571edo: Difference between revisions
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Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
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== Theory == | == Theory == | ||
The equal temperament [[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]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|571|columns=11}} | {{Harmonics in equal|571|columns=11}} | ||
=== Subsets and supersets === | |||
571edo is the 105th [[prime edo]]. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 23: | Line 24: | ||
| 2.3 | | 2.3 | ||
| {{monzo| -905 571 }} | | {{monzo| -905 571 }} | ||
| | | {{mapping| 571 905 }} | ||
| +0.0090 | | +0.0090 | ||
| 0.0090 | | 0.0090 | ||
| Line 30: | Line 31: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 8 14 -13 }}, {{monzo| -69 45 -1 }} | | {{monzo| 8 14 -13 }}, {{monzo| -69 45 -1 }} | ||
| | | {{mapping| 571 905 1326 }} | ||
| -0.0480 | | -0.0480 | ||
| 0.0810 | | 0.0810 | ||
| Line 37: | Line 38: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 14348907/14336000, 29360128/29296875 | | 2401/2400, 14348907/14336000, 29360128/29296875 | ||
| | | {{mapping| 571 905 1326 1603 }} | ||
| -0.0361 | | -0.0361 | ||
| 0.0731 | | 0.0731 | ||
| Line 44: | Line 45: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 3025/3024, 5632/5625, 14348907/14336000 | | 2401/2400, 3025/3024, 5632/5625, 14348907/14336000 | ||
| | | {{mapping| 571 905 1326 1603 1975 }} | ||
| +0.0119 | | +0.0119 | ||
| 0.1161 | | 0.1161 | ||
| Line 51: | Line 52: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653 | | 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653 | ||
| | | {{mapping| 571 905 1326 1603 1975 2113 }} | ||
| +0.0053 | | +0.0053 | ||
| 0.1070 | | 0.1070 | ||
| Line 58: | Line 59: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 1001/1000, 1089/1088, 1716/1715, 2601/2600, 3025/3024, 4096/4095 | | 1001/1000, 1089/1088, 1716/1715, 2601/2600, 3025/3024, 4096/4095 | ||
| | | {{mapping| 571 905 1326 1603 1975 2113 2334 }} | ||
| +0.0002 | | +0.0002 | ||
| 0.0999 | | 0.0999 | ||
| Line 67: | Line 68: | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 103: | Line 104: | ||
| [[Maviloid]] | | [[Maviloid]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
[[Category:Quasiorwell]] | [[Category:Quasiorwell]] | ||