Towards an Equational Theory of Rhythm Notation

International audienceTrees are classical representations of hierarchical structures in symbolic music, in particular for rhythm notations, where the durations are defined by a hierarchy of subdivisions. Structures called rhythm trees have been integrated since a long time into Computer Aided Composition environments such as Patchwork and OpenMusic , for programming rhythmic objects.Term rewriting and tree automata and transducers are well established formalisms for transforming and reasoning on trees. With solid theoretical foundations, they are used in a wide range of applications including automatic reasoning, natural language processing, and foundations of web data processing. In this work, we consider a tree structured representation of rhythm suitable for defining a set of rewrite rules (i.e. oriented equations) preserving rhythms, while enabling the simplification of notations. This set can be seen as an axiomatization of rhythm notation which can be applied to reasoning on equivalent notations in assisted composition