107edo

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107edo

108edo →

Prime factorization	107 (prime)
Step size	11.215 ¢
Fifth	63\107 (706.542 ¢)
Semitones (A1:m2)	13:6 (145.8 ¢ : 67.29 ¢)
Dual sharp fifth	63\107 (706.542 ¢)
Dual flat fifth	62\107 (695.327 ¢)
Dual major 2nd	18\107 (201.869 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

107edo is inconsistent to the 5-odd-limit and higher limits, with four mappings possible for the 7-limit: ⟨107 170 248 300] (patent val), ⟨107 169 248 300] (107b), ⟨107 170 249 300] (107c), and ⟨107 170 249 301] (107cd).

Using the patent val, it tempers out 3125/3072 (magic comma) and 33554432000/31381059609 in the 5-limit; 1029/1024, 2240/2187, and 3125/3087 in the 7-limit; 100/99, 1232/1215, and 1331/1323 in the 11-limit.

Using the 107b val, it tempers out 81/80 (syntonic comma) and [-61 -1 27⟩; in the 5-limit; 2401/2400, 2430/2401, and 234375/229376 in the 7-limit; 385/384, 1350/1331, 1375/1372, and 1944/1925 in the 11-limit.

Using the 107c val, it tempers out 1638400/1594323 (immunity comma) and 1990656/1953125 (valentine comma) in the 5-limit; 126/125, 1029/1024, and 307328/295245 in the 7-limit; 121/120, 176/175, 441/440, and 184877/177147 in the 11-limit.

Using the 107cd val, it tempers out 1728/1715, 4000/3969, and 28672/28125 in the 7-limit; 121/120, 896/891, 1375/1372, and 3168/3125 in the 11-limit.

Subsets and supersets

107edo is the 28th prime edo.

Odd harmonics

Approximation of odd harmonics in 107edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+4.59	-5.01	-4.34	-2.04	-1.79	+0.59	-0.42	-4.02	+5.29	+0.25	-0.24
	Relative (%)	+40.9	-44.6	-38.7	-18.2	-15.9	+5.3	-3.7	-35.9	+47.2	+2.2	-2.1
Steps (reduced)		170 (63)	248 (34)	300 (86)	339 (18)	370 (49)	396 (75)	418 (97)	437 (9)	455 (27)	470 (42)	484 (56)

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[339 -107⟩	⟨107 339]	+0.322	0.322	2.87
2.9.5	9765625/9565938, [-34 10 1⟩	⟨107 339 248]	+0.933	0.904	8.06
2.9.5.7	225/224, 84035/82944, [14 -6 7 -4⟩	⟨107 339 248 300]	+1.087	0.827	7.37
2.9.5.7.11	225/224, 441/440, 26411/26244, 161280/161051	⟨107 339 248 300 370]	+0.973	0.774	6.90
2.9.5.7.11.13	225/224, 325/324, 441/440, 847/845, 24500/24167	⟨107 339 248 300 370 396]	+0.783	0.823	7.33
2.9.5.7.11.13.17	170/169, 225/224, 325/324, 441/440, 847/845, 2000/1989	⟨107 339 248 300 370 396 437]	+0.812	0.765	6.82

Scales

Since 107edo has a step of 11.214953271 cents, it also allows one to use its mos scales as circulating temperaments^{[clarification needed]}.

Circulating temperaments in 107edo

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