Euclidean rhythm: Difference between revisions
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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 |
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. |
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==Open Source Hardware Projects== |
== Open Source Hardware Projects == |
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[[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] |
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==Other uses of Euclid's algorithm in music== |
== Other uses of Euclid's algorithm in music == |
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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> |
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==References== |
== References == |
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{{Reflist}} |
{{Reflist}} |
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==External links== |
== External links == |
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*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. |
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*[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 |
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*[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 |
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*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] |
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*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 |
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*[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 |
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* [http://plus.maths.org/issue40/features/wardhaugh/index.html Music and Euclid's algorithm] |
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[[Category:Euclid]] |
[[Category:Euclid]] |
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