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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. Another way of considering just intonation is as being based on members of the harmonic series. Thus, 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, but consonance is not always emphasized or a goal in music written with just intonation, and a great deal of dissonance may be featured in compositions.It is possible to tune the familiar diatonic scale or chromatic scale in just intonation, in many ways, all of which make certain chords purely tuned and as consonant as possible, and others considerably more dissonant and indeed out-of-tune sounding (see below for more on this). But many other justly tuned scales have also been used. 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 serialismSerialism is a rigorous system of composing music in which various elements of the piece are ordered according to a pre-determined ordered set or sets, and variations on them. The elements thus controlled may be the pitch of the notes, their length, their to acheive an atonal result. Composers often impose a limitJust 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 wit on how complex the ratios used are: for example, a composer may write in "7-limit JI", meaning that no prime numberIn mathematics, a prime number or prime for short, is a natural number whose only distinct positive divisors are 1 and itself; otherwise it is called a composite number . Hence a prime number has exactly two divisors. The number 1 is neither prime nor com 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 octaveIntervals : For the numerical computation software, see GNU Octave. In music, an octave (sometimes abbreviated 8ve or 8va is the interval between one musical note and another with half or double the frequency. For example, if one note is pitched at 400 Hzs of, or mathematically and tonally related to, lower primes (example: 12 is a double octave of 3, while 9 is a squareA square as a geometric shape is described and illustrated at square (geometry). There are other concepts derived from it: the geometric unit square; the square units of measurement, such as the square mile, square meter, square kilometer, square inch, an of 3).
Many composers have written in just intonation, including Glenn BrancaGlenn Branca is an avant garde composer and guitarist. In the early 1970s, Branca began experimenting with sound as the founder of an experimental theater group in Boston called Bastard Theater. He moved to New York in 1976, and his early music was perfor, Arnold DreyblattArnold Dreyblatt is a composer and visual artist. He studied with Pauline Oliveros, La Monte Young, and Alvin Lucier. His compositions are based on harmonics, and thus just intonation, played either through a bowing technique he developed for his modified, Kyle GannKyle Gann (b. 1955) is a composer and music critic from Texas. As a critic for the Village Voice and other publications he was a supportor of progressive music including totalism, his own music is often rhythmically complex and uses just intonation or alt, Lou Harrison, Ben Johnston, Harry Partch, Terry Riley, LaMonte Young, James Tenney, Pauline Oliveros, Stuart Dempster, Kraig Grady , Elodie Lauten and Wendy Carlos. 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.
