102edo

102edo is the equal division of the octave into 102 steps of size 11.765 cents each. In the 5-limit it tempers out the same commas (2048/2025, 15625/15552, 20000/19683) as 34edo. In the 7-limit it tempers out 686/675 and 1029/1024; in the 11-limit 385/384, 441/440 and 4000/3993; in the 13-limit 91/90 and 169/168; in the 17-limit 136/135 and 154/153; and in the 19-limit 133/132 and 190/189. It is the optimal patent val for 13-limit echidnic temperament, and the rank five temperament tempering out 91/90.

13-limit Echidnic

Degree	Cents	Difference from 46edo
2	23.529	-2.5575¢
4	47.059	-5.115¢
7	82.353	4.092¢
9	105.882	1.5345¢
11	129.412	-1.023¢
13	152.941	8.184¢
16	188.235	5.627¢
18	211.765	3.069¢
20	235.294	0.511¢
22	258.824	-2.046¢
24	282.353	-4.604¢
27	317.647	4.604¢
29	341.176	2.046¢
31	364.706	-0.5115¢
33	388.235	-3.069¢
35	411.765	-5.627¢
38	447.059	3.581¢
40	470.588	1.023¢
42	494.117	-1.5345¢
44	517.647	-4.092¢
47	552.941	5.115¢
49	576.471	2.5575¢

Since 102edo has a step of 11.765 cents, it also allows one to use its MOS scales as circulating temperaments. It is the first edo which truly allows one to use an MOS scale with 60 or more small steps as a circulating temperament.

Circulating temperaments in 102edo

Tones	Pattern	L:s
5	2L 3s	21:20
6	6edo	equal
7	4L 3s	15:14
8	6L 2s	13:12
9	3L 6s	12:11
10	2L 8s	11:10
11	3L 8s	10:9
12	6L 6s	9:8
13	11L 2s	8:7
14	4L 10s
15	12L 3s	7:6
16	6L 10s
17	17edo	equal
18	10L 8s	6:5
19	7L 12s
20	2L 18s
21	18L 3s	5:4
22	14L 8s
23	10L 13s
24	6L 18s
25	2L 23s
26	24L 2s	4:3
27	21L 6s
28	18L 10s
29	15L 14s
30	12L 18s
31	9L 22s
32	6L 26s
33	3L 30s
34	34edo	equal
35	32L 3s	3:2
36	30L 6s
37	28L 9s
38	26L 12s
39	24L 15s
40	22L 18s
41	20L 21s
42	18L 24s
43	16L 27s
44	14L 30s
45	12L 33s
46	10L 36s
47	8L 39s
48	6L 42s
49	4L 45s
50	2L 48s
51	51edo	equal
52	50L 2s	2:1
53	49L 4s
54	48L 6s
55	47L 8s
56	46L 10s
57	45L 12s
58	44L 14s
59	43L 16s
60	42L 18s
61	41L 20s
62	40L 22s
63	39L 24s
64	38L 26s
65	37L 28s
66	36L 30s
67	35L 32s
68	34L 34s
69	33L 36s
70	32L 38s
71	31L 40s
72	30L 42s
73	29L 44s
74	28L 46s
75	27L 48s
76	26L 50s
77	25L 52s
78	24L 54s
79	23L 56s
80	22L 58s
81	21L 60s