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The '''Euclidean Rythm''' is described by [[Godfried Toussaint]] in a 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms"<ref name="gtt">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&ndash;56.</ref> He describes how the [[Euclidean algorithm]] can generate a variety of [[World Music]] [[Rhythm|rhythms]].<ref name="gtt"/>
The '''Euclidean Rythm''' was discovered by [[Godfried Toussaint]] in 2004 and is described in a 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms"<ref name="gtpdf">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&ndash;56.</ref> The [[greatest common divisor]] of two numbers is used [[Rhythm|rhythmically]] giving the number of [[beats]] and silences, and generating almost all of the most important musical rhythms used in [[World Music]].<ref name="gtweb">[http://cgm.cs.mcgill.ca/~godfried/rhythm-and-mathematics.html Comparative Musicology - Musical Rhythm and Mathematics]</ref>


===Open Hardware projects===
===Open Hardware projects===

Revision as of 15:54, 29 June 2012

The Euclidean Rythm 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, and generating almost all of the most important musical rhythms used in World Music.[2]

Open Hardware projects

Open-source music hardware projects that can generate Euclidean rythms, include Mutable instruments' MIDIPal, 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 Euclid's algorithm in his reasoning.[3]

References

  1. ^ 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.
  2. ^ Comparative Musicology - Musical Rhythm and Mathematics
  3. ^ Musical pitch and Euclid's algorithm

External links

Template:Rhythm and meter

Template:Music-theory-stub