Euclidean rhythm: Difference between revisions

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&ndash;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>

 

[[Open-source hardware|Open-source music hardware]] projects that can generate Euclidean rythms, include Mutable instruments' [http://mutable-instruments.net/midipal/build MIDIPal], RebelTech's [[Stoicheia]] and Ruin & Wesen's [http://ruinwesen.com/products Minicommand]

 

In the 17th century [[Conrad Henfling]] writing to [[Gottfried Wilhelm Leibniz|Leibniz]] about music theory and the tuning of [[musical instruments]] makes use of [[Euclid]]'s algorithm in his reasoning.<ref name="plusmaths">[http://plus.maths.org/content/os/issue40/features/wardhaugh/index Musical pitch and Euclid's algorithm]</ref>