577edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
| Line 32: | Line 33: | ||
| {{monzo| -7 11 -12 }}, {{monzo| 125 -5 -47 }} | | {{monzo| -7 11 -12 }}, {{monzo| 125 -5 -47 }} | ||
| {{mapping| 577 1829 1340 }} | | {{mapping| 577 1829 1340 }} | ||
| | | −0.0637 | ||
| 0.1124 | | 0.1124 | ||
| 5.40 | | 5.40 | ||
| Line 39: | Line 40: | ||
| 26873856/26796875, 184528125/184473632, 1640558367/1638400000 | | 26873856/26796875, 184528125/184473632, 1640558367/1638400000 | ||
| {{mapping| 577 1829 1340 1620 }} | | {{mapping| 577 1829 1340 1620 }} | ||
| | | −0.0767 | ||
| 0.0999 | | 0.0999 | ||
| 4.80 | | 4.80 | ||
| Line 46: | Line 47: | ||
| 5632/5625, 102487/102400, 151263/151250, 472392/471625 | | 5632/5625, 102487/102400, 151263/151250, 472392/471625 | ||
| {{mapping| 577 1829 1340 1620 1996 }} | | {{mapping| 577 1829 1340 1620 1996 }} | ||
| | | −0.0503 | ||
| 0.1038 | | 0.1038 | ||
| 4.99 | | 4.99 | ||
| Line 53: | Line 54: | ||
| 1001/1000, 10648/10647, 10985/10976, 75712/75625, 472392/471625 | | 1001/1000, 10648/10647, 10985/10976, 75712/75625, 472392/471625 | ||
| {{mapping| 577 1829 1340 1620 1996 2135 }} | | {{mapping| 577 1829 1340 1620 1996 2135 }} | ||
| | | −0.0275 | ||
| 0.1076 | | 0.1076 | ||
| 5.17 | | 5.17 | ||
Latest revision as of 12:43, 21 February 2025
| ← 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 (%) | +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
- "iloveinstallations" from albumwithoutspaces (2024) – Spotify | Bandcamp | YouTube
- "Gore Pile" from You Are A... (2024) – Spotify | Bandcamp | YouTube
- "QUACK" from CAPSLOCK (2024) – Spotify | Bandcamp | YouTube
- "Rolling My Eye Ball" from Abbreviations Gone Wrong (2024) – Spotify | Bandcamp | YouTube