59edo

The 59 equal division divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is stretched about 9.91 cents from the just interval, and yet its major third is nearly pure (stretched only 0.127 cents), as the denominator of a convergent to log₂5. 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