577edo
| ← 576edo | 577edo | 578edo → |
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
| 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 (%) | +48 | +25 | +16 | -5 | -9 | -15 | -28 | -47 | -5 | -37 | -10 | |
| 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 |