Computational Music Representation based on the Generative Theory of Tonal Music and the Deductive Object-Oriented Database,
Keiji Hirata and Tatsuya Aoyagi

Abstract:
This article presents a new framework for representing and manipulating polyphony based on the generative theory of tonal music (GTTM) and the deductive object-oriented database (DOOD). Since music theory can serve as a basis for analyzing and understanding the vague and subjective meanings of music, it is expected to contribute to the enhancement of a music knowledge representation. First, we design a formal representation method of music knowledge so that time-span reduction in GTTM corresponds to the subsumption relation in the DOOD. Then we introduce three primitive operators to manipulate polyphony represented in our method. By several examples, we show how well our framework can represent listener's intuition and provide operators for manipulating polyphony. This paper primarily describes music representation, not applications of our framework, and we would say that before computers can automatically derive a time-span analysis from a musical score, major work, i.e., formal representation of music, needs to be done.