Rhythm Quantization

Pierre Donat-Bouillud
Last updated on 17 Apr 2023 Computer Music
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Rhythm trees associated to standard notation examples.

We represent rhythms as trees. Rhythm trees can be changed into other rhythm trees using rewriting rules. It makes it possible to define an equivalence relation between rythms. Some of the rewriting rules simplify the rhythms and are used to quantify them.

Examples of rythms with slurs and dots and their tree representation.
Rewrite sequence starting from the tree (d) of previous figure.
music rhythm quantization

Publications

A Structural Theory of Rhythm Notation based on Tree Representations and Term Rewriting
We present a tree-based symbolic representation of rhythm notation suitable for processing with purely syntactic theoretical tools such …
Florent Jacquemard, Pierre Donat-Bouillud, Jean Bresson
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Towards an Equational Theory of Rhythm Notation
Trees are classical representations of hierarchical structures in symbolic music, in particular for rhythm notations, where the …
Pierre Donat-Bouillud, Florent Jacquemard, Masahiko Sakai
PDF Cite Project
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 …
Florent Jacquemard, Pierre Donat-Bouillud, Jean Bresson
PDF Cite Project