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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|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|rhythmically]] giving the number of [[beat (music)|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 [[India#Performing_arts|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 [[Bresenham's line algorithm|Bresenham]] algorithm.
The '''Euclidean Rhythm''' 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. 47–56.</ref> The [[greatest common divisor]] of two numbers is used [[Rhythm|rhythmically]] giving the number of [[beat (music)|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 [[India#Performing arts|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 [[Bresenham's line algorithm|Bresenham]] algorithm.


==Open Source Hardware Projects==
== Open Source Hardware Projects ==


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


==Other uses of Euclid's algorithm in music==
== Other uses of Euclid's algorithm in music ==


In the 17th century [[Conrad Henfling]] writing to [[Gottfried Wilhelm Leibniz|Leibniz]] about music theory and the tuning of [[musical instruments]] makes use of the [[Euclidean algorithm]] in his reasoning.<ref name="plusmaths">[http://plus.maths.org/content/os/issue40/features/wardhaugh/index Musical pitch and Euclid's algorithm]</ref>
In the 17th century [[Conrad Henfling]] writing to [[Gottfried Wilhelm Leibniz|Leibniz]] about music theory and the tuning of [[musical instruments]] makes use of the [[Euclidean 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 ==
{{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. 47–56.
* 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. 47–56.
*[http://ruinwesen.com/blog?id=216 Generating African rhythms using the euclidean algorithm] by Ruin & Wesen
* [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
* [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]
*A tutorial on [http://cgm.cs.mcgill.ca/~mcleish/644/Projects/DerekRivait.1/ The ''Euclidean Algorithm'' Generates Traditional Musical Rhythms] by Derek Rivait
* A tutorial on [http://cgm.cs.mcgill.ca/~mcleish/644/Projects/DerekRivait.1/ The ''Euclidean Algorithm'' Generates Traditional Musical Rhythms] by Derek Rivait
*[http://www.soundhelix.com SoundHelix] is a free software for algorithmic random music composition that supports Euclidean rhythms
* [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]


[[Category:Euclid]]
[[Category:Euclid]]

Revision as of 18:39, 7 November 2014

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

Template:Rhythm and meter

Template:Music-theory-stub

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