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 [28 -22 3⟩ 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 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.

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 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.

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)

Subsets and supersets

107edo is the 28th prime edo. 214edo, which doubles it, provides correction for the approximation to harmonics 3, 5, and 7.

Intervals

Steps	Cents	Approximate ratios	Ups and downs notation (Dual flat fifth 62\107)	Ups and downs notation (Dual sharp fifth 63\107)
0	0	1/1	D	D
1	11.2		^D, ^^E♭♭♭	^D, v5E♭
2	22.4		^^D, v3E♭♭	^^D, v4E♭
3	33.6		^3D, vvE♭♭	^3D, v3E♭
4	44.9	39/38, 41/40	vvD♯, vE♭♭	^4D, vvE♭
5	56.1	31/30, 32/31	vD♯, E♭♭	^5D, vE♭
6	67.3		D♯, ^E♭♭	^6D, E♭
7	78.5	22/21, 23/22, 45/43	^D♯, ^^E♭♭	v6D♯, ^E♭
8	89.7		^^D♯, v3E♭	v5D♯, ^^E♭
9	100.9		^3D♯, vvE♭	v4D♯, ^3E♭
10	112.1	16/15	vvD𝄪, vE♭	v3D♯, ^4E♭
11	123.4	44/41	vD𝄪, E♭	vvD♯, ^5E♭
12	134.6	40/37	D𝄪, ^E♭	vD♯, ^6E♭
13	145.8	37/34	^D𝄪, ^^E♭	D♯, v6E
14	157	23/21	^^D𝄪, v3E	^D♯, v5E
15	168.2	32/29, 43/39	^3D𝄪, vvE	^^D♯, v4E
16	179.4	41/37	vvD♯𝄪, vE	^3D♯, v3E
17	190.7	29/26	E	^4D♯, vvE
18	201.9		^E, ^^F♭♭	^5D♯, vE
19	213.1	26/23, 43/38	^^E, v3F♭	E
20	224.3	33/29	^3E, vvF♭	^E, v5F
21	235.5		vvE♯, vF♭	^^E, v4F
22	246.7	15/13	vE♯, F♭	^3E, v3F
23	257.9		E♯, ^F♭	^4E, vvF
24	269.2		^E♯, ^^F♭	^5E, vF
25	280.4	20/17	^^E♯, v3F	F
26	291.6	45/38	^3E♯, vvF	^F, v5G♭
27	302.8	31/26	vvE𝄪, vF	^^F, v4G♭
28	314		F	^3F, v3G♭
29	325.2	41/34	^F, ^^G♭♭♭	^4F, vvG♭
30	336.4	17/14	^^F, v3G♭♭	^5F, vG♭
31	347.7		^3F, vvG♭♭	^6F, G♭
32	358.9	16/13	vvF♯, vG♭♭	v6F♯, ^G♭
33	370.1	26/21	vF♯, G♭♭	v5F♯, ^^G♭
34	381.3		F♯, ^G♭♭	v4F♯, ^3G♭
35	392.5		^F♯, ^^G♭♭	v3F♯, ^4G♭
36	403.7	24/19	^^F♯, v3G♭	vvF♯, ^5G♭
37	415	33/26	^3F♯, vvG♭	vF♯, ^6G♭
38	426.2		vvF𝄪, vG♭	F♯, v6G
39	437.4		vF𝄪, G♭	^F♯, v5G
40	448.6	22/17	F𝄪, ^G♭	^^F♯, v4G
41	459.8	30/23, 43/33	^F𝄪, ^^G♭	^3F♯, v3G
42	471	21/16	^^F𝄪, v3G	^4F♯, vvG
43	482.2	37/28, 41/31	^3F𝄪, vvG	^5F♯, vG
44	493.5		vvF♯𝄪, vG	G
