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| ISBN-13: | 9780691632810 |
|---|---|
| Publisher: | Princeton University Press |
| Publication date: | 04/19/2016 |
| Series: | Princeton Legacy Library , #379 |
| Pages: | 184 |
| Product dimensions: | 6.10(w) x 9.30(h) x 0.70(d) |
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The Music Theory of Godfrey Winham
By Leslie David Blasius
PRINCETON UNIVERSITY PRESS
Copyright © 1997 Bethany Beardslee WinhamAll rights reserved.
ISBN: 978-0-691-01227-8
CHAPTER 1
PART 1
Godfrey Winham's Conception of Music Theory
The Problem of Musical Significance
The music theory that comes into being in the late 1950s and through the 1960s is the product of various factors unique to that moment in the American academy. Among these, five deserve mention. The first must be the establishment of historical musicology as an autonomous, scientific, and professionalized discipline; the second, the growth of a theoretically aware compositional community; the third, the introduction and dissemination of Scheriker's analysis of music (with its claims to displace a more impressionistic or heuristic critique of musical works); the fourth, the availability of various analytic tools in contemporary writings on logic and mathematics; and the fifth, the advent and promise of electronic computation. Thus the composers and theorists of the time are compelled to create a discipline matching the autonomy and professionalism of musicology in its rigor, emboldened by Schenker's claims to envision fresh analytic worlds (particularly through the reconciliation of Schenker's analysis with modern music), and especially, encouraged to appropriate the authority and epistemological surety that seems within reach of contemporary philosophy.
Given this situation, it comes as no surprise that Winham's ostensible project involves the creation of a sort of metalanguage within which musical structure can come under scrutiny, and the subsequent reconstruction of the foundations of musical logic. In fact, what is most striking about Winham's work is the degree to which it is indebted to the intellectual disciplines of analytic philosophy, in particular to the work of Rudolph Carnap. (Winham also appropriates elements of Alfred Tarski's semantics, Bertrand Russell's systematic logic, and Herman Weyl's work on geometric spaces. Nelson Goodman and Willard Quine make brief appearances in the archive.) For example, in the undated and incomplete draft of a letter to Allen Forte [N22: 36–39], written in reference to a prospective "Princeton issue" of the Journal of Music Theory, Winham first confides:
This subject is not worth writing about except in full, vigorous detail.
Believe me, nobody but nobody bar myself has any idea of the complexity of this field (I had to take 18 months out to study logic and semantics and another 6 to work out how it could be applied to the musical case, and even now I can at most claim to have cleared away the major obstacles on the road to solutions).
He then sketches the contents of his proposal at length, cutting immediately to the epistemological issues that lie at the heart of music theory.
Group I. What does music theory actually say? Does it state empirical facts? If so, are they the same kind of facts as in physical science, or is there a basic difference? What are the criteria of truth for music theory? What kind of evidence is properly invoked by it? Conversely, how can a theory about music be refuted?
Group II. What is the relation between analysis and evaluation, i.e., can analysis demonstrate coherence or incoherence, etc., of individual works? Relatedly, (a) is theory anything more than analysis of individual works?, (b) is it even possible to analyze an incoherent work? More fundamentally still: What is coherence? What is simplicity? Complexity? etc.
The questions in the first section (accompanied by a series of casual references to outside authorities) are then given focus as a series of logical or metamathematical problems: the distinction between descriptive and analytic statements, the construction of a descriptive language within which musical relations can be examined, the definitions of musical structure and (most important) significance.
The following is a tentative order of exposition:
1. Introductory, on the nature of the following enterprise; specifically (1) on the concept of "explication", in which this is an essay; (2) on the language used: namely, a simplification of ordinary English, such that it can be translated into certain artificial languages for which there is a demonstrable criterion (i.e. this language is used for the central definitions and asserts; there is also a running commentary not subject to this constraint).
2. Musical analysis is stated to be the showing that certain significant relations, when confined to their exemplification in a given class of events, have a certain (logical) structure. The criteria of significance are discussed, and a proof of the necessity for such a prior criteria for significance, i.e. on the assumption that the significance of relations is a function of context, any analysis of any work A can be mechanically translated into an analysis of any other work. [This is shown to be a consequence of a theorem of Tarski; since the latter is in different terminology and in fact a different mode of speech (in Carnap's sense) from mine, it will be necessary to spend some space explaining how this theorem applies here. But this can perhaps be done with an appendix or long footnote.]
