Chain-of-fifths notation: Difference between revisions
added 34edo |
tried to a a bit of space between the fifth and the derived intervals |
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| Line 4: | Line 4: | ||
{{EDOs| 12, 17, 19, 22, 26, 29, 31, and 34edo }}. | {{EDOs| 12, 17, 19, 22, 26, 29, 31, and 34edo }}. | ||
{| class="wikitable" | {| class="wikitable center-all" | ||
! EDO | ! EDO | ||
! Fifth (cents) | ! Fifth (cents) | ||
! Delta | ! Delta !! | ||
! Wholetone | ! Wholetone | ||
! Accidental | ! Accidental | ||
| Line 13: | Line 13: | ||
| 12 | | 12 | ||
| 7\12 (700.0) | | 7\12 (700.0) | ||
| -2.0 | | -2.0 || | ||
| 2\12 | | 2\12 | ||
| 1\12 | | 1\12 | ||
| Line 19: | Line 19: | ||
| 17 | | 17 | ||
| 10\17 (705.9) | | 10\17 (705.9) | ||
| +3.9 | | +3.9 || | ||
| 3\17 | | 3\17 | ||
| 2\17 | | 2\17 | ||
| Line 25: | Line 25: | ||
| 19 | | 19 | ||
| 11\19 (694.7) | | 11\19 (694.7) | ||
| -7.2 | | -7.2 || | ||
| 3\19 | | 3\19 | ||
| 1\19 | | 1\19 | ||
| Line 31: | Line 31: | ||
| 22 | | 22 | ||
| 13\22 (709.1) | | 13\22 (709.1) | ||
| +7.1 | | +7.1 || | ||
| 4\22 | | 4\22 | ||
| 3\22 | | 3\22 | ||
| Line 37: | Line 37: | ||
| 26 | | 26 | ||
| 15\26 (692.3) | | 15\26 (692.3) | ||
| -9.6 | | -9.6 || | ||
| 4\26 | | 4\26 | ||
| 1\26 | | 1\26 | ||
| Line 43: | Line 43: | ||
| 29 | | 29 | ||
| 17\29 (703.4) | | 17\29 (703.4) | ||
| +1.5 | | +1.5 || | ||
| 5\29 | | 5\29 | ||
| 3\29 | | 3\29 | ||
| Line 49: | Line 49: | ||
| 31 | | 31 | ||
| 18\31 (696.8) | | 18\31 (696.8) | ||
| -5.2 | | -5.2 || | ||
| 5\31 | | 5\31 | ||
| 2\31 | | 2\31 | ||
| Line 55: | Line 55: | ||
| 34 | | 34 | ||
| 20\34 (705.9) | | 20\34 (705.9) | ||
| +3.9 | | +3.9 || | ||
| 6\34 | | 6\34 | ||
| 4\34 | | 4\34 | ||
Revision as of 22:33, 14 November 2020
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 |