22ed5

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Division of the 5th harmonic into 22 equal parts (22ed5) is a good hyperpyth tuning. The step size about 126.6506 cents. It is compared 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 -4.4 cents from 9/5
9 1139.8556 85/44
10 1266.5062
11 1393.1569 38/17, 85/38
12 1519.8075
13 1646.4581 44/17 -7.8 cents from 13/5
14 1773.1087 39/14
15 1899.7593 3/1
16 2026.4100
17 2153.0606 52/15 +34.4 cents from 17/5
18 2279.7112 56/15 -31.5 cents from 19/5
19 2406.3618 225/56
20 2533.0125 95/22 +48.5 cents from 21/5
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, 161edo, and 180edo among others.