241edo: Difference between revisions
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{{Infobox ET | {{Infobox ET}} | ||
{{ED intro}} | |||
}} | |||
{{ | |||
== Theory == | == Theory == | ||
241edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. As an equal temperament, it [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]], [[19683/19600]] and [[3136/3125]] in the [[7-limit]], [[540/539]], 43923/43904, [[65536/65219]], and [[151263/151250]] in the [[11-limit]], and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[subpental]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|241}} | {{Harmonics in equal|241}} | ||
=== Subsets and supersets === | |||
241edo is the 53rd [[prime edo]]. | |||
== 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]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 29: | Line 25: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 382 -241 }} | | {{monzo| 382 -241 }} | ||
| | | {{mapping| 241 382 }} | ||
| | | −0.038 | ||
| 0.038 | | 0.038 | ||
| 0.76 | | 0.76 | ||
| Line 36: | Line 32: | ||
| 2.3.5 | | 2.3.5 | ||
| 78732/78125, {{monzo| 56 -28 -5 }} | | 78732/78125, {{monzo| 56 -28 -5 }} | ||
| | | {{mapping| 241 382 560 }} | ||
| | | −0.322 | ||
| 0.403 | | 0.403 | ||
| 8.10 | | 8.10 | ||
| Line 43: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 3136/3125, 19683/19600, 829940/823543 | | 3136/3125, 19683/19600, 829940/823543 | ||
| | | {{mapping| 241 382 560 677 }} | ||
| | | −0.431 | ||
| 0.397 | | 0.397 | ||
| 7.97 | | 7.97 | ||
| Line 50: | Line 46: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 540/539, 3136/3125, 8019/8000, 15488/15435 | | 540/539, 3136/3125, 8019/8000, 15488/15435 | ||
| | | {{mapping| 241 382 560 677 834 }} | ||
| | | −0.425 | ||
| 0.355 | | 0.355 | ||
| 7.14 | | 7.14 | ||
| Line 57: | Line 53: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 351/350, 540/539, 676/675, 3136/3125, 10648/10647 | | 351/350, 540/539, 676/675, 3136/3125, 10648/10647 | ||
| | | {{mapping| 241 382 560 677 834 892 }} | ||
| | | −0.397 | ||
| 0.330 | | 0.330 | ||
| 6.63 | | 6.63 | ||
| Line 65: | Line 61: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per | |- | ||
! Generator | ! Periods<br />per 8ve | ||
! Cents | ! Generator* | ||
! Associated<br>ratio | ! Cents* | ||
! Associated<br />ratio* | |||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 102: | Line 99: | ||
| [[Gary]] | | [[Gary]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
[[Category:Subpental]] | [[Category:Subpental]] | ||