72 Equal Temperament

In music, 72 equal temperament, called twelfth-tone, 72-tet, 72-edo, or 72-et, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps (equal frequency ratios). Play Each step represents a frequency ratio of 21/72, or 16.67 cents, which divides the 100 cent "halftone" into 6 equal parts (100/16.6 = 6) and is thus a "twelfth-tone" ( Play).

This division of the octave has attracted much attention from tuning theorists, since on the one hand it subdivides the standard 12 equal temperament and on the other hand it accurately represents overtones up to the twelfth partial tone, and hence can be used for 11-limit music. It was theoreticized in the form of twelfth-tones by Alois Hába and Ivan Wyschnegradsky, who considered it as a good approach to the continuum of sound. 72-et is also cited among the divisions of the tone by Julián Carrillo, who preferred the sixteenth-tone as an approximation to continuous sound in discontinuous scales.

A number of composers have made use of it, and these represent widely different points of view and types of musical practice. These include Alois Hába, Julián Carrillo, Ivan Wyschnegradsky and Iannis Xenakis.

Many other composers use it freely and intuitively, such as jazz musician Joe Maneri, and classically-oriented composers such as Julia Werntz and others associated with the Boston Microtonal Society. Others, such as New York composer Joseph Pehrson are interested in it because it supports the use of miracle temperament, and still others simply because it approximates higher-limit just intonation, such as Ezra Sims and James Tenney. There was also an active Soviet school of 72 equal composers, with less familiar names: Evgeny Alexandrovich Murzin, Andrei Volkonsky, Nikolai Nikolsky, Eduard Artemiev, Alexander Nemtin, Andrei Eshpai, Gennady Gladkov, Pyotr Meshchianinov, and Stanislav Kreichi.