Most computational models of musical understanding have focused on procedural aspects of analysis, suggesting techniques for parsing, comparing, and transforming various representations of a piece, or adapting discovery procedures of artificially intelligent (AI) inference systems, which plan and follow agendas and goals. Much contemporary AI research, however, also focuses on declarative aspects of knowledge, attempting to define data representations and relations that are commensurate with human cognition. Naturally, musical analysis has both procedural and declarative aspects: the declarative determines what the form of the analysis is, and the procedural determines how the analysis is obtained. However, a predominantly procedural analysis risks sacrificing the form of musical understanding to obtain efficiency or compatibility with a particular computer language. In this article I argue that, for a significant body of twentieth-century music, a declarative system models the structure of analytical understanding better than do existing procedural programs, and I present a functioning declarative system that infers complex musical structures from the elementary musical relations that it identifies.


Similarly, Hasty (1981)
Arbib's (1979)


Alphonce, B.H. Music analysis by computer- A field for theory formation. Computer Music Journal, 1980, 4(2), 26-35.
Arbib, M. A. Local organizing processes and motion schémas in visual perception. Machine Intelligence, 1979, 9, 287-298.
Babbitt, M. Remarks on the recent Stravinsky. In Boretz & E. T. Cone (Eds.), Perspectives on Schoenberg and Stravinsky. New York: Norton, 1972, pp. 165-185.
Beach, D. Pitch structure and the analytic process in atonal music: An interpretation of the theory of sets. Music Theory Spectrum, 1979, 1, 7-22.
Berry, W. Structural functions in music. Englewood Cliffs, NJ: Prentice-Hall, 1976.
Boretz, B. Meta- Variations (I). Perspectives of New Music, 1969, 8(8), 1-74.
Boretz, B. Conversation with Elliott Carter. Perspectives of New Music, 1970a, 8(2), 1-22.
Boretz, B. Sketch of a musical system (Meta- Variations, Part II). Perspectives of New Music, 1970b, 8(2), 49-111.
Clocksin, W. F., & Mellish, C. S. Programming in Prolog (2d ed.). New York:Springer- Verlag, 1984.
Forte, A. A program for the analytic reading of scores. Journal of Music Theory, 1966, 10(2), 330-364.
Forte, A. Set and nonsets in Schoenberg's atonal music. Perspectives of New Music, 1972, 11(1), 43-64.
Forte, A. The structure of atonal music. New Haven and London: Yale University Press, 1973.
Forte, A. Analysis Symposium :Webern, Orchestral Pieces (1913), Movement I (Bewegt). Journal of Music Theory, 197 r4, 18, 13-43.
Forte, A. Pitch-class set analysis today. Music Analysis, 1985, 4(1 & 2), 29-58.
Hasty, C. Segmentation and process in post-tonal music. Music Theory Spectrum, 1981, 3, 54-73.
Laske, O. Keith: A rule-system for making music-analytical discoveries. In M. Baroni & L. Callegari (Eds.), Musical grammars and computer analysis, Florence: Leo S. Olschki, 1984, 165-199.
Lenat, D. B., & Harris, G. Designing a rule system that searches for scientific discoveries. In D. A. Waterman & F. Hayes-Roth, (Eds.), Pattern-Directed Inference Systems. New York: Academic Press, 1978, 25-52.
Rahn, J. Logic, set theory, music theory. College Music Symposium, 1979, 19(1), 114-127.
Rahn, J. Basic atonal theory. New York: Longman, 1980.
Regener, E. On Allen Forte's theory of chords. Perspectives of New Music, 1974, 13(1), 191-212.
Roads, C. An overview of music representations. In M. Baroni & L. Callegar (Eds.), Musical grammars and computer analysis. Florence: Leo S. Olschki, 1984, 7-37.
Smoliar, S. W. Review of Musical grammars and computer analysis. Journal of Music The- ory, 1986, 30(1), 130-141.
Williams, E. W. Jr. On Mod 12 complementary interval sets. In Theory Only, 1983, 7(2), 34-43.
Wintle, C. An early version of derivation: Webern's Op. 11/III. Perspectives of New Music, 1975, 13(12), 165-177.
This content is only available via PDF.