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577edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|577}}
{{ED intro}}


== Theory ==
== Theory ==
577et is consistent to the [[7-odd-limit]] and its [[harmonic]] [[3/1|3]] is about halfway its steps. Using the patent val, it tempers out 26873856/26796875, 184528125/184473632 and [[1640558367/1638400000]] in the 7-limit; [[5632/5625]], 151263/151250, 472392/471625 and 102487/102400 in the 11-limit.
577edo is [[consistent]] to the [[7-odd-limit]], but its [[harmonic]] [[3/1|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 ===
=== Odd harmonics ===
{{Harmonics in equal|577}}
{{Harmonics in equal|577}}


===Subsets and supersets===
=== 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 its consistent to the [[11-odd-limit]].
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 ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.9
! rowspan="2" | [[Subgroup]]
|{{monzo|-1829 577}}
! rowspan="2" | [[Comma list]]
|{{mapping|577 1829}}
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.9
| {{monzo| -1829 577 }}
| {{mapping| 577 1829 }}
| +0.0153
| +0.0153
| 0.0153
| 0.0153
| 0.74
| 0.74
|-
|-
|2.9.5
| 2.9.5
|{{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
| −0.0637
| 0.1124
| 0.1124
| 5.40
| 5.40
|-
|-
|2.9.5.7
| 2.9.5.7
|26873856/26796875, 184528125/184473632, 1640558367/1638400000
| 26873856/26796875, 184528125/184473632, 1640558367/1638400000
|{{mapping|577 1829 1340 1620}}
| {{mapping| 577 1829 1340 1620 }}
| -0.0767
| −0.0767
| 0.0999
| 0.0999
| 4.80
| 4.80
|-
|-
|2.9.5.7.11
| 2.9.5.7.11
|5632/5625, 151263/151250, 472392/471625, 102487/102400
| 5632/5625, 102487/102400, 151263/151250, 472392/471625
|{{mapping|577 1829 1340 1620 1996}}
| {{mapping| 577 1829 1340 1620 1996 }}
| -0.0503
| −0.0503
| 0.1038
| 0.1038
| 4.99
| 4.99
|-
|-
|2.9.5.7.11.13
| 2.9.5.7.11.13
|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
| −0.0275
| 0.1076
| 0.1076
| 5.17
| 5.17
|}
|}
== Music ==
; [[Francium]]
* "iloveinstallations" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/0vmk6yMSwTdBI53cx8XsVM Spotify] | [https://francium223.bandcamp.com/track/iloveinstallations Bandcamp] | [https://www.youtube.com/watch?v=Buv51YyfYdo YouTube]
* "Gore Pile" from ''You Are A...'' (2024) – [https://open.spotify.com/track/0P0WNf7bAm0WHgDlGlGgY5 Spotify] | [https://francium223.bandcamp.com/track/gore-pile Bandcamp] | [https://www.youtube.com/watch?v=DLJdsP5AvdA YouTube]
* "QUACK" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/2JVr8aUTYoM4pqSDZ2v8Jc Spotify] | [https://francium223.bandcamp.com/track/quack Bandcamp] | [https://www.youtube.com/watch?v=jnDMYcyEFmk YouTube]
* "Rolling My Eye Ball" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/4M9rZmFwo7Wh7E2FUWcxR3 Spotify] | [https://francium223.bandcamp.com/track/rolling-my-eye-ball Bandcamp] | [https://www.youtube.com/watch?v=j6LEETAtTos YouTube]
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