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. Just intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. ... In music the common practice period is a long period in western musical history spanning from before the classical era proper to today, dated, on the outside, as 1600-1900. ... Jazz is a musical art form characterized by blue notes, syncopation, swing, call and response, polyrhythms, and improvisation. ... Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). ...

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. In mathematics, a prime number, or prime for short, is a natural number greater than one and whose only distinct positive divisors are 1 and itself. ... The integers consist of the positive natural numbers (1, 2, 3, …) the negative natural numbers (−1, −2, −3, ...) and the number zero. ...

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. Harry Partch (June 24, 1901 – September 3, 1974) was an American composer. ...

External links

• Just Intonation Explained
• The Tuning List on Yahoo! Groups