Chain-of-fifths notation
The circle-of-fifths notation is suitable to open up the variety of tones of a selection of EDOs. 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 7 root notes and 5 different accidentals (neutral, sharp, flat, double sharp, and double flat, of which the neutral can be regarded as implicit). From this basic material, 35 different pitches can be constructed; accordingly, the system becomes impracticable beyond 35 EDO.
The 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). These are(/include) 12, 17, 19, 22, 26, 29, 31, and 34edo.
| 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 | |
| 34 | 20\34 (705.9) | +3.9 | 6\34 | 4\34 |