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.

Interaction features for prediction of perceptual segmentation: Effects of musicianship and experimental task

“…The main advantage of this circumscription of the notion of music segmentation is that it allows for a systematic analytic approach ultimately based on correlation between two time series. However, an important shortcoming should be mentioned at this point: musical segments are viewed as built upon boundary indications, whereas as a matter of fact, segments are concomitants of hierarchical representations of musical structure (Marsden, 2005). Moreover, our approach is not conceptually driven, as it disregards higher-level notions of musical motives, phrases, melodies, and themes, which embrace the complexity inherent in musical structures and point to the necessity of taking musical repetition and variation (i.e., parallelism) into account (see Cambouropoulos, 2006;Lartillot & Toiviainen, 2007b).…”

Between mind and mathematics. Different kinds of computational representations of music

“…The question of how to represent a piece of music for processing by computer therefore does not have a single answer" [Marsden, 2005]. So, different kinds of representations are possible and probably desirable for different theoretical or practical aims.…”

Music and Human-Computer Interaction

“…Research in these areas often focusses on the representation of the music (Marsden 2005). When stochastic processes are involved, as in most evo/gen music, good representations are necessary to produce good music.…”

“…MIDI-style) representation typical of mainstream music tools, these representations are often generative, grammatical, process-based, or algorithmic. They often have the property that they impose structure on the music in a natural way (Marsden 2005). Small changes in such a representation may lead to many changes at the surface of the music, even though structure is retained.…”