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. |
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 [[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> |
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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 |
[[Open-source hardware|Open-source music hardware]] projects that can generate Euclidean rhythms, include Mutable instruments' [http://mutable-instruments.net/midipal/build MIDIPal], 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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==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. |
*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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*Extended version of [http://cgm.cs.mcgill.ca/~godfried/publications/banff-extended.pdf The Euclidean Algorithm Generates Traditional Musical Rhythms], by Godfried Toussaint, of the paper that appeared in the Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science, Banff, Alberta, Canada, July 31 |
*Extended version of [http://cgm.cs.mcgill.ca/~godfried/publications/banff-extended.pdf The Euclidean Algorithm Generates Traditional Musical Rhythms], by Godfried Toussaint, 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. |
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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 |