23 equal temperament
In music, 23 equal temperament, called 23-TET, 23-
History and use
23-EDO was advocated by ethnomusicologist
Notation
There are two ways to notate the 23-tone system with the traditional letter names and system of sharps and flats, called melodic notation and harmonic notation.
Harmonic notation preserves harmonic structures and interval arithmetic, but sharp and flat have reversed meanings. Because it preserves harmonic structures, 12-EDO music can be reinterpreted as 23-EDO harmonic notation, so it is also called conversion notation.
An example of these harmonic structures is the Circle of Fifths below (shown in 12-EDO, harmonic notation, and melodic notation.)
Melodic notation preserves the meaning of sharp and flat, but harmonic structures and interval arithmetic no longer work.
Interval size
Interval name / comments | Size (steps) | Size (cents) | MIDI |
---|---|---|---|
Octave | 23 | 1200 | |
21 | 1095.65 | ⓘ | |
Major sixth (3 cents sharp of 5/3) | 17 | 886.96 | ⓘ |
"Blown fifth" interval (24 cents flat of a 3/2 perfect fifth) | 13 | 678.26 | ⓘ |
11 | 573.91 | ⓘ | |
Fourth (octave inversion of "blown fifth") | 10 | 521.74 | ⓘ |
9 | 469.57 | ⓘ | |
8 | 417.39 | ⓘ | |
Major third (21 cents flat of 5/4) | 7 | 365.22 | ⓘ |
Minor third (3 cents flat of 6/5) | 6 | 313.04 | ⓘ |
5 | 260.87 | ⓘ | |
Large step appearing between B-C or E-F | 4 | 208.70 | ⓘ |
"Whole step" between A-B or C-D (actually smaller than the step from B-C) | 3 | 156.52 | ⓘ |
2 | 104.35 | ⓘ | |
Single step - this is the interval by which ♯ and ♭ modify pitches | 1 | 52.17 | ⓘ |
Scale diagram
Modes
This section is missing information about 23EDO modes.(February 2019) |
See also
References
- ^ Monzo, Joe (2005). "Equal-Temperament". Tonalsoft Encyclopedia of Microtonal Music Theory. Joe Monzo. Retrieved 20 February 2019.
- ISBN 9781852337971. Retrieved 20 February 2019.