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The '''Euclidean Rythm''' in music was discovered by [[Godfried Toussaint]] in 2004 and is described in a 2005 paper "The [[Euclidean algorithm|Euclidean Algorithm]] Generates Traditional Musical Rhythms"<ref name="gtpdf">[http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf 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&ndash;56.</ref> The [[greatest common divisor]] of two numbers is used [[Rhythm|rhythmically]] giving the number of [[beats]] and silences, generating almost all of the most important [[World Music]] rhythms<ref name="gtweb">[http://cgm.cs.mcgill.ca/~godfried/rhythm-and-mathematics.html Comparative Musicology - Musical Rhythm and Mathematics]</ref>.<!--, (but not [[Indian]])--><ref name="extv">The Euclidean Algorithm Generates Traditional Musical Rhythms, by Godfried Toussaint, [http://cgm.cs.mcgill.ca/~godfried/publications/banff-extended.pdf 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.</ref>
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".<ref name="gtpdf">[http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf 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.</ref> The greatest common divisor of two numbers is used [[rhythm]]ically giving the number of beats and silences, generating almost all of the most important World Music rhythms,<ref name="gtweb">[http://cgm.cs.mcgill.ca/~godfried/rhythm-and-mathematics.html Comparative Musicology – Musical Rhythm and Mathematics]</ref> (except Indian).<ref name="extv">The Euclidean Algorithm Generates Traditional Musical Rhythms, by Godfried Toussaint, [http://cgm.cs.mcgill.ca/~godfried/publications/banff-extended.pdf 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.</ref> The beats in the resulting rhythms are as equidistant as possible; the same results can be obtained from the [https://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm Bresenham's line algorithm].


===Open Source Hardware Projects===
== Open-source hardware projects ==
[[Open-source hardware|Open-source music hardware]] projects that can generate Euclidean rythms, include Mutable instruments' [http://mutable-instruments.net/midipal/build MIDIPal], RebelTech's [[Stoicheia]] and Ruin & Wesen's [http://ruinwesen.com/products Minicommand]
[[Open source music hardware projects]] that can generate Euclidean rhythms, include [[Mutable Instruments]] [[Mutable Instruments MIDIPal|MIDIPal]] and [[Mutable Instruments Grids|Grids]] and [[RebelTech Stoicheia|RebelTech's Stoicheia]].


== See also ==
===Other uses of Euclid's algorithm in music===
* [[Polyrhythm]]
In the 17th century [[Conrad Henfling]] writing to [[Gottfried Wilhelm Leibniz|Leibniz]] about music theory and the tuning of [[musical instruments]] makes use of [[Euclid]]'s algorithm in his reasoning.<ref name="plusmaths">[http://plus.maths.org/content/os/issue40/features/wardhaugh/index Musical pitch and Euclid's algorithm]</ref>


==References==
== References ==
{{From Wikipedia}}
{{Reflist}}
{{Reflist}}


==External links==
== External links ==
*G. T. Toussaint, ''"[http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf 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&ndash;56.
* G. T. Toussaint, [http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf 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.&nbsp;47–56.
*[http://ruinwesen.com/blog?id=216 Generating African rhythms using the euclidean algorithm]
* [https://web.archive.org/web/20131114124454/http://ruinwesen.com/blog?id=216 Generating African rhythms using the euclidean algorithm] by Ruin & Wesen
*[http://plus.maths.org/content/os/issue40/features/wardhaugh/index Musical pitch and Euclid's algorithm] by Benjamin Wardhaugh on Plus
* [http://plus.maths.org/content/os/issue40/features/wardhaugh/index Musical pitch and Euclid's algorithm] by Benjamin Wardhaugh
*Links to videos about and a Flash app for experimenting with [http://www.hisschemoller.com/2011/euclidean-rhythms/ Euclidean rhythms]
* Links to videos about and a Flash app for experimenting with [http://www.hisschemoller.com/2011/euclidean-rhythms/ Euclidean rhythms]
* [http://dbkaplun.github.io/euclidean-rhythm/ Euclidean rhythm demo]
* A tutorial on [https://web.archive.org/web/20130211035641/http://cgm.cs.mcgill.ca/~mcleish/644/Projects/DerekRivait.1/ The ''Euclidean Algorithm'' Generates Traditional Musical Rhythms] by Derek Rivait
* [https://web.archive.org/web/20141101222427/http://www.soundhelix.com/ SoundHelix] is a free software for algorithmic random music composition that supports Euclidean rhythms
* [http://plus.maths.org/issue40/features/wardhaugh/index.html Music and Euclid's algorithm]
* [https://archive.org/details/DonBuchlaMetronome Don Buchla - How Complicated Could a Metronome Be?], Archive.org
* [https://en.wikipedia.org/wiki/Euclidean_rhythm Euclidean rhythm], Wikipedia


[[Category:Euclid]]
[[Category:Music theory]]
[[Category:Music theory]]
[[Category:Musical analysis]]

{{Rhythm and meter}}

{{Music-theory-stub}}

Latest revision as of 12:18, 17 December 2021

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's line algorithm.

Open-source hardware projects

Open source music hardware projects that can generate Euclidean rhythms, include Mutable Instruments MIDIPal and Grids and RebelTech's Stoicheia.

See also

References

This page uses Creative Commons Licensed content from Wikipedia:Euclidean_rhythm (view authors).

  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.

External links

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