112edo

← 111edo

112edo

113edo →

Prime factorization	24 × 7
Step size	10.7143 ¢
Fifth	66\112 (707.143 ¢) (→ 33\56)
Semitones (A1:m2)	14:6 (150 ¢ : 64.29 ¢)
Dual sharp fifth	66\112 (707.143 ¢) (→ 33\56)
Dual flat fifth	65\112 (696.429 ¢)
Dual major 2nd	19\112 (203.571 ¢)
Consistency limit	3
Distinct consistency limit	3

112edo has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the patent fifth- is identical to the perfect fifth of 56edo, a great inverse gentle fifth where +5 fifths gives a near-just 28:27 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.

Odd harmonics

Approximation of odd harmonics in 112edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+5.19	-0.60	-4.54	-0.34	-4.89	-4.81	+4.59	+2.19	+2.49	+0.65	+3.87
	Relative (%)	+48.4	-5.6	-42.4	-3.2	-45.6	-44.9	+42.8	+20.4	+23.2	+6.0	+36.1
Steps (reduced)		178 (66)	260 (36)	314 (90)	355 (19)	387 (51)	414 (78)	438 (102)	458 (10)	476 (28)	492 (44)	507 (59)

Circulating temperaments

Since 112edo has a step of 10.714 cents, it also allows one to use its MOS scales as circulating temperaments.

Circulating temperaments in 112edo

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

Music in 112EDO

• Circulating 2.3.7.11.13 Floaty Piano Improv by Cam Taylor