109edo

109edo is the equal division of the octave into 109 parts of 11.009 cents each. It tempers out 20000/19683 in the 5-limit; 245/243, 2401/2400 and 65625/65536 in the 7-limit; 385/384, 1375/1372, and 4000/3993 in the 11-limit. It provides the optimal patent val for 7-limit octacot temperament, and 11 and 13 limit leapweek; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.

109edo is the 29th prime EDO.

Since 109edo has a step of 11.009 cents, it also allows one to use its MOS scales as circulating temperaments. It is also the first edo which also allows one to use an MOS scale one octave of which fills a standard piano keyboard as a circulating temperament.

Circulating temperaments in 109edo

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