Towards an Equational Theory of Rhythm Notation

Pierre Donat-Bouillud 1, 2, 3 Florent Jacquemard 2, 3 Masahiko Sakai 4
2 Repmus - Représentations musicales
STMS - Sciences et Technologies de la Musique et du Son
3 MuTant - Synchronous Realtime Processing and Programming of Music Signals
Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, IRCAM, CNRS - Centre National de la Recherche Scientifique
Abstract : Trees 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.
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Pierre Donat-Bouillud, Florent Jacquemard, Masahiko Sakai. Towards an Equational Theory of Rhythm Notation. Music Encoding Conference 2015, May 2015, Florence, Italy. ⟨hal-01105418⟩

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