A Temporal Generative Graph Grammar for Harmonic and Metrical Structure

Authors:

Donya Quick and Paul Hudak

Abstract:

Most grammars that have been proposed for automated music composition fall into conventional linguistic categories, such as context-free, context-sensitive, and probabilistic versions of each. For parsing (i.e. musical analysis) these distinctions are important, because of the computational complexity of parsing using these different grammars. But, for generation (i.e. derivation), the complexity issues are sometimes different, and other goals for having a generative grammar come into play.

In this paper we describe a new category of grammar for generating abstract harmonic and metrical structure. This class of grammars has two distinctive features. First, it is temporal, meaning that production rules are parameterized by the duration of phrases, thus allowing us to express the metrical structure of a composition. Second, it is a graph grammar, meaning that the parse trees (or derivation trees) are actually graphs allowing shared nodes, thus enabling us to express the sharing, i.e. repetition, of specific musical phrases. We formally define this class of grammars, describe our generative implementation of it, and present a realistic example of its use: a specific grammar tailored to some styles of classical Western music. In addition, we show that this class of grammars integrates nicely with the notion of chord spaces to generate concrete chords from the abstract harmonic structure generated from the grammar.

Bibtex:

 @inproceedings{tggg,
    author = {Donya Quick and Paul Hudak},
    title = {A Temporal Generative Graph Grammar for Harmonic and Metrical Structure},
    booktitle = {Proceedings of the International Computer Music Conference},
    year = {2013},
} 

Links:

icmc2013.zip