly, an "each-piece" theory, "Theory E," the function of which is to determine a methodology for the analysis and explication of a given piece or for the generation of a new one.2
In characterizing each of these theories I have found it useful to apply some of the principles and to employ some of the terminology of modern logic, especially those aspects of it which deal with linguistic analysis; for such analysis, it seems to me, has enormous relevance to the theory of music.3
Theory A, then, in logical terms, establishes an ontology whereby a given object is or is not to be regarded as a "piece of music." (An example of such an ontology is to be found in Richard Martin's description of the "ontological status" of a musical composition as "merely a virtual class of virtual [cardinal] couples" of pitch-classes with times.4 This description would thus exclude a piece whose materials include sounds other than tones from consideration as a piece of music. Such a construction is probably too narrow for a comprehensive theory of music, but it nevertheless serves to illustrate what a possible ontology might be.) Whatever the ontology, its establishment in turn necessitates the choice of appropriate primitive or undefined constants; the definition of terms to be used in the theory, including the term "music"; the determination of the "ultimate constituents" of music5—for example, "pitch-events," as in Martin's theory, or perhaps more comprehensively, "sound-events"; and the formulation of axioms regarding coherence, or "pieceness"—axioms, that is, that determine under what conditions a succession of such ultimate constituents is to be regarded as constituting a "piece" for purposes of theoretical study.
Theory E, in logical terms, construes a given piece of music as a musical "object language" with its own musical syntax. Thus the pragmatics of Theory E would comprise observations in the metalanguage—for example, English—regarding compositional practices of the composer as these might affect the given piece, information about the history of the manuscript or its publication, and other musicological data; and especially, observations regarding the use of pitches, pitch classes, pitch structures, durational patterns, timbre, dynamics, and so forth, in the given piece. It should be noted here that much of what purports to be "theory" in music theory texts and articles ought not to be granted that status, but ought rather to be considered merely as the pragmatics of a potential theory of music.
As for the syntax and semantics of Theory E, there would entail hearing the piece as a "semantic" interpretation of a system of nested or intersecting syntactic models. Such models, of which a Roman numeral string or a Schenker sketch are by now classic examples, are derived from the piece by rules of reduction—these rules themselves to be determined by the theory. Such a derivation of models is of course a post-dictive and analytical process.
In the case of a pre-scriptive version of Theory E, formulation of the syntactic models precedes or accompanies the composition of the piece, which is generated from the models by rules of interpretation.6 The compositional process, however, differs in a very important way from the analytical process in that it is non-dualistic with respect to the syntactic-semantic distinction; in other words, to compose is, ideally at least, to weave a seamless syntactic-semantic fabric.
In the light of Theory E as I have described it, I should like to comment briefly on musical values. Single events in a rich piece can characteristically be heard as simultaneously interpreting a multiplicity of syntactic models. Therefore, any analysis which regards a given event in such a piece as an interpretation of only one or two syntactic models will probably fail to capture the full significance of that event.7 For example, if the pitches in measure 2 of Beethoven's Piano Sonata, Op. 28, are merely heard as constituting a "V7/IV in D," or even if the top voice is heard as a "structural 5," but if at the same time the dyad D-C natural in the two lowest voices is not heard as a syntactic unit, then the subsequent history of the D-C natural dyad, which is one of the many stories that the piece tells, and a very important one, will not be accounted for in the theory.
With this I conclude my foundational sketch. I shall end with a note on the limits of music theory: If a piece of music is regarded as a world, then a theory of music is as limited in its capacity to account for every aspect of that world as is a theory in any one of the empirical sciences to account for every aspect of a given object in the domain of that theory. One of the wonderful attributes of the best music is that our experience of the piece itself invariably transcends and subrates our experience of even the best theoretical formulations of it, however comprehensive or elegant such formulations may be.8 If this were not so, we would not value the musical experience as we do. Or as Wittgenstein put it, in another context: "Whereof one cannot speak, thereof one must be silent."
1For the analogy of "piece" to "world" I am indebted to Benjamin Boretz' paper, "Musical Cosmology," for the American Association for the Advancement of Science, Boston, Mass., Feb. 19, 1976.
2Regarding an "all-music" theory and an "each-piece" theory, cf. Boretz, op. cit.
3For valuable discussions of such aspects, see Rudolph Carnap, Foundation of Logic and Mathematics, Chicago, 1939, and Carl G. Hempel, Fundamentals of Concept Formation in Empirical Science, Chicago, 1952.
4Richard M. Martin, "On the Proto-theory of Musical Structure," in Perspectives on Contemporary Music Theory, edited by B. Boretz and E.T. Cone, New York, 1972, p. 95.
5Martin, op. cit., p. 94.
6For a detailed discussion of syntax and semantics as these relate to composition, see Paul Lansky: Affine Music, Ph.D. dissertation, Princeton University, 1973.
7For a similar view, cf. Charles J. Smith, "Towards the Construction of Intersecting Divergent Models for Chopin's 'Three against Two' Etude" in In Theory Only, Vol. I, No. 3, Ann Arbor, Michigan, June, 1975.
8Regarding subration, see Carlton Gamer, "The Role of the Composer as Theorist: Some Introductory Remarks" in Proceedings of the American Society of University Composers, Vol. 7-8, 1972-73, p. 13.