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