72 equal temperament
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In music, 72 equal temperament, called 72-tet, 72-edo, or 72-et, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equally large steps. Each step represents a frequency ratio of 21/72, or 16.667 cents.
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 accuately represents overtones up to the twelfth partial tone, and hence can be used for 11-limit music.
A number of composers have made use of it, and these represent widely different points of view and types of musical practice. Many 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. Other composers who have used it include Alois Haba, Julian Carrillo, Ivan Wyschnegradsky and Iannis Xenakis. 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.
[edit] Byzantine Music
The 72 equal temperament is used in Byzantine music theory, dividing the octave into 72 equal moria, which itself derives from interpretations of the theories of Aristoxenos, who used something similar. Although the 72 equal temperament is based on irrational intervals (see above), as is the 12 tone equal temperament mostly commonly used in Western music (and which is contained as a subset within 72 equal temperament), 72 equal temperament, as a much finer division of the octave, is an excellent tuning for both representing the division of the octave according to the diatonic and the chromatic genera in which intervals are based on ratios between notes, and for representing with great accuracy many rational intervals as well as irrational intervals.
[edit] Theoretical properties
In terms of tuning theory, the 72 equal harmonic system equates to the unison, or "tempers out", the small intervals 225/224, 243/242, 1029/1024, 385/384, 441/440, 540/539, as well as the Pythagorean comma and 15625/15552, among inumerable others; this gives it its own particular character in terms of functional harmony. It also means that 72 supports various temperaments which temper out some, but not all, of the above small intervals.
It is important to notice, however, that it does not temper out the syntonic comma of 81/80, and is therefore not a meantone system. Instead, 81/80 becomes one step of the scale. Hence, common practice music needs to be adapted for it to be played in this harmonic system, though the option always remains to use only twelve of the 72 notes.
[edit] External links
- Tonalsoft page on 72-tone equal-temperament / 72-edo
- Tonalsoft page on morion
- The Boston Microtonal Society official site
- 72note.com
- Maneri-Sims notation for 72-et
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| Pythagorean · Just intonation · Harry Partch's 43-tone scale | |||||
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| Well temperament | |||||
