634edo

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← 633edo

634edo

635edo →

Prime factorization	2 × 317
Step size	1.89274 ¢
Fifth	371\634 (702.208 ¢)
Semitones (A1:m2)	61:47 (115.5 ¢ : 88.96 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

634edo is a good 13-limit and no-17 higher-limit system. It tempers out the [-53 10 16⟩ (kwazy comma); 420175/419904 (wizma), 703125/702464 (meter), and 33554432/33480783 (garischisma) in the 7-limit; 9801/9800, 19712/19683, 41503/41472 in the 11-limit; 1716/1715, 2080/2079, 4096/4095, 4225/4224, 14641/14625, and 31250/31213 in the 13-limit.

Prime harmonics

Approximation of prime harmonics in 634edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.253	-0.194	+0.259	-0.529	-0.149	-0.854	-0.352	+0.117	+0.076	+0.075
	Relative (%)	+0.0	+13.4	-10.2	+13.7	-28.0	-7.9	-45.1	-18.6	+6.2	+4.0	+4.0
Steps (reduced)		634 (0)	1005 (371)	1472 (204)	1780 (512)	2193 (291)	2346 (444)	2591 (55)	2693 (157)	2868 (332)	3080 (544)	3141 (605)

Subsets and supersets

634edo has subset edos 2edo and 317edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[1005 -634⟩	[⟨634 1005]]	-0.0799	0.0799	4.22
2.3.5	[-53 10 16⟩, [33 -34 9⟩	[⟨634 1005 1472]]	-0.0254	0.1009	5.33
2.3.5.7	420175/419904, 703125/702464, 33554432/33480783	[⟨634 1005 1472 1780]]	-0.0422	0.0921	4.86
2.3.5.7.11	9801/9800, 19712/19683, 41503/41472, 703125/702464	[⟨634 1005 1472 1780 2193]]	-0.0031	0.1135	6.00
2.3.5.7.11.13	1716/1715, 2080/2079, 4096/4095, 14641/14625, 31250/31213	[⟨634 1005 1472 1780 2193 2346]]	+0.0041	0.1048	5.54

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
1	241\634	456.15	125/96	Qak
1	263\634	497.79	4/3	Gary
2	86\634	162.78	1125/1024	Kwazy