22 equal temperament

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In music, 22 equal temperament, called 22-tet, 22-edo, or 22-et, is the tempered scale derived by dividing the octave into 22 equal steps (equal frequency ratios). About this sound Play  Each step represents a frequency ratio of 222, or 54.55 cents (About this sound Play ).

The idea of dividing the octave into 22 steps of equal size seems to have originated with ninéteenth-century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the music theory of India, Bosanquet noted that an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after 19 equal temperament, and J. Murray Barbour in his survey of tuning history, Tuning and Temperament. Contemporary advocates of 22 equal temperament include music theorist Paul Erlich.

Interval size[edit]

Here are the sizes of some common intervals in this system:

interval name size (steps) size (cents) midi just ratio just (cents) midi error
17:10 wide major sixth 17 927.27 About this sound Play  17:10 920.64 08.63
major sixth 16 872.73 About this sound Play  5:3 884.36 About this sound Play  −11.63
perfect fifth 13 709.09 About this sound Play  3:2 701.95 About this sound Play  +07.14
septendecimal tritone 11 600.00 About this sound Play  17:12 603.00 03.00
septimal tritone 11 600.00 7:5 582.51 About this sound Play  +17.49
11:8 wide fourth 10 545.45 About this sound Play  11:80 551.32 About this sound Play  05.87
15:11 wide fourth 10 545.45 15:11 536.95 About this sound Play  +08.50
perfect fourth 09 490.91 About this sound Play  4:3 498.05 About this sound Play  07.14
septendecimal supermajor third 08 436.36 About this sound Play  22:17 446.36 −10.00
septimal major third 08 436.36 9:7 435.08 About this sound Play  +01.28
undecimal major third 08 436.36 14:11 417.51 About this sound Play  +18.86
major third 07 381.82 About this sound Play  5:4 386.31 About this sound Play  04.49
undecimal neutral third 06 327.27 About this sound Play  11:90 347.41 About this sound Play  −20.14
septendecimal supraminor third 06 327.27 17:14 336.13 About this sound Play  08.86
minor third 06 327.27 6:5 315.64 About this sound Play  +11.63
septendecimal augmented second 05 272.73 About this sound Play  20:17 281.36 08.63
septimal minor third 05 272.73 7:6 266.88 About this sound Play  +05.85
septimal whole tone 04 218.18 About this sound Play  8:7 231.17 About this sound Play  −12.99
septendecimal major second 04 218.18 17:15 216.69 +01.50
whole tone, major tone 04 218.18 9:8 203.91 About this sound Play  +14.27
whole tone, minor tone 03 163.64 About this sound Play  10:90 182.40 About this sound Play  −18.77
neutral second, greater undecimal 03 163.64 11:10 165.00 About this sound Play  01.37
neutral second, lesser undecimal 03 163.64 12:11 150.64 About this sound Play  +13.00
septimal diatonic semitone 02 109.09 About this sound Play  15:14 119.44 About this sound Play  −10.35
diatonic semitone, just 02 109.09 16:15 111.73 About this sound Play  02.64
17th harmonic 02 109.09 17:16 104.95 About this sound Play  +04.13
Arabic lute index finger 02 109.09 18:17 098.95 About this sound Play  +10.14
septimal chromatic semitone 02 109.09 21:20 084.47 About this sound Play  +24.62
chromatic semitone, just 01 054.55 About this sound Play  25:24 070.67 About this sound Play  −16.13
septimal third-tone 01 054.55 28:27 062.96 About this sound Play  08.42
undecimal quarter tone 01 054.55 33:32 053.27 About this sound Play  +01.27
septimal quarter tone 01 054.55 36:35 048.77 About this sound Play  +05.78

External links[edit]

References[edit]

  • Barbour, James Murray, Tuning and temperament, a historical survey, East Lansing, Michigan State College Press, 1953 [c1951]
  • Bosanquet, R.H.M. "On the Hindoo division of the octave, with additions to the theory of higher orders" (Archived 2009-10-22), Proceedings of the Royal Society of London vol. 26 (March 1, 1877 to December 20, 1877) Taylor & Francis, London 1878, pp. 372-384. (Reproduced in Tagore, Sourindro Mohun, Hindu Music from Various Authors, Chowkhamba Sanskrit Series, Varanasi, India, 1965)