Hemimean clan: Difference between revisions
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== Hemithirds == | == Hemithirds == | ||
{{Main| Hemithirds }} | {{Main| Hemithirds }} | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]]: ~28/25 = {{monzo| 1/10 -1/20 0 1/20 }} | * [[7-odd-limit]]: ~28/25 = {{monzo| 1/10 -1/20 0 1/20 }} | ||
: {{monzo list| 1 0 0 0 | 5/2 3/4 0 -3/4 | 11/5 -1/10 0 1/10 | 5/2 -1/4 0 1/4 }} | |||
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3 | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3 | ||
* [[9-odd-limit]]: ~28/25 = {{monzo| 6/ | * [[9-odd-limit]]: ~28/25 = {{monzo| 6/35 -2/35 0 1/35 }} | ||
: {{monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 82/35 -4/35 0 2/35 | 20/7 -2/7 0 1/7 }} | |||
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7 | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7 | ||
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Minimax tuning: | Minimax tuning: | ||
* 11-odd-limit: ~28/25 = {{monzo| 5/27 0 0 1/27 -1/27 }} | * 11-odd-limit: ~28/25 = {{monzo| 5/27 0 0 1/27 -1/27 }} | ||
: | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 0 0 -5/9 5/9 }}, {{monzo| 64/27 0 0 2/27 -2/27 }}, {{monzo| 79/27 0 0 5/27 -5/27 }}, {{monzo| 79/27 0 0 -22/27 22/27 }}] | ||
: Eigenmonzos (unchanged-intervals): 2, 11/7 | |||
{{Optimal ET sequence|legend=1| 25e, 31, 87, 118 }} | {{Optimal ET sequence|legend=1| 25e, 31, 87, 118 }} | ||