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 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].
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 ==
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== 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. 47–56.
* 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.
* [https://web.archive.org/web/20131114124454/http://ruinwesen.com/blog?id=216 Generating African rhythms using the euclidean algorithm] by Ruin & Wesen
* [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
* [http://plus.maths.org/content/os/issue40/features/wardhaugh/index Musical pitch and Euclid's algorithm] by Benjamin Wardhaugh
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[[Category:Music theory]]
[[Category:Music theory]]

⚫
{{From Wikipedia}}

Revision as of 21:33, 19 October 2019

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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