577edo

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577edo

578edo →

Prime factorization	577 (prime)
Step size	2.07972 ¢
Fifth	338\577 (702.946 ¢)
Semitones (A1:m2)	58:41 (120.6 ¢ : 85.27 ¢)
Dual sharp fifth	338\577 (702.946 ¢)
Dual flat fifth	337\577 (700.867 ¢)
Dual major 2nd	98\577 (203.813 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

577edo is consistent to the 7-odd-limit, but its harmonic 3 is about halfway its steps. In the 2.9.5.7.11 subgroup interpretation, it tempers out 26873856/26796875, 184528125/184473632 and 1640558367/1638400000 in the 7-limit; 5632/5625, 102487/102400, 151263/151250, and 472392/471625 in the 11-limit.

Odd harmonics

Approximation of odd harmonics in 577edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.991	+0.515	+0.325	-0.097	-0.191	-0.320	-0.574	-0.969	-0.113	-0.764	-0.198
	Relative (%)	+47.7	+24.7	+15.6	-4.7	-9.2	-15.4	-27.6	-46.6	-5.4	-36.7	-9.5
Steps (reduced)		915 (338)	1340 (186)	1620 (466)	1829 (98)	1996 (265)	2135 (404)	2254 (523)	2358 (50)	2451 (143)	2534 (226)	2610 (302)

Subsets and supersets

577edo is the 106th prime edo. 1154edo, which doubles it, gives a good correction to the harmonic 3, but it does poorly in the harmonics 5 and 7. 2308edo, which quadruples it, also gives a good correction to the harmonic 3 and is consistent to the 11-odd-limit.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[-1829 577⟩	[⟨577 1829]]	+0.0153	0.0153	0.74
2.9.5	[-7 11 -12⟩, [125 -5 -47⟩	[⟨577 1829 1340]]	-0.0637	0.1124	5.40
2.9.5.7	26873856/26796875, 184528125/184473632, 1640558367/1638400000	[⟨577 1829 1340 1620]]	-0.0767	0.0999	4.80
2.9.5.7.11	5632/5625, 102487/102400, 151263/151250, 472392/471625	[⟨577 1829 1340 1620 1996]]	-0.0503	0.1038	4.99
2.9.5.7.11.13	1001/1000, 10648/10647, 10985/10976, 75712/75625, 472392/471625	[⟨577 1829 1340 1620 1996 2135]]	-0.0275	0.1076	5.17

Music

Francium

• "iloveinstallations" from albumwithoutspaces (2024) – Bandcamp | YouTube