Starling temperaments: Difference between revisions
m →13-limit: Fix a typo: Replace a period with a comma. |
Cmloegcmluin (talk | contribs) unchanged interval → unchanged-interval |
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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| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 9/10 9/10 0 0 }}, {{monzo| 17/10 7/10 0 0 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 9/10 9/10 0 0 }}, {{monzo| 17/10 7/10 0 0 }}] | ||
: [[Eigenmonzo]]s (unchanged intervals): 2, 3 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 3 | ||
{{Val list|legend=1| 27, 31, 58, 89 }} | {{Val list|legend=1| 27, 31, 58, 89 }} | ||
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* [[7-odd-limit]]: ~21/20 = {{monzo| 1/6 1/12 0 -1/12 }} | * [[7-odd-limit]]: ~21/20 = {{monzo| 1/6 1/12 0 -1/12 }} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 17/6 5/12 0 -5/12 }}, {{monzo| 5/2 -1/4 0 1/4 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 17/6 5/12 0 -5/12 }}, {{monzo| 5/2 -1/4 0 1/4 }}] | ||
: [[Eigenmonzo]]s (unchanged intervals): 2, 7/6 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 7/6 | ||
* [[9-odd-limit]]: ~21/20 = {{monzo| 1/21 2/21 0 -1/21}} | * [[9-odd-limit]]: ~21/20 = {{monzo| 1/21 2/21 0 -1/21}} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 47/21 10/21 0 -5/21 }}, {{monzo| 20/7 -2/7 0 1/7 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 47/21 10/21 0 -5/21 }}, {{monzo| 20/7 -2/7 0 1/7 }}] | ||
: [[Eigenmonzo]]s (unchanged intervals): 2, 9/7 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 9/7 | ||
[[Algebraic generator]]: smaller root of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents. | [[Algebraic generator]]: smaller root of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents. | ||
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* [[11-odd-limit]]: ~21/20 = {{monzo| 0 0 0 -1/10 1/10 }} | * [[11-odd-limit]]: ~21/20 = {{monzo| 0 0 0 -1/10 1/10 }} | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}] | ||
: Eigenmonzos (unchanged intervals): 2, 11/7 | : Eigenmonzos (unchanged-intervals): 2, 11/7 | ||
Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5. | Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5. | ||
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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| 1 0 0 0 }}, {{monzo| -5/13 0 11/13 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| -3/13 0 17/13 0 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| -5/13 0 11/13 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| -3/13 0 17/13 0 }}] | ||
: [[Eigenmonzo]]s (unchanged intervals): 2, 5 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 5 | ||
* [[9-odd-limit]]: ~49/45 = {{monzo| 3/11 -1/11 }} | * [[9-odd-limit]]: ~49/45 = {{monzo| 3/11 -1/11 }} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 5/11 13/11 0 0 }}, {{monzo| 4/11 17/11 0 0 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 5/11 13/11 0 0 }}, {{monzo| 4/11 17/11 0 0 }}] | ||
: [[Eigenmonzo]]s (unchanged intervals): 2, 3 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 3 | ||
{{Val list|legend=1| 8d, 23d, 31, 101, 132c, 163c }} | {{Val list|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 }}] | ||
: Eigenmonzos (unchanged intervals): 2, 11/9 | : Eigenmonzos (unchanged-intervals): 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. | ||