Abstract
Several operations on Euclidean rhythms based on musical motivations are defined. The operations defined are complementation, alternation, and decomposition. Some mathematical properties are proved for each and the conditions under which a given operation preserves the Euclidean property are examined. Finally, connections are shown to interlocking Euclidean rhythms and tiling canons, and tiling quasi-canons are introduced.
Original language | English (US) |
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Pages (from-to) | 15-30 |
Number of pages | 16 |
Journal | Journal of Mathematics and Music |
Volume | 3 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2009 |
Keywords
- Alternation
- Complement
- Decomposition
- Euclidean rhythms
- Interlocking rhythms
- Operations
ASJC Scopus subject areas
- Modeling and Simulation
- Music
- Computational Mathematics
- Applied Mathematics