Euclidean rhythm

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The Euclidean rhythm in music was discovered by Godfried Toussaint in 2004 and is described in a 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms".[1] The greatest common divisor of two numbers is used rhythmically giving the number of beats and silences, generating almost all of the most important World Music rhythms,[2] (except Indian).[3] The beats in the resulting rhythms are as equidistant as possible; the same results can be obtained from the Bresenham algorithm.

Open-source hardware projects[edit]

Open-source music hardware projects that can generate Euclidean rhythms include Mutable Instruments MIDIPal and Grids, RebelTech's Stoicheia and Ruin & Wesen's Minicommand

Other uses of Euclid's algorithm in music[edit]

In the 17th century Conrad Henfling writing to Leibniz about music theory and the tuning of musical instruments makes use of the Euclidean algorithm in his reasoning.[4]

See also[edit]


  1. ^ The Euclidean algorithm generates traditional musical rhythms by G. T. Toussaint, Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science, Banff, Alberta, Canada, July 31 to August 3, 2005, pp. 47–56.
  2. ^ Comparative Musicology – Musical Rhythm and Mathematics
  3. ^ The Euclidean Algorithm Generates Traditional Musical Rhythms, by Godfried Toussaint, Extended version of the paper that appeared in the Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science’’, Banff, Alberta, Canada, July 31–August 3, 2005, pp. 47–56.
  4. ^ Musical pitch and Euclid's algorithm

External links[edit]