Limit (music)
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Just intonation tunings and scales can be described by giving an upper bound on the complexity of the harmonies admitted by the tuning or scale. This upper bound is called a limit. For example, the major and minor triads of Common practice music fall within 5-limit just intonation. By extension it may be said that Common practice music is a 5-limit genre, because those major and minor triads are the most complex harmonies considered consonant in it. Jazz and other 20th-century genres go beyond the 5-limit, but the correspondence to just intonation is less clear because of the nature of 12-tone equal temperament. 7-limit tunings are properly found in barbershop singing, and a few other relatively isolated genres.
There are two distinct types of limit in music theory literature: prime limit and odd limit. Not all authors are aware of the distinction.
In a just intonation tuning, intervals between pitches are drawn from the rational numbers. In an n-limit prime limit tuning, intervals between pitches are drawn from rational numbers that can be factored using prime numbers no greater than n, where n is prime. In an n-limit odd limit tuning, intervals between pitches are drawn from rational numbers which, after all factors of 2 are removed, have numerators and denominators no greater than n, where n is an odd whole number. Note that prime limit and odd limit do not cover the same scales even when n is an odd prime.
Harry Partch based his music on the 11-limit tonality diamond, which contains all the intervals of odd limit 11. But he also developed scales, including his famous 43-tone scale, based on a prime limit of 11.
External links
- Just Intonation Explained (http://home.earthlink.net/~kgann/tuning.html)
- The Tuning List on Yahoo! Groups (http://groups.yahoo.com/group/tuning/)