Irrational rhythm

In music, the term irrational rhythm is usually applied to a rhythm in which an unusual number of beats is superimposed on the predominating tempo. More precisely, if n evenly-spaced beats are played in the time of m beats of the underlying tempo then the rhythm is irrational if and only if m and n are coprime. The use of the term "irrational" in this context is quite different to the mathematical use of the term: indeed, rhythms of this sort are, in the mathematical sense, rational, as they are precisely defined by the ratio of beats played to beats in the underlying tempo.

Related Topics:
Music - Rhythm - Number - Beats - Tempo - Coprime - Rational - Defined - Ratio

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The most familiar example is the triplet, in which three beats are played in the space of two. In compound time, the triplet can form the basic rhythmic unit (one triplet is 38, two triplets is 68, and so on), and so a common irrational rhythm in compound time is the duplet. Claude Debussy's famous composition Au Clair du Lune is written mostly in 98 but makes characteristic use of duplets and their derivatives, including 6:9 (which is really just three successive duplets).

Related Topics:
Triplet - Compound time - Claude Debussy

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Irrational rhythms are hence to be distinguished from polyrhythms, which are two separate rhythms played against one another, whereas an irrational rhythm can occur in the context of a single part. When irrational rhythms in one part are played against the underlying rhythm in another part, however, the outcome is a polyrhythm.

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