110edo

110edo is the equal division of the octave into 110 parts of 10.9090909091 cents each. It tempers out 15625/15552 and 3486784401/3355443200 in the 5-limit. Using the patent val, it tempers out 1728/1715, 3125/3087, and 3645/3584 in the 7-limit.

Since 110edo has a step of 10.9090909091 cents, it also allows one to use its MOS scales as circulating temperaments. As 10*11edo, it is the first edo which allows one to use consecutive smaller edos as circulating temperaments.

Circulating temperaments in 110edo

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