# 577edo

 ← 576edo 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

577 equal divisions of the octave (abbreviated 577edo or 577ed2), also called 577-tone equal temperament (577tet) or 577 equal temperament (577et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 577 equal parts of about 2.08 ¢ each. Each step represents a frequency ratio of 21/577, or the 577th root of 2.

## 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

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