241edo: Difference between revisions
m Infobox ET now computes most parameters automatically |
Expand on theory and misc. cleanup |
||
| Line 3: | Line 3: | ||
== 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. The equal temperament [[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|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal 8ve <br> | ! rowspan="2" | Optimal 8ve <br>Stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning Error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 23: | Line 24: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 382 -241 }} | | {{monzo| 382 -241 }} | ||
| | | {{mapping| 241 382 }} | ||
| -0.038 | | -0.038 | ||
| 0.038 | | 0.038 | ||
| Line 30: | Line 31: | ||
| 2.3.5 | | 2.3.5 | ||
| 78732/78125, {{monzo| 56 -28 -5 }} | | 78732/78125, {{monzo| 56 -28 -5 }} | ||
| | | {{mapping| 241 382 560 }} | ||
| -0.322 | | -0.322 | ||
| 0.403 | | 0.403 | ||
| Line 37: | Line 38: | ||
| 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 | | -0.431 | ||
| 0.397 | | 0.397 | ||
| Line 44: | Line 45: | ||
| 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 | | -0.425 | ||
| 0.355 | | 0.355 | ||
| Line 51: | Line 52: | ||
| 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 | | -0.397 | ||
| 0.330 | | 0.330 | ||
| Line 60: | Line 61: | ||
{| 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> | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 96: | Line 97: | ||
| [[Gary]] | | [[Gary]] | ||
|} | |} | ||
<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:Subpental]] | [[Category:Subpental]] | ||