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Encyclopedia of Microtonal Music Theory

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EDO / edo

[Joe Monzo]

Acronym for "Equal Divisions of the Octave". First used publicly by Dan Stearns, some microtonalists feel that in certain cases this term is better than ET for describing equal-temperaments that are divisions of an 'octave' (assumed to be tuned to the ratio 2:1), because the 'octave' is not the only interval that may be evenly divided.

For example, 19-tET or 19-ET, altho they standardly refer to 2^(19/19), could mean 19 divisions of any pitch range, not neccesarily an octave. An illustration of this is provided by the equal-tempered version of Bohlen-Pierce tuning, in which the 3:1 'perfect 12th' (that is, 'octave' plus 'fifth') is divided into 19 equal parts: 3^(19/19).

An important distinction between the use of "EDO" and "ET" is that composers do not always intend for an EDO to be a temperament of a just-intonation tuning. For example, in much 20th-century music, composers used 12-edo in a manner which does not refer in any way to its being a temperament of just-intonation -- a good example of this is Schoenberg's "12-tone method" (also called "serialism"). In this compositional technique, the intervals of the 12-edo chromatic scale are not meant to represent tempered versions of the intervals of classic 5-limit JI, rather, the 12-edo scale is treated as a set of intervals with its own intrinsic properties unrelated to those of JI. Therefore, in this usage "12-ET" really does not give an accurate impression of the composer's intentions, and "12-edo" is preferred. Stearns applied this same idea to non-12-edos.

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