Generative structural representation of tonal music

Abstract

The usefulness and desirability of representation schemes which explicitly show musical structure has often been commented upon. A particular aim of music theory and analysis has been to describe and derive musical structure, and this article discusses computational systems based on this work. Six desirable properties of a structural representation are described: that it should be constructive, derivable, meaningful, decomposable, hierarchical, and generative. Previous computational work based on the generative and reductional theories of Schenker and of Lerdahl and Jackendoff is examined in the light of these properties. Proposals are made for a representational framework which promises the desirable properties. The framework shares characteristics with earlier work but does not use pure trees as a representational structure, instead allowing joining of branches in limited circumstances to make directed acyclic graphs. Important issues in developing a representation scheme within this framework are discussed, especially concerning the representation of polyphonic music, of rhythmic patterns, and of up-beats. An example is given of two alternative representations within this framework of the same segment of music used to exemplify earlier work: the opening of the theme of Mozart's piano sonata in A major, K.331.