Just intonation

Just intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series. Although in theory two notes tuned in the frequency ratio 1024:927 might be said to be justly tuned, in practice only ratios using quite small numbers tend to be called just. Intervals used are then capable of being more consonant.

Western composers who specified just intonation

Most composers don't specify how instruments are to be tuned, although historically most have assumed one tuning system which was common in their time; in the 20th century most composers assumed equal temperament would be used. However, a few have specified just intonation systems for some or all of their compositions, including Glenn Branca, Wendy Carlos, Stuart Dempster, Arnold Dreyblatt, Kyle Gann, Kraig Grady, Lou Harrison, Ben Johnston, Elodie Lauten, Pauline Oliveros, Harry Partch, Robert Rich, Terry Riley, James Tenney, and LaMonte Young. Eivind Groven is often considered a just intonation composer but just intonation purists will disagree. His tuning system was in fact schismatic temperament, which is indeed capable of far closer approximations to just intonation consonances than 12-note equal temperament or even meantone temperament, but still alters the pure ratios of just intonation slightly in order to achieve a simpler and more flexible system than true just intonation.

Related Topics:
Equal temperament - Glenn Branca - Wendy Carlos - Stuart Dempster - Arnold Dreyblatt - Kyle Gann - Kraig Grady - Lou Harrison - Ben Johnston - Elodie Lauten - Pauline Oliveros - Harry Partch - Robert Rich - Terry Riley - James Tenney - LaMonte Young - Eivind Groven - Schismatic temperament - Meantone temperament

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Music written in just intonation is most often tonal but need not be; some music of Kraig Grady uses just intonation scales designed by Erv Wilson explicitly for a consonant form of atonality, and Ben Johnston's Sonata for Microtonal Piano (1964) uses serialism to achieve an atonal result. Composers often impose a limit on how complex the ratios used are: for example, a composer may write in "7-limit JI", meaning that no prime number larger than 7 features in the ratios they use. Under this scheme, the ratio 10:7, for example, would be permitted, but 11:7 would not be, as all non-prime numbers are octaves of, or mathematically and tonally related to, lower primes (example: 12 is a double octave of 3, while 9 is a square of 3).

Related Topics:
Tonal - Erv Wilson - Consonant - Atonality - Ben Johnston - Serialism - Limit - Prime number - Octave - Square

~ ~ ~ ~ ~ ~ ~ ~ ~ ~