The concept of 'structure' involved is precisely defined. [Here, however, there crops up a difficulty which I have not fully resolved yet: that the above definition in the most useful form seems to be translatable only into artificial languages of a certain debatable kind, namely one having no standard model in the sense of Henkin. This difficulty also arises in the process of changing the mode of speech in applying the Tarski proof, but it is not so serious there (the reason for this is too long to explain here).]
In this section I also intend to expound at length the manner in which a recursive definition of significance can be given, and a proof that no explicit definition can be given. Probably a good way to do this from the point of view of trying to make it comprehensible will be to refer continually to the discussion of significance in geometry in Weyl's book 'Philosophy of mathematics and natural science', pointing out the similarities and differences in the cases of music and geometry. In the course of this I produce incidental explications of the concepts:
"Significant in a given context"
"Significant if ... is significant"
"Having a significant relationship to ..." and other notions involving significance.
An important difficulty in theory is our simple lack of knowledge of certain factors, E.G., of the structure of timbral relationships. How this affects the situation of theory in general will be discussed.
Other incidental matters cleared up along the way: (1) I give a precise distinction between analysis and mere description. Also some examples, perhaps, to show how one can determine whether writings in ordinary language are analytical or merely descriptive. (2) I show that either theory is no more than a collection of analyses, or else it must imply something about evaluation (see section 2).
He then seems to change his mind, and to redraft the previous section. (Although the previous section is not crossed out in the manuscript, there is a line break before this new material, and it returns to the same numbering and covers the same ground.)
2. I show that to the extent that an "analysis" is analytical and not merely descriptive, it can be made to directly imply something about coherence. This is so because the terms involved in defining "coherent" can be the same ones used in the assertions of analysis, namely (1) "significant" and related terms, (2) purely logico-mathematical terms such as "structure" and "relation."
In that case, the difference between theory and analysis would seem to be best construed thus: theory attempts to show that certain kinds of musical techniques or procedures are justified or unjustified in general, because of their effect on significance and hence on coherence. E.G. (trivially) that the technique of transposition is justified because it preserves all significant relations ('preserves' is among the words defined in part 1). This it can do without ever referring to specific works at all; thus in a sense it is "more than" mere analysis, or rather completely different. But nevertheless the two use the same vocabulary.
Holding this revision in abeyance for the moment (I do think it important and will return to it later), we can reconstruct to a certain extent the contents of this hypothetical article, or at least rehearse some of the applicable arguments. For example, a complex of problems surrounds the notions of the musical work, the musical score, and the notion of musical structure. Again, his unpacking of these notions has its origin in the pragmatic problem of translating the musical entity into some usable metalanguage (or at least some sort of language that would give a complete and efficient description of a piece, one amenable to analytic operations). Specifically, he begins by rejecting the simple assumption of the musical score (or musical notation in general) as itself a logically recuperable descriptive language for music [N19: 1–2].
Evidently the closest we can come to a paradigm of this is a musical score, and indeed in a sense it would be absurd to ask for a more complete description than the score, the musical work itself being definable as whatever satisfies the description given by the score. However, the "language" of scores is rather unsatisfactory in several ways. It includes elements and distinctions of problematic or no significance, such as (respectively) bar lines and differences of note-stem length; it is not always clear whether directions for physical performance or description of the intended resulting auditory affect is intended; it is vague or ambiguous in many ways; but chiefly—and this defect includes all the others—it is not the same as (or directly translatable by well known rules into) some subsystem of an ordinary verbal language (say English) for which we have more or less agreed rules of logical transformation, or alternatively into a formalized language with an interpretation. It is, of course, translatable into ordinary English as a whole, but this is quite an inadequate criterion, as can be seen from some parts of English which occur in scores, such as words like "Tranquilly" or phrases like "as fast as possible" (the former being objectionable as a descriptive term on the grounds of indeterminacy and nonuniformity of usage, and the latter on the ground that it presupposes a language containing modalities, where logic is far from a well-understood and agreed matter).
As with most topics in Winham's work, though, he elsewhere reconsiders this problem from a different angle, now bringing into play the relation between the musical work and the musical score [N14:12].
