Schenker's theory of tonal music—its explication through computational processes
✍ Scribed by R.E. Frankel; S.J. Rosenschein; S.W. Smoliar
- Publisher
- Elsevier Science
- Year
- 1978
- Weight
- 905 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0020-7373
No coin nor oath required. For personal study only.
✦ Synopsis
t has been possible to depict the constructs of a theory of tonal music developed by Heinrich Schenker as a system of computational processes. The basis of Schenker's theory involves the existence of musical proto-structures which expand into tonal compositions through a welt-defined set of rewriting rules. On the basis of these rewriting rules, it becomes possible to describe musical structure in terms of tree transformations. Using the programming language LISP, we have implemented a data structure that models the process by which the hierarchy is created. To demonstrate our system, we present structural descriptions of excerpts of tonal music as LISP programs. While our data and control structures help to clarify many of Schenker's ideas, we shall also focus upon those aspects of the theory found during the course of this study to be problematic.
Methodological procedures
Computer applications in music research are now sufficiently ubiquitous that it is no longer necessary to justify the revelance of the computer as a scholarly tool. What remains open to question, however, are the means by which the computer is used. Most scholars who have turned to the computer have tended to apply a variety of traditional computational and data processing operations to various "musical data bases" in an attempt to infer music-theoretic results from their printouts. The title of an article by Frederick Crane & Judith Fiehler (1970) "Numerical methods of comparing musical styles," says it all; and the anthology in which this article appears, The Computer and Music, edited by Harry B. , has a host of articles bearing out this numericallyoriented methodology. Unfortunately, these numerical methods tend to concentrate on properties based on note-to-note relationships; and the possibility of any properties involving deeper structural principles is generally ignored.
In our research we have used the computer in an entirely different manner. We regard music theory as the study of musical structures: the principles under which such structures may be generated, and the means by which musical compositions may be parsed so that their underlying structures may be inferred. Consequently, we feel that it should be possible to implement any "useful" theory of music in terms of some rigorously defined collection of symbol manipulation algorithms. Furthermore, we feel that such a collection of algorithms may serve as a model of the theory (in the sense of the word as defined by Minsky, 1965), to the extent that music theoretic questions may be resolved by translating them into questions about their corresponding algorithms and answering the questions in the computational domain.
Very little work has been done in this area, but there are two projects (one past, one current) which should be cited.