112edo

112EDO has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which is identical to the perfect fifth of 56edo, a slightly large fifth where +5 fifths gives a near-just 27:28 while -8 fifths gives a near-just 32:39 (identical to 2 degrees of 7edo) and +9 fifths gives a close approximation to 17:21.

One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from 17edo, but sharing a similar structure.

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	?	?	55/54	55/54
2	250/243	49/48	49/48	49/48
3	?	?	56/55	56/55
4	81/80	28/27	28/27	28/27
5	?	?	33/32	33/32
6	25/24	25/24	25/24	25/24
7	?	?	22/21	22/21
8	648/625	21/20	21/20	21/20
9	?	?	35/33	35/33
10	16/15	16/15	16/15	16/15
11	?	?	81/77	81/77
12	625/576	15/14	15/14	13/12
13	?	?	189/176	189/176
14	27/25	27/25	27/25	27/25
15	?	?	11/10	11/10
16	10/9	10/9	10/9	10/9
17	?	?	49/44	49/44
18	2187/2000	28/25	28/25	28/25
19	?	?	55/49	44/39
20	9/8	9/8	9/8	9/8
21	?	?	25/22	25/22
22	125/108	8/7	8/7	8/7
23	?	?	63/55	63/55
24	144/125	7/6	7/6	7/6
25	?	?	64/55	64/55
26	32/27	32/27	32/27	32/27
27	?	?	33/28	13/11
28	729/625	25/21	25/21	25/21
29	?	?	77/64	77/64
30	6/5	6/5	6/5	6/5
31	?	?	11/9	11/9
32	100/81	49/40	49/40	39/32
33	?	?	154/125	154/125
34	243/200	56/45	56/45	16/13
35	?	?	27/22	27/22
36	5/4	5/4	5/4	5/4
37	?	?	44/35	44/35
38	625/486	63/50	63/50	63/50
39	?	?	14/11	14/11
40	32/25	32/25	32/25	32/25
41	?	?	128/99	128/99
42	125/96	9/7	9/7	9/7
43	?	?	55/42	55/42
44	162/125	21/16	21/16	21/16
45	?	?	33/25	33/25
46	4/3	4/3	4/3	4/3
47	?	?	110/81	110/81
48	1000/729	49/36	49/36	35/26
49	?	?	66/49	66/49
50	27/20	27/20	27/20	27/20
51	?	?	11/8	11/8
52	25/18	25/18	25/18	25/18
53	?	?	88/63	88/63
54	864/625	7/5	7/5	7/5
55	?	?	77/54	55/39
56	45/32	45/32	45/32	45/32
57	?	?	99/70	78/55
58	625/432	10/7	10/7	10/7
59	?	?	63/44	63/44
60	36/25	35/24	35/24	35/24
61	?	?	16/11	16/11
62	40/27	40/27	40/27	40/27
63	?	?	49/33	49/33
64	729/500	72/49	72/49	52/35
65	?	?	81/55	81/55
66	3/2	3/2	3/2	3/2
67	?	?	50/33	50/33
68	125/81	32/21	32/21	32/21
69	?	?	77/50	77/50
70	192/125	14/9	14/9	14/9
71	?	?	99/64	99/64
72	25/16	25/16	25/16	25/16
73	?	?	11/7	11/7
74	972/625	63/40	63/40	63/40
75	?	?	35/22	35/22
76	8/5	8/5	8/5	8/5
77	?	?	44/27	44/27
78	400/243	45/28	45/28	13/8
79	?	?	125/77	125/77
80	81/50	80/49	80/49	64/39
81	?	?	18/11	18/11
82	5/3	5/3	5/3	5/3
83	?	?	128/77	128/77
84	1250/729	42/25	42/25	42/25
85	?	?	56/33	22/13
86	27/16	27/16	27/16	27/16
87	?	?	55/32	55/32
88	125/72	12/7	12/7	12/7
89	?	?	110/63	110/63
90	216/125	7/4	7/4	7/4
91	?	?	44/25	44/25
92	16/9	16/9	16/9	16/9
93	?	?	98/55	39/22
94	2187/1250	25/14	25/14	25/14
95	?	?	88/49	88/49
96	9/5	9/5	9/5	9/5
97	?	?	11/6	11/6
98	50/27	50/27	50/27	50/27
99	?	?	231/125	231/125
100	729/400	28/15	28/15	13/7
101	?	?	81/44	81/44
102	15/8	15/8	15/8	15/8
103	?	?	66/35	66/35
104	625/324	40/21	40/21	40/21
105	?	?	21/11	21/11
106	48/25	35/18	35/18	25/13
107	?	?	64/33	64/33
108	125/64	27/14	27/14	27/14
109	?	?	55/28	55/28
110	243/125	63/32	63/32	63/32
111	?	?	99/50	99/50
112	2/1	2/1	2/1	2/1

Music in 112EDO

Circulating 2.3.7.11.13 Floaty Piano Improv by Cam Taylor