Microtonal, just intonation, electronic music software Microtonal, just intonation, electronic music software

Encyclopedia of Microtonal Music Theory

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5/12-tone, five-twelfth-tone

[Joe Monzo]

Calculated as the 72nd root of 25 -- 72√25, or 2(5/72) -- an irrational proportion with the approximate ratio of 1 : 1.049312535, and an interval size of exactly 83 1/3 cents. It is the size of 5 degrees in the 72-edo (or 72-tET) scale, and in 72-edo approximations of just intonation, functions as a 5-limit chromatic semitone (ratio 25:24 = 2,3,5-monzo [-3 -1, 2>) and the pythagorean diatonic semitone or limma (ratio 256:243 = 2,3-monzo [8 -5,>).

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