961edo: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
961edo has a reasonable 7-limit interpretation. The equal temperament [[Tempering out|tempers out]] the [[schisma]] in the 5-limit; [[4375/4374]], [[65625/65536]], and [[14348907/14336000]] in the 7-limit, supporting [[pontiac]], the 395 & 566 temperament. | 961edo has a reasonable 7-limit interpretation. The equal temperament [[Tempering out|tempers out]] the [[schisma]] in the 5-limit; [[4375/4374]], [[65625/65536]], and [[14348907/14336000]] in the 7-limit, supporting [[pontiac]], the {{nowrap|395 & 566}} temperament. | ||
In the 11-limit, the 961e [[val]] {{val| 961 1523 2231 '''2698''' '''3324''' }} scores the best, which tempers out 102487/102400 and 234375/234256. It prompts us to consider the 961de val {{val| 961 1523 2231 '''2697''' '''3324''' }}, which tempers out [[3025/3024]] and 184877/184320. The [[patent val]] {{val| 961 1523 2231 '''2698''' '''3325''' }} tempers out [[4000/3993]] and 46656/46585. | In the 11-limit, the 961e [[val]] {{val| 961 1523 2231 '''2698''' '''3324''' }} scores the best, which tempers out 102487/102400 and 234375/234256. It prompts us to consider the 961de val {{val| 961 1523 2231 '''2697''' '''3324''' }}, which tempers out [[3025/3024]] and 184877/184320. The [[patent val]] {{val| 961 1523 2231 '''2698''' '''3325''' }} tempers out [[4000/3993]] and 46656/46585. | ||
| Line 16: | Line 16: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|-1523 961}} | | {{monzo|-1523 961}} | ||
| {{mapping| 961 1523 }} | | {{mapping| 961 1523 }} | ||
| 0.0587 | | +0.0587 | ||
| 0.0587 | | 0.0587 | ||
| 4.70 | | 4.70 | ||
| Line 28: | Line 37: | ||
| 32805/32768, {{monzo| -22 -137 103 }} | | 32805/32768, {{monzo| -22 -137 103 }} | ||
| {{mapping| 961 1523 2231 }} | | {{mapping| 961 1523 2231 }} | ||
| 0.1060 | | +0.1060 | ||
| 0.0823 | | 0.0823 | ||
| 6.59 | | 6.59 | ||
| Line 35: | Line 44: | ||
| 4375/4374, 32805/32768, {{monzo| 15 9 14 -22 }} | | 4375/4374, 32805/32768, {{monzo| 15 9 14 -22 }} | ||
| {{mapping| 961 1523 2231 2698 }} | | {{mapping| 961 1523 2231 2698 }} | ||
| 0.0648 | | +0.0648 | ||
| 0.1008 | | 0.1008 | ||
| 8.01 | | 8.01 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 48: | Line 64: | ||
| 4/3 | | 4/3 | ||
| [[Pontiac]] | | [[Pontiac]] | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Scales == | == Scales == | ||