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Schismatic family: Difference between revisions

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Cmloegcmluin (talk | contribs)
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unchanged interval → unchanged-interval
Line 71: Line 71:
* [[7-odd-limit]]: ~3/2 = {{monzo| 2/3 1/15 0 -1/15 }}
* [[7-odd-limit]]: ~3/2 = {{monzo| 2/3 1/15 0 -1/15 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 1/15 0 -1/15 }}, {{monzo| 5/3 -8/15 0 8/15 }}, {{monzo| 5/3 -14/15 0 14/15 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 1/15 0 -1/15 }}, {{monzo| 5/3 -8/15 0 8/15 }}, {{monzo| 5/3 -14/15 0 14/15 }}]
: [[Eigenmonzo basis]]: 2.7/3
: [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.7/3
* [[9-odd-limit]]: ~3/2 = {{monzo| 9/16 1/8 0 -1/16 }}
* [[9-odd-limit]]: ~3/2 = {{monzo| 9/16 1/8 0 -1/16 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/16 1/8 0 -1/16 }}, {{monzo| 5/2 -1 0 1/2 }}, {{monzo| 25/8 -7/4 0 7/8 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/16 1/8 0 -1/16 }}, {{monzo| 5/2 -1 0 1/2 }}, {{monzo| 25/8 -7/4 0 7/8 }}]
: Eigenmonzo basis: 2.7/3
: Eigenmonzo basis (unchanged-interval basis): 2.7/3


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 100: Line 100:
Minimax tuning:
Minimax tuning:
* 11-odd-limit: ~3/2 = {{monzo| 9/16 1/8 0 -1/16 }}
* 11-odd-limit: ~3/2 = {{monzo| 9/16 1/8 0 -1/16 }}
: Eigenmonzo basis: 2.9/7
: Eigenmonzo basis (unchanged-interval basis): 2.9/7


Tuning ranges:  
Tuning ranges:  
Line 122: Line 122:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~3/2 = {{monzo| 19/34 0 0 -1/34 0 1/34 }}
* 13- and 15-odd-limit: ~3/2 = {{monzo| 19/34 0 0 -1/34 0 1/34 }}
: Eigenmonzo basis: 2.13/7
: Eigenmonzo basis (unchanged-interval basis): 2.13/7


Tuning ranges:  
Tuning ranges:  
Line 225: Line 225:
Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~3/2 = {{monzo| 3/5 1/10 0 0 -1/20 }}
* 11-odd-limit: ~3/2 = {{monzo| 3/5 1/10 0 0 -1/20 }}
: Eigenmonzo basis: 2.11/9
: Eigenmonzo basis (unchanged-interval basis): 2.11/9


Tuning ranges:  
Tuning ranges:  
Line 247: Line 247:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~3/2 = {{monzo| 14/23 2/23 0 0 0 -1/23 }}
* 13- and 15-odd-limit: ~3/2 = {{monzo| 14/23 2/23 0 0 0 -1/23 }}
: Eigenmonzo basis: 2.13/9
: Eigenmonzo basis (unchanged-interval basis): 2.13/9


Tuning ranges:  
Tuning ranges:  
Line 350: Line 350:
Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~3/2 = {{monzo| 19/32 1/16 0 0 -1/32 }}
* 11-odd-limit: ~3/2 = {{monzo| 19/32 1/16 0 0 -1/32 }}
: Eigenmonzo basis: 2.11/9
: Eigenmonzo basis (unchanged-interval basis): 2.11/9


Optimal GPV sequence: {{Val list| 12, 41e, 53, 118d, 171de }}
Optimal GPV sequence: {{Val list| 12, 41e, 53, 118d, 171de }}
Line 367: Line 367:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~3/2 = {{monzo| 19/32 1/16 0 0 -1/32 }}
* 13- and 15-odd-limit: ~3/2 = {{monzo| 19/32 1/16 0 0 -1/32 }}
: Eigenmonzo basis: 2.11/9
: Eigenmonzo basis (unchanged-interval basis): 2.11/9


