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In music, 96 equal temperament, called 96-TET, 96-EDO ("Equal Division of the Octave"), or 96-ET, is the tempered scale derived by dividing the octave into 96 equal steps (equal frequency ratios). Each step represents a frequency ratio of ${\displaystyle {\sqrt{2}}}$, or 12.5 cents. Since 96 factors into 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96, it contains all of those temperaments. Most humans can only hear differences of 6 cents on notes that are played sequentially, and this amount varies according to the pitch, so the use of larger divisions of octave can be considered unnecessary. Smaller differences in pitch may be considered vibrato or stylistic devices.

History and use

96-EDO was first advocated by Julián Carrillo in 1924, with a 16th-tone piano. It was also advocated more recently by Pascale Criton and Vincent-Olivier Gagnon.

Notation

Since 96 = 24 × 4, quarter-tone notation can be used and split into four parts.

One can split it into four parts like this:

C, C↑, C↑↑/C↓↓, C↓, C, ..., C↓, C

As it can become confusing with so many accidentals, Julián Carrillo proposed referring to notes by step number from C (e.g. 0, 1, 2, 3, 4, ..., 95, 0)

Since the 16th-tone piano has a 97-key layout arranged in 8 conventional piano "octaves", music for it is usually notated according to the key the player has to strike. While the entire range of the instrument is only C₄–C₅, the notation ranges from C₀ to C₈. Thus, written D0 corresponds to sounding C↑↑₄ or note 2, and written A♭/G♯₂ corresponds to sounding E₄ or note 32.

Interval size

Below are some intervals in 96-EDO and how well they approximate just intonation.

Moving from 12-EDO to 96-EDO allows the better approximation of a number of intervals, such as the minor third and major sixth.

Scale diagram

This section is missing information about the scale diagram. Please expand the section to include this information. Further details may exist on the talk page. (February 2019)

Modes

96-EDO contains all of the 12-EDO modes. However, it contains better approximations to some intervals (such as the minor third).

See also

• Musical temperament
• Equal temperament

References

1. Monzo, Joe (2005). "Equal-Temperament". Tonalsoft Encyclopedia of Microtonal Music Theory. Joe Monzo. Retrieved 26 February 2019.

Further reading

• Sonido 13, Julián Carrillo's theory of 96-EDO

v t e Microtonal music
Composers	Richard Barrett Béla Bartók Easley Blackwood Jr. Heinz Bohlen Julián Carrillo Franklin Cox Mildred Couper John Eaton Brian Ferneyhough Michael Finnissy Bjørn Fongaard Alois Hába Christiaan Huygens Charles Ives Ben Johnston György Ligeti Stu Mackenzie Claus-Steffen Mahnkopf Joel Mandelbaum Joe Maneri Roger Redgate John Schneider Sevish Ezra Sims Nicola Vicentino Claude Vivier Elaine Walker Ivan Wyschnegradsky La Monte Young
Inventors	Glenn Branca Wendy Carlos Ivor Darreg Adriaan Fokker Lou Harrison Yuri Landman Harry Partch Tui St. George Tucker Nicola Vicentino
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 23 24 31 34 41 53 58 72 96 Just intonation Harry Partch's 43-tone scale Double diatonic
Concepts and techniques	Limit Otonality and Utonality Semitone Sonido 13 Xenharmonicity Tonality diamond
Groups and publications	Boston Microtonal Society Genesis of a Music Huygens-Fokker Foundation
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 Flying Microtonal Banana K.G. L.W.
Other topics	Enharmonic keyboard Generalized keyboard Modernism (music)

• Equal temperaments
• Microtonality