Chain-of-fifths notation
The circle-of-fifths notation is suitable to open up the variety of tones of a selection of EDOs and regular temperaments of fifth generator. The principle is based on one of the intervals taking over the role of the fifth of the traditional classical notation system of music (in 12-EDO or the meantone tuning). The classical notation system uses seven root notes and accidentals (♯, ♭ and their multiples) to sharpen and flatten these root notes by the same amount (which is an octave-reduced stack of 7 fifths).
EDOs that are best supported by this system are those whose fifth does not deviate too much from the pure fifth 3/2 (702 cent) and that can be represented by only one ring of fifths (24edo, as a counter-example, contains two rings). These include 12, 17, 19, 22, 26, 29, and 31edo.
| EDO | Fifth (cents) | Delta | Wholetone | Accidental | |
|---|---|---|---|---|---|
| 12 | 7\12 (700.0) | -2.0 | 2\12 | 1\12 | |
| 17 | 10\17 (705.9) | +3.9 | 3\17 | 2\17 | |
| 19 | 11\19 (694.7) | -7.2 | 3\19 | 1\19 | |
| 22 | 13\22 (709.1) | +7.1 | 4\22 | 3\22 | |
| 26 | 15\26 (692.3) | -9.6 | 4\26 | 1\26 | |
| 29 | 17\29 (703.4) | +1.5 | 5\29 | 3\29 | |
| 31 | 18\31 (696.8) | -5.2 | 5\31 | 2\31 |