# Structural properties of euclidean rhythms

Francisco Gómez-Martín, Perouz Taslakian, Godfried Toussaint

Research output: Contribution to journalArticle

### Abstract

In this paper we investigate the structure of Euclidean rhythms and show that a Euclidean rhythm is formed of a pattern, called the main pattern, repeated a certain number of times, followed possibly by one extra pattern, the tail pattern. We thoroughly study the recursive nature of Euclidean rhythms when generated by Bjorklund's algorithm, one of the many algorithms that generate Euclidean rhythms. We make connections between Euclidean rhythms and Bezout's theorem. We also prove that the decomposition obtained is minimal.

Original language English (US) 1-14 14 Journal of Mathematics and Music 3 1 https://doi.org/10.1080/17459730902819566 Published - Jan 1 2009

### Fingerprint

Structural Properties
Structural properties
Euclidean
Decomposition
Bezout's Theorem
Tail
Rhythm
Decompose

### Keywords

• Euclidean rhythms
• Maximally even

### ASJC Scopus subject areas

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

### Cite this

Structural properties of euclidean rhythms. / Gómez-Martín, Francisco; Taslakian, Perouz; Toussaint, Godfried.

In: Journal of Mathematics and Music, Vol. 3, No. 1, 01.01.2009, p. 1-14.

Research output: Contribution to journalArticle

Gómez-Martín, Francisco ; Taslakian, Perouz ; Toussaint, Godfried. / Structural properties of euclidean rhythms. In: Journal of Mathematics and Music. 2009 ; Vol. 3, No. 1. pp. 1-14.
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