56ed5

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Division of the 5th harmonic into 56 equal parts (56ed5) is related to 24 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 49.7556 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. This tuning is also a hyperpyth, tempering out 135/133, 171/169, 225/221, and 1521/1445 in the patent val.

degree cents value corresponding
JI intervals
comments
0 0.0000 exact 1/1
1 49.7556 36/35, 35/34
2 99.5112 18/17
3 149.2668 12/11
4 199.0224 55/49
5 248.7780 15/13
6 298.5336 19/16
7 348.2892 11/9
8 398.0448 34/27 pseudo-5/4
9 447.8004 35/27
10 497.5560 4/3
11 547.3116 70/51
12 597.0672 24/17
13 646.8228
14 696.5784 meantone fifth
(pseudo-3/2)
15 746.3340 20/13
16 796.0896 19/12
17 845.8452 44/27, 75/46
18 895.6008 57/34 pseudo-5/3
19 945.3564 19/11
20 995.1120 16/9 pseudo-9/5
21 1044.8676 64/35
22 1094.6232 32/17
23 1144.3788
24 1194.1344 255/128 pseudo-octave
25 1243.8901 80/39, 39/19
26 1293.6457 19/9
27 1343.4013 50/23
28 1393.1569 38/17, 85/38 meantone major second plus an octave
29 1442.9125 23/10
30 1492.6681 45/19
31 1542.4237 39/16
32 1592.1793 128/51 pseudo-5/2
33 1641.9349 pseudo-13/5
34 1691.6905 85/32
35 1741.4461 175/64
36 1791.2017 45/16
37 1840.9573 55/19
38 1890.7129 170/57 pseudo-3/1
39 1940.4685 46/15, 135/44
40 1990.2241 60/19
41 2039.9797 13/4
42 2089.7353 meantone major sixth plus an octave
(pseudo-10/3)
43 2139.4909 pseudo-17/5
44 2189.2465 85/24
45 2239.0021 51/14
46 2288.7577 15/4 pseudo-19/5
47 2338.5133 27/7
48 2388.2689 135/34 pseudo-4/1
49 2438.0245 45/11
50 2487.7801 80/19 pseudo-21/5
51 2537.5357 13/3
52 2587.2913 49/11
53 2637.0469 55/12
54 2686.8025 85/18
55 2736.5581 34/7
56 2786.3137 exact 5/1 just major third plus two octaves