22ed5
Division of the 5th harmonic into 22 equal parts (22ed5) is a good hyperpyth tuning. The step size about 126.6506 cents. It is similar to 15edt and every second step of 19edo, but with the 5/1 rather than 2/1 or 3/1 being just.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 126.6506 | 14/13 | |
| 2 | 253.3012 | 22/19 | |
| 3 | 379.9519 | 56/45 | |
| 4 | 506.6025 | 75/56 | |
| 5 | 633.2531 | 75/52 | |
| 6 | 759.9037 | ||
| 7 | 886.5544 | 5/3 | |
| 8 | 1013.2050 | 70/39 | |
| 9 | 1139.8556 | 85/44 | |
| 10 | 1266.5062 | ||
| 11 | 1393.1569 | 38/17, 85/38 | |
| 12 | 1519.8075 | ||
| 13 | 1646.4581 | 44/17 | |
| 14 | 1773.1087 | 39/14 | |
| 15 | 1899.7593 | 3/1 | |
| 16 | 2026.4100 | ||
| 17 | 2153.0606 | 52/15 | |
| 18 | 2279.7112 | 56/15 | |
| 19 | 2406.3618 | 225/56 | |
| 20 | 2533.0125 | 95/22 | |
| 21 | 2659.6631 | 65/14 | |
| 22 | 2786.3137 | exact 5/1 | just major third plus two octaves |
22ed5 as a generator
22ed5 can also be thought of as a generator of the 19-limit mowgli temperament, which tempers out 351/350, 476/475, 495/494, 969/968, 1445/1444, and 1701/1690, which is a cluster temperament with nine clusters of notes in an octave. This temperament is supported by 19edo and 161edo.