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

557edo is only consistent to the 5-odd-limit. Using the patent val, the equal temperament tempers out [3 -18 11⟩ (quartonic comma) and [-74 13 23⟩ (sesesix comma), as well as [77 -31 -12⟩ (lafa comma) in the 5-limit; 65625/65536, 420175/419904 and 2460375/2458624 in the 7-limit; 1375/1372, 4000/3993, 19712/19683, 43923/43904, 180224/180075, and 322102/321489 in the 11-limit. It supports fifthplus, although 171edo is better suited for that purpose.

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*	Cents*	Associated ratio*	Temperaments
1	228\557	491.203	3645/2744	Fifthplus

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

Scales

• Laz5
• Laz9

Music

Francium

• "Are You A Youth Medium?" from Questions (2024) – Spotify | Bandcamp | YouTube – sidi in 557edo tuning