Euclidean rhythm: Difference between revisions
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The '''Euclidean rhythm''' in music was discovered by |
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|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> (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]. |
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== Open-source hardware projects == |
== Open-source hardware projects == |
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[[Open source projects]] that can generate Euclidean rhythms, include [[Mutable Instruments]] [[Mutable Instruments MIDIPal|MIDIPal]] and [[Mutable Instruments Grids|Grids]], [[RebelTech Stoicheia|RebelTech's Stoicheia]] and [[Ruin & Wesen Minicommand|Ruin & Wesen's Minicommand]]. |
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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] |
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== 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> |
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== See also == |
== See also == |
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* [http://plus.maths.org/issue40/features/wardhaugh/index.html Music and Euclid's algorithm] |
* [http://plus.maths.org/issue40/features/wardhaugh/index.html Music and Euclid's algorithm] |
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[[Category:Euclid]] |
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[[Category:Music theory]] |
[[Category:Music theory]] |
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{{iwWikipedia}}{{From Wikipedia}} |
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[[Category:Musical analysis]] |
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{{Rhythm and meter}} |
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{{Music-theory-stub}} |
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Revision as of 21:49, 2 March 2016
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 projects that can generate Euclidean rhythms, include Mutable Instruments MIDIPal and Grids, RebelTech's Stoicheia and Ruin & Wesen's Minicommand.
See also
References
- ^ 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.
External links
- 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.
- Generating African rhythms using the euclidean algorithm by Ruin & Wesen
- Musical pitch and Euclid's algorithm by Benjamin Wardhaugh
- Links to videos about and a Flash app for experimenting with Euclidean rhythms
- Euclidean rhythm demo
- 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
- Music and Euclid's algorithm
Template:IwWikipediaThis page uses Creative Commons Licensed content from Wikipedia:Euclidean_rhythm (view authors).