669edo

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669edo

670edo →

Prime factorization	3 × 223
Step size	1.79372 ¢
Fifth	391\669 (701.345 ¢)
Semitones (A1:m2)	61:52 (109.4 ¢ : 93.27 ¢)
Dual sharp fifth	392\669 (703.139 ¢)
Dual flat fifth	391\669 (701.345 ¢)
Dual major 2nd	114\669 (204.484 ¢) (→ 38\223)
Consistency limit	7
Distinct consistency limit	7

669edo is consistent in the 7-odd-limit, although it has significant errors on the 3rd and the 5th harmonics. Besides that, 669c val is a tuning for the sensipent temperament in the 5-limit.

669edo appears much more useful as a higher-limit system, with harmonics 37 through 53 all having an error of 20% or less, with a comma basis for the 2.37.41.43.47.53 subgroup being {75809/75776, 1874161/1873232, 151124317/151101728, 9033613312/9032089499, 9795995841727/9788230467584}.

Overall, the subgroup which provides satisfactory results for 669edo is 2.7.19.29.37.41.43.47.53.

Harmonics

Approximation of odd harmonics in 669edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.610	-0.663	-0.216	+0.574	-0.645	+0.728	+0.521	+0.874	+0.245	-0.826	-0.472
	Relative (%)	-34.0	-37.0	-12.0	+32.0	-36.0	+40.6	+29.0	+48.7	+13.6	-46.0	-26.3
Steps (reduced)		1060 (391)	1553 (215)	1878 (540)	2121 (114)	2314 (307)	2476 (469)	2614 (607)	2735 (59)	2842 (166)	2938 (262)	3026 (350)