45	504.7		G	^G, v5A♭
46	515.9	31/23	^G, ^^A♭♭♭	^^G, v4A♭
47	527.1	42/31	^^G, v3A♭♭	^3G, v3A♭
48	538.3	15/11	^3G, vvA♭♭	^4G, vvA♭
49	549.5	11/8	vvG♯, vA♭♭	^5G, vA♭
50	560.7	29/21	vG♯, A♭♭	^6G, A♭
51	572	32/23	G♯, ^A♭♭	v6G♯, ^A♭
52	583.2	7/5	^G♯, ^^A♭♭	v5G♯, ^^A♭
53	594.4	31/22	^^G♯, v3A♭	v4G♯, ^3A♭
54	605.6	44/31	^3G♯, vvA♭	v3G♯, ^4A♭
55	616.8	10/7	vvG𝄪, vA♭	vvG♯, ^5A♭
56	628	23/16	vG𝄪, A♭	vG♯, ^6A♭
57	639.3	42/29	G𝄪, ^A♭	G♯, v6A
58	650.5	16/11	^G𝄪, ^^A♭	^G♯, v5A
59	661.7	22/15, 41/28	^^G𝄪, v3A	^^G♯, v4A
60	672.9	31/21	^3G𝄪, vvA	^3G♯, v3A
61	684.1	43/29, 46/31	vvG♯𝄪, vA	^4G♯, vvA
62	695.3		A	^5G♯, vA
63	706.5		^A, ^^B♭♭♭	A
64	717.8		^^A, v3B♭♭	^A, v5B♭
65	729	32/21	^3A, vvB♭♭	^^A, v4B♭
66	740.2	23/15	vvA♯, vB♭♭	^3A, v3B♭
67	751.4	17/11	vA♯, B♭♭	^4A, vvB♭
68	762.6	45/29	A♯, ^B♭♭	^5A, vB♭
69	773.8		^A♯, ^^B♭♭	^6A, B♭
70	785		^^A♯, v3B♭	v6A♯, ^B♭
71	796.3	19/12	^3A♯, vvB♭	v5A♯, ^^B♭
72	807.5		vvA𝄪, vB♭	v4A♯, ^3B♭
73	818.7		vA𝄪, B♭	v3A♯, ^4B♭
74	829.9	21/13	A𝄪, ^B♭	vvA♯, ^5B♭
75	841.1	13/8	^A𝄪, ^^B♭	vA♯, ^6B♭
76	852.3		^^A𝄪, v3B	A♯, v6B
77	863.6	28/17	^3A𝄪, vvB	^A♯, v5B
78	874.8		vvA♯𝄪, vB	^^A♯, v4B
79	886		B	^3A♯, v3B
80	897.2		^B, ^^C♭♭	^4A♯, vvB
81	908.4		^^B, v3C♭	^5A♯, vB
82	919.6	17/10	^3B, vvC♭	B
83	930.8		vvB♯, vC♭	^B, v5C
84	942.1		vB♯, C♭	^^B, v4C
85	953.3	26/15	B♯, ^C♭	^3B, v3C
86	964.5		^B♯, ^^C♭	^4B, vvC
87	975.7		^^B♯, v3C	^5B, vC
88	986.9	23/13	^3B♯, vvC	C
89	998.1		vvB𝄪, vC	^C, v5D♭
90	1009.3	43/24	C	^^C, v4D♭
91	1020.6		^C, ^^D♭♭♭	^3C, v3D♭
92	1031.8	29/16	^^C, v3D♭♭	^4C, vvD♭
93	1043	42/23	^3C, vvD♭♭	^5C, vD♭
94	1054.2		vvC♯, vD♭♭	^6C, D♭
95	1065.4	37/20	vC♯, D♭♭	v6C♯, ^D♭
96	1076.6	41/22	C♯, ^D♭♭	v5C♯, ^^D♭
97	1087.9	15/8	^C♯, ^^D♭♭	v4C♯, ^3D♭
98	1099.1		^^C♯, v3D♭	v3C♯, ^4D♭
99	1110.3		^3C♯, vvD♭	vvC♯, ^5D♭
100	1121.5	21/11, 44/23	vvC𝄪, vD♭	vC♯, ^6D♭
101	1132.7		vC𝄪, D♭	C♯, v6D
102	1143.9	31/16	C𝄪, ^D♭	^C♯, v5D
103	1155.1		^C𝄪, ^^D♭	^^C♯, v4D
104	1166.4		^^C𝄪, v3D	^3C♯, v3D
105	1177.6		^3C𝄪, vvD	^4C♯, vvD
106	1188.8		vvC♯𝄪, vD	^5C♯, vD
107	1200	2/1	D	D

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