Musical syntactic and semantic structures in APL2

ABSTRACT

APL2 provides an excellent platform for implementing both syntactic and semantic representations of music, and for effecting transformations between the two. We use general arrays to represent syntactic information in the form of Musical Instrument Digital Interface (MIDI) data streams and illustrate a semantic structure by defining a diatonic scale. Chords are created within that scale using the “each” operator to facilitate this development. Finally, we make a few observations regarding relationships and transformations between these representations.

REFERENCES

• 1: Chomsky, N., Syntactic Structures, The Hague, Mouton, 1957.
• 2: S. Jordan, APL for music, Conference proceedings on APL as a tool of thought, p.205-214, July 1989, New York City, New York, United States
• 3: Lerdahl, F., and R. Jackendoff, A Generative Theory of Tonal Music, MIT Press, Cambridge, Massachusetts, 1983.
• 4: Marvin L. Minsky, Semantic Information Processing, The MIT Press, 1969
• 5: Minsky, M., Music, Mind, and Meaning, MIT Press, Cambridge, Massachusetts, 1981.
• 6: Morris, Robert, Composition with Pitch Classes: A Theory of Compositional Design, Yale University Press, New Haven and London, 1987.
• 7: Musical Instrument Digital Interface (,MIDI) Specification 1.0, The International MIDI Association (IMA), Sun Valley, California, August 1983.
• 8: Rhodes, Curtis, "G~arnrnars as Representations for ;Llusic," Computer Yklusic Journal Vol. 3, No. 1, MIT Press, Cambridge, Massachusetts, 1987.
• 9: Starr, Daniel, Derivation and Polyphony in Twelve-Tone Music, Ph.D dissertation, Princeton University, 1980.
• 10: Xenakis, Iannis, Formalized Music, Indiana University Press, Bloomington, Indiana, 1971.

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

Additional Classification:
  J. Computer Applications
  J.5 ARTS AND HUMANITIES
      Subjects: Music**
      Nouns: MIDI

General Terms:
Languages