673edo

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673edo

674edo →

Prime factorization	673 (prime)
Step size	1.78306 ¢
Fifth	394\673 (702.526 ¢)
Semitones (A1:m2)	66:49 (117.7 ¢ : 87.37 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

673edo is consistent to the 5-odd-limit. Using the 2.3.5.17.19.41 subgroup, it tempers out 4624/4617, 131072/130815, 53136/53125, 10584064/10546875 and 19178125/19131876.

Odd harmonics

Approximation of odd harmonics in 673edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.571	+0.611	-0.624	-0.641	-0.352	-0.706	-0.602	+0.245	+0.258	-0.053	-0.637
	Relative (%)	+32.0	+34.2	-35.0	-36.0	-19.7	-39.6	-33.7	+13.8	+14.5	-3.0	-35.7
Steps (reduced)		1067 (394)	1563 (217)	1889 (543)	2133 (114)	2328 (309)	2490 (471)	2629 (610)	2751 (59)	2859 (167)	2956 (264)	3044 (352)

Subsets and supersets

673edo is the 122nd prime EDO. 2019edo, which triples it, gives a good correction to the harmonic 7.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[1067 -673⟩	[⟨673 1067]]	-0.1801	0.1801	10.10
2.3.5	[32 -7 -9⟩, [19 -53 28⟩	[⟨673 1067 1563]]	-0.2077	0.1521	8.53

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	31\673	55.275	16875/16384	Escapade

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct