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.
The final, definitive version of this article has been published in the Journal, Journal of New Music Research 34 (4), 2005, © Informa Plc
Published in a special issue Sound and Music Computing, edited by G'rard Assayag, this article develops the system first presented in output 1 to represent not just melodies but any polyphonic tonal music, and to improve its formal properties. A formal, computable system for the representation of polyphonic Schenkerian musical structure is presented here for the first time. This system of representation is compared with alternatives, based in the theories of both Schenker and of Lerdahl