Starling temperaments: Difference between revisions
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m Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) " |
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* 7- and [[9-odd-limit]]: ~6/5 = {{monzo| 1/10 1/10 0 0}} | * 7- and [[9-odd-limit]]: ~6/5 = {{monzo| 1/10 1/10 0 0}} | ||
: {{monzo list| 1 0 0 0 | 0 1 0 0 | 9/10 9/10 0 0 | 17/10 7/10 0 0 }} | : {{monzo list| 1 0 0 0 | 0 1 0 0 | 9/10 9/10 0 0 | 17/10 7/10 0 0 }} | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3 | ||
{{Optimal ET sequence|legend=1| 27, 31, 58, 89 }} | {{Optimal ET sequence|legend=1| 27, 31, 58, 89 }} | ||
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* [[7-odd-limit]]: ~49/45 = {{monzo| 4/13 0 -1/13 }} | * [[7-odd-limit]]: ~49/45 = {{monzo| 4/13 0 -1/13 }} | ||
: {{monzo list| 1 0 0 0 | -5/13 0 11/13 0 | 0 0 1 0 | -3/13 0 17/13 0 }} | : {{monzo list| 1 0 0 0 | -5/13 0 11/13 0 | 0 0 1 0 | -3/13 0 17/13 0 }} | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5 | ||
* [[9-odd-limit]]: ~49/45 = {{monzo| 3/11 -1/11 }} | * [[9-odd-limit]]: ~49/45 = {{monzo| 3/11 -1/11 }} | ||
: {{monzo list| 1 0 0 0 | 0 1 0 0 | 5/11 13/11 0 0 | 4/11 17/11 0 0 }} | : {{monzo list| 1 0 0 0 | 0 1 0 0 | 5/11 13/11 0 0 | 4/11 17/11 0 0 }} | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3 | ||
{{Optimal ET sequence|legend=1| 8d, 23d, 31, 101, 132c, 163c }} | {{Optimal ET sequence|legend=1| 8d, 23d, 31, 101, 132c, 163c }} | ||
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* [[11-odd-limit]]: ~11/10 = {{monzo| 1/10 -1/5 0 0 1/10 }} | * [[11-odd-limit]]: ~11/10 = {{monzo| 1/10 -1/5 0 0 1/10 }} | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 19/10 11/5 0 0 -11/10 }}, {{monzo| 27/10 13/5 0 0 -13/10 }}, {{monzo| 33/10 17/5 0 0 -17/10 }}, {{monzo| 19/5 12/5 0 0 -6/5 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 19/10 11/5 0 0 -11/10 }}, {{monzo| 27/10 13/5 0 0 -13/10 }}, {{monzo| 33/10 17/5 0 0 -17/10 }}, {{monzo| 19/5 12/5 0 0 -6/5 }}] | ||
: | : unchanged-interval (eigenmonzo) basis: 2.11/9 | ||
Algebraic generator: positive root of 15''x''<sup>2</sup> - 10''x'' - 7, or (5 + sqrt (130))/15, at 154.6652 cents. The recurrence converges very quickly. | Algebraic generator: positive root of 15''x''<sup>2</sup> - 10''x'' - 7, or (5 + sqrt (130))/15, at 154.6652 cents. The recurrence converges very quickly. | ||