Euclidean rhythm

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

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

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]

References

  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