207edo

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207edo

208edo →

Prime factorization	32 × 23
Step size	5.7971 ¢
Fifth	121\207 (701.449 ¢)
Semitones (A1:m2)	19:16 (110.1 ¢ : 92.75 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

It tempers out 32805/32768 in the 5-limit, 6144/6125 and 19683/19600 in the 7-limit, 441/440 and 43923/43904 in the 11-limit, and 351/350, 847/845, 676/675, 729/728, 1716/1715 in the 13-limit. It serves as the patent val in the 11- and 13-limits for swetneus temperament. It is significantly more accurate on the 2.3.7.11.13 subgroup, a favorite of many people, and one which contains both 729/728 and 10648/10647, which it tempers out.

Prime harmonics

Approximation of prime harmonics in 207edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.51	+2.09	-0.71	-0.59	+0.05	-0.61	-1.86	-2.19	+2.31	+2.79
	Relative (%)	+0.0	-8.7	+36.1	-12.2	-10.2	+0.9	-10.5	-32.1	-37.7	+39.8	+48.1
Steps (reduced)		207 (0)	328 (121)	481 (67)	581 (167)	716 (95)	766 (145)	846 (18)	879 (51)	936 (108)	1006 (178)	1026 (198)

Subsets and supersets

207 factors into 3² × 23, with subset edos 3, 9, 23, and 69.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-328 207⟩	⟨207 328]	+0.1595	0.1596	2.75
2.3.5	32805/32768, [2 31 -22⟩	⟨207 328 481]	-0.1942	0.5166	8.91
2.3.5.7	6144/6125, 19683/19600, 32805/32768	⟨207 328 481 581]	-0.0825	0.4874	8.41
2.3.5.7.11	441/440, 3388/3375, 3773/3750, 6144/6125	⟨207 328 481 581 716]	-0.0317	0.4477	7.72
2.3.5.7.11.13	351/350, 441/440, 676/675, 847/845, 3584/3575	⟨207 328 481 581 716 766]	-0.0287	0.4087	7.05
2.3.5.7.11.13.17	441/440, 561/560, 676/675, 936/935, 1632/1625, 8624/8619	⟨207 328 481 581 716 766 846]	-0.0034	0.3834	6.61

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	25\207	144.93	49/45	Swetneus
1	43\207	249.28	15/13	Hemischis
1	86\207	498.55	4/3	Helmholtz