116edo

116edo is the equal division of the octave into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for submajor temperament.

Since 116edo has a step of 10.3448 cents, it also allows one to use its MOS scales as circulating temperaments.

Circulating temperaments in 116edo

Tones	Pattern	L:s
5	1L 4s	24:23
6	2L 4s	20:19
7	4L 3s	17:16
8	4L 4s	15:14
9	8L 1s	13:12
10	6L 4s	12:11
11	6L 5s	11:10
12	8L 4s	10:9
13	12L 1s	9:8
14	4L 10s
15	11L 4s	8:7
16	4L 12s
17	14L 3s	7:6
18	8L 10s
19	2L 17s
20	16L 4s	6:5
21	11L 10s
22	6L 16s
23	1L 22s
24	20L 4s	5:4
25	16L 9s
26	12L 14s
27	8L 19s
28	4L 24s
29	29edo	equal
30	26L 4s	4:3
31	23L 8s
32	20L 12s
33	17L 16s
34	14L 20s
35	11L 24s
36	8L 28s
37	5L 32s
38	2L 36s
39	38L 1s	3:2
40	36L 4s
41	34L 7s
42	32L 10s
43	30L 13s
44	28L 16s
45	26L 19s
46	24L 22s
47	22L 25s
48	20L 28s
49	18L 31s
50	16L 34s
51	14L 37s
52	12L 40s
53	10L 43s
54	8L 46s
55	6L 49s
56	4L 52s
57	2L 55s
58	58edo	equal
59	57L 2s	2:1
60	56L 4s
61	55L 6s
62	54L 8s
63	53L 10s
64	52L 12s
65	51L 14s
66	50L 16s
67	49L 18s
68	48L 20s
69	47L 22s
70	46L 24s
71	45L 26s
72	44L 28s
73	43L 30s
74	42L 32s
75	41L 34s
76	40L 36s
77	39L 38s
78	38L 40s
79	37L 42s
80	36L 44s
81	35L 46s
82	34L 48s
83	33L 50s
84	32L 52s
85	31L 54s
86	30L 56s
87	29L 58s
88	28L 60s
89	27L 62s
90	26L 64s
91	25L 66s
92	24L 68s