961edo: Difference between revisions
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{{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 30: | Line 30: | ||
| {{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 37: | 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 44: | 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 | ||
| Line 65: | Line 65: | ||
| [[Pontiac]] | | [[Pontiac]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||