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.
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 ]
References [ edit ]
- ^ 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.
- ^ Comparative Musicology – Musical Rhythm and Mathematics
- ^ 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.
- ^ Musical pitch and Euclid's algorithm
External links [ edit ]
- G. T. Toussaint, The Euclidean algorithm generates traditional musical rhythms, Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science, Banff, Alberta, Canada, July 31 to August 3, 2005, pp. 47–56.
- Phil Baljeu and Manuel Odendahl (Ruin & Wesen). "Generating African rhythms using the euclidean algorithm". Archived from the original on 2013-11-14.
- Benjamin Wardhaugh (1 September 2006). "Music and Euclid's algorithm".
- Links to videos about and a Flash app for experimenting with Euclidean rhythms
- Euclidean rhythm demo — interactive browser-based tool for experimenting with Euclidean rhythms
- A tutorial on The Euclidean Algorithm Generates Traditional Musical Rhythms by Derek Rivait
- SoundHelix is a free software for algorithmic random music composition that supports Euclidean rhythms
- Euclidian rhythms list - a list of all Euclidian rhythms E(i,2 to 32), indicating if they are Winograd-deep, Erdős-deep, Authentic Aksak, Quasi-Aksak or Pseudo-Aksak
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