Interlocking and euclidean rhythms

Francisco Gómez-Martín, Perouz Taslakian, Godfried Toussaint

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)15-30
Number of pages16
JournalJournal of Mathematics and Music
Volume3
Issue number1
DOIs
StatePublished - Jan 1 2009

Fingerprint

Euclidean
Tiling
Decomposition
Complementation
Alternation
Decompose
Rhythm
Canon

Keywords

  • Alternation
  • Complement
  • Decomposition
  • Euclidean rhythms
  • Interlocking rhythms
  • Operations

ASJC Scopus subject areas

  • Modeling and Simulation
  • Music
  • Computational Mathematics
  • Applied Mathematics

Cite this

Interlocking and euclidean rhythms. / Gómez-Martín, Francisco; Taslakian, Perouz; Toussaint, Godfried.

In: Journal of Mathematics and Music, Vol. 3, No. 1, 01.01.2009, p. 15-30.

Research output: Contribution to journalArticle

Gómez-Martín, Francisco ; Taslakian, Perouz ; Toussaint, Godfried. / Interlocking and euclidean rhythms. In: Journal of Mathematics and Music. 2009 ; Vol. 3, No. 1. pp. 15-30.
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