22 equal temperament

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).  Play  Each step represents a frequency ratio of 2^1/22, or 54.55 cents ( 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

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

External links

• Erlich, Paul, "Tuning, Tonality, and Twenty-Two Tone Temperament", William A. Sethares.
• Pachelbel's Canon in 22edo, Herman Miller

References

• 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)

Microtonal music
Composers	Easley Blackwood Jr. Heinz Bohlen Wendy Carlos Julián Carrillo Mildred Couper Ivor Darreg John Eaton Adriaan Fokker Alois Hába Lou Harrison Christiaan Huygens Ben Johnston Joel Mandelbaum Joe Maneri Harry Partch Ezra Sims Nicola Vicentino Elaine Walker Ivan Wyschnegradsky
Tunings and scales	Non-octave- repeating scales Alpha scale Beta scale Gamma scale Delta scale Lambda scale (Bohlen–Pierce scale) Equal temperament 15 17 19 22 24 31 34 41 53 58 72 Just intonation Harry Partch's 43-tone scale Triple diatonic
Concepts and techniques	Limit Otonality and Utonality Semitone Sonido 13 Xenharmonicity
Groups and publications	Boston Microtonal Society Genesis of a Music Huygens-Fokker Foundation Tonalsoft Xenharmonic Bulletin
Compositions	Beauty in the Beast quarter tone pieces just pieces Mother Sonata for Microtonal Piano Suite for Microtonal Piano Twelve Microtonal Etudes for Electronic Music Media
Other topics	Enharmonic keyboard Generalized keyboard Modernism (music)

Musical tunings
Measurement	Pitch Cent Millioctave Savart Interval Interval ratio Pitch class Consonance and dissonance List of musical intervals List of intervals in 5-limit just intonation List of meantone intervals Microtone
Just intonation	Euler–Fokker genus Harmonic Scale Harry Partch's 43-tone scale Hexany Limit 5-limit 7-limit List of compositions Numerary nexus Otonality Ptolemy's intense diatonic scale Pythagorean tuning Scale of harmonics Tonality diamond Tonality flux
Temperaments	Equal 6-tone 12-tone 15-tone 17-tone 19-tone 22-tone 24-tone (pieces) 31-tone 34-tone 41-tone 53-tone 58-tone 72-tone Linear Meantone (quarter-comma, septimal) Schismatic Miracle Magic Regular diatonic Irregular Well temperament/Temperament ordinaire (Kirnberger, Werckmeister, Young)
Traditional non-Western	Chinese musicology Shí-èr-lǜ Dastgah Maqam Arabian maqam Makam Mugham Muqam Octoechos Pelog Raga (Carnatic raga) Slendro Tetrachord
Non-octave	833 cents scale A12 scale Alpha scale Beta scale Gamma scale Delta scale Lambda scale (Bohlen-Pierce)