By a musical work or composition we understand an abstract entity of a certain kind which may (but need not) be designated by a musical score or other linguistic or notational entity. Adopting the terminology of semantics, we may consider the musical score as a predicate-expression. Indeed a score in ordinary musical notation could obviously be translated into English (for example) if there is even any serious objection to considering that notation to simply be a part of English; and would then obviously be a predicate-expression (rather than a sentence or individual name) in that it might denote or be satisfied by a class of configurations (viz., the 'occurrences of' the work in question).
The configurations in question are of course sounds, in principle restricted only in that all the sounds of a configuration belong to the same aural field, although in practice theory has to confine itself to a much narrower subject-matter (such other restrictions in principle as might seems natural, such as the example that the configurations must occupy continuous segments in time, run the risk of being confronted by counter-examples—in this case "The Ring" will serve; also it ought to be mentioned here that the null class of sound-configurations must be counted as a composition in view of the fact that it has actually been composed by Mr. Cage, although we need not countenance the possibility of more than one such composition raised by its title, since we can (and do) take the view that the same sounds would satisfy any such allegedly distinct indications calling for different "amounts of silence."
And yet more intriguingly, Winham in a third passage reconceives the problem in formal terms [N28: 44–47]:
It seems obvious that the semiotical status of musical scores is that of predicates (as opposed, for example, to that of sentences). The extension of such a predicate is a class of configurations of musical events, which may be taken to be physical or phenomenal sounds, or events such as contacts between bows and strings, or various other entities, depending on the "domain" or sublanguage x such that we are considering the predicate to be a predicate-of-x.
The questions we are concerned with in this discussion are unaffected by these distinctions, so we will simply speak ambiguously of "musical events." This is not to deny that in some contexts these distinctions are of course highly relevant.
The question arises: What is the semiotic relation of a musical work to the score "of" that work?
We may quickly dispose of certain plausible suggestions:
I. The work is the extension of the score, and is denoted by it (the work is the class of configurations mentioned above).
This fails because different unperformed or unheard (etc., depending on the domain) works would all be identical with the null class of configurations and hence with each other.
II. The work is the intention of the score, and is designated by it (the work is a property of configurations of events).
This fails because logically non-equivalent scores (having, therefore, different intentions) may nevertheless be scores of the same work. This happens, for example, if two scores have the same non-null extension, i.e., are equivalent, but are nevertheless not logically equivalent in some such way as the following:
Score (a) calls for three events x, y, z to stand in the relation that x is louder than y, while y is louder than z; score (b) calls for three events x, y, z to stand in the relation that ? is louder than y and y is louder than ? and ? is louder than z. They are not logically equivalent, because the transitivity of louder is not determined by logic. But they are in fact equivalent, and such a difference as this would not prevent the two scores from being scores of the same work.
One might perhaps attempt to circumvent this difficulty by claiming that score (a) is not really a "complete" score, in that it does not specify whether x is louder than z. Actually it would be easy to construct similar examples for which this device would be useless; but it is important to notice that in any case the device is illegitimate because it would not allow a score to be "purposely" unspecific, e.g., to allow various different interpretations or improvisatory passages. To require that a "complete score" determine, for every relation it mentions at all, whether this relation holds between any events for which it requires any relation to hold, would rule out the majority of actual scores.
Another attempt to circumvent the difficulty would be to suppose that the transitivity of louder is after all logically determined. This would require a concept of logical truth based on "meaning" rather than form, with all the attendant problems. But again, it is easy to construct other examples which would defeat such attempts. For example, certain timbres cannot belong to tones of above a certain height in pitch. But it is difficult to envisage any coherent concept of logical truth by which such facts would become logically true (at this point we are not even in full possession of a theory of sound from which they all follow).
III. The work is the class of all scores notationally similar to the given score (in some appropriate sense of 'notationally similar').
This cannot be coherently maintained in the face of the fact that (just as with verbal predicates) the same score may be a score of different works according to the language to which it is being considered to belong, even if its syntax is the same in both languages. For example, by a simple mapping of one such language on another, a score in ordinary notation may be mapped on the "retrograde" of the same score, both scores being well-formed expressions of both languages, but with interchange of the works of which they are scores.
(Continues...)
Excerpted from The Music Theory of Godfrey Winham by Leslie David Blasius. Copyright © 1997 Bethany Beardslee Winham. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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Table of Contents
Godfrey Winham: A Personal Note Introduction PART 1 Godfrey Winham's Conception of Music Theory PART 2 Selected Excerpts PART 3 The Contents of the Winham Archive