557edo

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557edo

558edo →

Prime factorization	557 (prime)
Step size	2.1544 ¢
Fifth	326\557 (702.334 ¢)
Semitones (A1:m2)	54:41 (116.3 ¢ : 88.33 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

557et tempers out 645700815/645657712, 2460375/2458624, 65625/65536 and 420175/419904 in the 7-limit; 820125/819896, 2097152/2096325, 4000/3993, 78675968/78594219, 536870912/535869675, 180224/180075, 1375/1372, 184549376/184528125, 19712/19683, 43923/43904, 20614528/20588575 and 322102/321489 in the 11-limit.

Prime harmonics

Approximation of prime harmonics in 557edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.379	-0.676	+0.653	+0.208	-0.312	+0.610	-0.206	+0.810	+0.225	-1.050
	Relative (%)	+0.0	+17.6	-31.4	+30.3	+9.7	-14.5	+28.3	-9.6	+37.6	+10.5	-48.7
Steps (reduced)		557 (0)	883 (326)	1293 (179)	1564 (450)	1927 (256)	2061 (390)	2277 (49)	2366 (138)	2520 (292)	2706 (478)	2759 (531)

Subsets and supersets

557edo is the 102nd prime EDO.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[883 -557⟩	⟨557 883]	-0.1195	0.1195	5.55
2.3.5	[3 -18 11⟩, [-74 13 23⟩	⟨557 883 1293]	+0.0174	0.2169	10.07

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	228\557	491.203	4/3	Sesesix

Scales

• Laz5
• Laz9