A Term Rewriting Based Structural Theory of Rhythm Notation

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. It can be used to explore the space of Using complementary tree automata formalisms, one can restrict the search space according to notations preferences regarding e.g. metre or other user defined syntactic constraints