571edo: Difference between revisions
Cleanup; +prime error table; +categories |
+infobox; +RTT table and rank-2 temperaments |
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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]], | == 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 | 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]] | ||