571edo: Difference between revisions

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{{Infobox ET
| Prime factorization = 571 (prime)
| Step size = 2.10158¢
| Fifth = 334\571 (701.93¢)
| Semitones = 54:43 (113.49¢ : 90.37¢)
| Consistency = 9
}}
{{EDO intro|571}}
{{EDO intro|571}}


571edo [[tempering out|tempers out]] the [[parakleisma]], 1224440064/1220703125 and the [[counterschisma]], {{monzo| -69 45 -1 }} in the [[5-limit]], as well as the lafa comma, {{monzo| 77 -31 -12 }}; [[2401/2400]], 14348907/14336000, and 29360128/29296875 in the [[7-limit]]; [[3025/3024]], 5632/5625, [[41503/41472]], and 17537553/17500000 in the [[11-limit]]; [[1001/1000]], [[1716/1715]], [[4096/4095]], 17303/17280, and 107811/107653 in the [[13-limit]], supporting the 13-limit [[quasiorwell]] temperament; [[1089/1088]], [[1701/1700]], 2431/2430, [[2601/2600]], [[5832/5831]] and 7744/7735 in the [[17-limit]]. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log<sub>2</sub>7, after [[109edo|109]] and before [[2393edo|2393]].
== Theory ==
571edo [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}, and the [[counterschisma]], {{monzo| -69 45 -1 }}, in the [[5-limit]], as well as the lafa comma, {{monzo| 77 -31 -12 }}; [[2401/2400]], 14348907/14336000, and 29360128/29296875 in the [[7-limit]]; [[3025/3024]], 5632/5625, [[41503/41472]], and 17537553/17500000 in the [[11-limit]]; [[1001/1000]], [[1716/1715]], [[4096/4095]], 17303/17280, and 107811/107653 in the [[13-limit]], supporting the 13-limit [[quasiorwell]] temperament; [[1089/1088]], [[1701/1700]], 2431/2430, [[2601/2600]], [[5832/5831]] and 7744/7735 in the [[17-limit]]. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log<sub>2</sub>7, after [[109edo|109]] and before [[2393edo|2393]].


571edo is the 105th [[prime EDO]].
571edo is the 105th [[prime edo]].


=== Prime harmonics ===
{{Harmonics in equal|571|columns=11}}
{{Harmonics in equal|571|columns=11}}
== Regular temperament properties ==
{| 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]] (%)
|-
| 2.3
| {{monzo| -905 571 }}
| [{{val| 571 905 }}]
| +0.0090
| 0.0090
| 0.43
|-
| 2.3.5
| {{monzo| 8 14 -13 }}, {{monzo| -69 45 -1 }}
| [{{val| 571 905 1326 }}]
| -0.0480
| 0.0810
| 3.85
|-
| 2.3.5.7
| 2401/2400, 14348907/14336000, 29360128/29296875
| [{{val| 571 905 1326 1603 }}]
| -0.0361
| 0.0731
| 3.48
|-
| 2.3.5.7.11
| 2401/2400, 3025/3024, 5632/5625, 14348907/14336000
| [{{val| 559 886 1298 1569 1934 }}]
| +0.0119
| 0.1161
| 5.53
|-
| 2.3.5.7.11.13
| 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653
| [{{val| 559 886 1298 1569 1934 2113 }}]
| +0.0053
| 0.1070
| 5.09
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per Octave
! Generator<br>(Reduced)
! Cents<br>(Reduced)
! Associated<br>Ratio
! Temperaments
|-
| 1
| 123\571
| 258.49
| {{monzo| -32 13 5 }}
| [[Lafa]]
|-
| 1
| 129\571
| 271.10
| 90/77
| [[Quasiorwell]]
|-
| 1
| 147\571
| 315.24
| 6/5
| [[Parakleismic]] (5-limit)
|-
| 1
| 237\571
| 498.07
| 4/3
| [[Counterschismic]]
|-
| 1
| 247\571
| 519.09
| 875/648
| [[Maviloid]]
|}


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Prime EDO]]
[[Category:Prime EDO]]
[[Category:Quasiorwell]]
[[Category:Quasiorwell]]

Revision as of 00:04, 30 August 2022

← 570edo 571edo 572edo →
Prime factorization 571 (prime)
Step size 2.10158 ¢ 
Fifth 334\571 (701.926 ¢)
Semitones (A1:m2) 54:43 (113.5 ¢ : 90.37 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

Theory

571edo tempers out the parakleisma, [8 14 -13⟩, and the counterschisma, [-69 45 -1⟩, in the 5-limit, as well as the lafa comma, [77 -31 -12⟩; 2401/2400, 14348907/14336000, and 29360128/29296875 in the 7-limit; 3025/3024, 5632/5625, 41503/41472, and 17537553/17500000 in the 11-limit; 1001/1000, 1716/1715, 4096/4095, 17303/17280, and 107811/107653 in the 13-limit, supporting the 13-limit quasiorwell temperament; 1089/1088, 1701/1700, 2431/2430, 2601/2600, 5832/5831 and 7744/7735 in the 17-limit. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log27, after 109 and before 2393.

571edo is the 105th prime edo.

Prime harmonics

Approximation of prime harmonics in 571edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.029 +0.376 +0.001 -0.705 +0.103 +0.123 +0.911 +0.097 +0.195 +0.323
Relative (%) +0.0 -1.4 +17.9 +0.0 -33.5 +4.9 +5.9 +43.3 +4.6 +9.3 +15.4
Steps
(reduced) 		571
(0) 		905
(334) 		1326
(184) 		1603
(461) 		1975
(262) 		2113
(400) 		2334
(50) 		2426
(142) 		2583
(299) 		2774
(490) 		2829
(545)

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [-905 571⟩ [⟨571 905]] +0.0090 0.0090 0.43
2.3.5 [8 14 -13⟩, [-69 45 -1⟩ [⟨571 905 1326]] -0.0480 0.0810 3.85
2.3.5.7 2401/2400, 14348907/14336000, 29360128/29296875 [⟨571 905 1326 1603]] -0.0361 0.0731 3.48
2.3.5.7.11 2401/2400, 3025/3024, 5632/5625, 14348907/14336000 [⟨559 886 1298 1569 1934]] +0.0119 0.1161 5.53
2.3.5.7.11.13 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653 [⟨559 886 1298 1569 1934 2113]] +0.0053 0.1070 5.09

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per Octave 		Generator
(Reduced) 		Cents
(Reduced) 		Associated
Ratio 		Temperaments
1 123\571 258.49 [-32 13 5⟩ Lafa
1 129\571 271.10 90/77 Quasiorwell
1 147\571 315.24 6/5 Parakleismic (5-limit)
1 237\571 498.07 4/3 Counterschismic
1 247\571 519.09 875/648 Maviloid
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