577edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|577}} == Theory == 577et is consistent to the 7-odd-limit and its harmonic 3 is about halfway its steps. Using the patent val, it t..."
 
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== 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" | [[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
! colspan="2" | Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.9
| 2.9
|{{monzo|-1829 577}}
| {{monzo| -1829 577 }}
|{{mapping|577 1829}}
| {{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
|}
|}

Revision as of 11:11, 7 March 2024

← 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

Template:EDO intro

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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