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The 59 equal division divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its major third is nearly pure. It is a good porcupine tuning, giving in fact the optimal patent val for 11-limit porcupine. This patent val tempers out 250/243 in the 5-limit, 64/63 and 16875/16807 in the 7-limit, and 55/54, 100/99 and 176/175 in the 11-limit. 59edo is an excellent tuning for the 2.9.5.21.11 11-limit 2*59 subgroup, on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&59 temperament with a subminor third generator provides an interesting temperament.

Using the flat fifth instead of the sharp one allows for the 12&35 temperament, which is a kind of bizarre cousin to garibaldi temperament with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth.

59edo is the 17th prime edo.

Degrees
Cents Value
1
20.339
2
40.678
3
61.017
4
81.356
5
101.695
6
122.034
7
142.373
8
162.712
9
183.051
10
203.390
11
223.729
12
244.068
13
264.407
14
284.746
15
305.085
16
325.424
17
345.763
18
366.102
19
386.441
20
406.780
21
427.119
22
447.458
23
467.797
24
488.136
25
508.475
26
528.814
27
549.153
28
569.492
29
589.831
30
610.169
31
630.508
32
650.847
33
671.186
34
691.525
35
711.864
36
732.203
37
752.542
38
772.881
39
793.220
40
813.559
41
833.898
42
854.237
43
874.576
44
894.915
45
915.254
46
935.593
47
955.932
48
976.271
49
996.610
50
1016.949
51
1037.288
52
1057.627
53
1077.966
54
1098.305
55
1118.644
56
1138.983
57
1159.322
58
1179.661