A structural theory of rhythm notation based on tree representations and term rewriting

Florent Jacquemard

Pierre Donat-Bouillud

Jean Bresson

pp. 3-15

in: Tom Collins, David Mérédith, Anja Volk (eds), Mathematics and computation in music, Berlin, Springer, 2015

Abstract

We present a tree-based symbolic representation of rhythm notation suitable for processing with purely syntactic theoretical tools such as term rewriting systems or tree automata. Then we propose an equational theory, defined as a set of rewrite rules for transforming these representations. This theory is complete in the sense that from a given rhythm notation the rules permit to generate all notations of equivalent durations.