Optimal GPV sequence: {{Val list| 12f, 41ef, 53, 118d, 171de }}
Optimal GPV sequence: {{Val list| 12f, 41ef, 53, 118d, 171de }}
Line 545: Line 545:
* [[7-odd-limit]]: ~3/2 = {{monzo| 27/47 0 -1/47 1/47 }}
* [[7-odd-limit]]: ~3/2 = {{monzo| 27/47 0 -1/47 1/47 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 74/47 0 -1/47 1/47 }}, {{monzo| 113/47 0 8/47 -8/47 }}, {{monzo| 113/47 0 -39/47 39/47 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 74/47 0 -1/47 1/47 }}, {{monzo| 113/47 0 8/47 -8/47 }}, {{monzo| 113/47 0 -39/47 39/47 }}]
: [[Eigenmonzo basis]]: 2.7/5
: [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.7/5
* [[9-odd-limit]]: ~3/2 = {{monzo| 1/2 1/5 -1/10 }}
* [[9-odd-limit]]: ~3/2 = {{monzo| 1/2 1/5 -1/10 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 1/5 -1/10 0 }}, {{monzo| 3 -8/5 4/5 0 }}, {{monzo| -1/2 39/5 -39/10 0 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 1/5 -1/10 0 }}, {{monzo| 3 -8/5 4/5 0 }}, {{monzo| -1/2 39/5 -39/10 0 }}]
: Eigenmonzo basis: 2.9/5
: Eigenmonzo basis (unchanged-interval basis): 2.9/5


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 572: Line 572:
Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~3/2 = {{monzo| 41/69 0 0 1/69 -1/69 }}
* 11-odd-limit: ~3/2 = {{monzo| 41/69 0 0 1/69 -1/69 }}
: Eigenmonz basis: 2.11/7
: Eigenmonzo basis (unchanged-interval basis): 2.11/7


Optimal GPV sequence: {{Val list| 53, 118, 289e, 407de }}
Optimal GPV sequence: {{Val list| 53, 118, 289e, 407de }}
Line 589: Line 589:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~3/2 = {{monzo| 43/72 0 0 1/72 -1/72 }}
* 13- and 15-odd-limit: ~3/2 = {{monzo| 43/72 0 0 1/72 -1/72 }}
: Eigenmonzo basis: 2.13/7
: Eigenmonzo basis (unchanged-interval basis): 2.13/7


Optimal GPV sequence: {{Val list| 53, 118, 171e }}
Optimal GPV sequence: {{Val list| 53, 118, 171e }}
Line 606: Line 606:
Minimax tuning:  
Minimax tuning:  
* 17-odd-limit: ~3/2 = {{monzo| 18/31 0 0 0 0 -1/93 1/93 }}
* 17-odd-limit: ~3/2 = {{monzo| 18/31 0 0 0 0 -1/93 1/93 }}
: Eigenmonzo basis: 2.17/13
: Eigenmonzo basis (unchanged-interval basis): 2.17/13


Optimal GPV sequence: {{Val list| 53, 118, 171e, 289ef, 460eef }}
Optimal GPV sequence: {{Val list| 53, 118, 171e, 289ef, 460eef }}
Line 664: Line 664:
Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~3/2 = {{monzo| 36/61 0 0 1/122 -1/122 }}
* 11-odd-limit: ~3/2 = {{monzo| 36/61 0 0 1/122 -1/122 }}
: Eigenmonzo basis: 2.11/7
: Eigenmonzo basis (unchanged-interval basis): 2.11/7


Optimal GPV sequence: {{Val list| 53, 171, 224, 1291cde, 1515cde, 1739cddee, 1963cddee, 2187ccddee }}
Optimal GPV sequence: {{Val list| 53, 171, 224, 1291cde, 1515cde, 1739cddee, 1963cddee, 2187ccddee }}
Line 681: Line 681:
Minimax tuning:  
Minimax tuning:  
* 13 and 15-odd-limit: ~3/2 = {{monzo| 36/61 0 0 1/122 -1/122 }}
* 13 and 15-odd-limit: ~3/2 = {{monzo| 36/61 0 0 1/122 -1/122 }}
: Eigenmonzo basis: 2.11/7
: Eigenmonzo basis (unchanged-interval basis): 2.11/7


Optimal GPV sequence: {{Val list| 53, 171, 224 }}
Optimal GPV sequence: {{Val list| 53, 171, 224 }}
Line 698: Line 698:
Minimax tuning:  
Minimax tuning:  
* 17-odd-limit: ~3/2 = {{monzo| 83/143 0 0 0 -1/143 0 1/143 }}
* 17-odd-limit: ~3/2 = {{monzo| 83/143 0 0 0 -1/143 0 1/143 }}
: Eigenmonzo basis: 2.17/11
: Eigenmonzo basis (unchanged-interval basis): 2.17/11


Optimal GPV sequence: {{Val list| 53, 171, 224, 395e, 619eg }}
Optimal GPV sequence: {{Val list| 53, 171, 224, 395e, 619eg }}
Line 717: Line 717:
Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~3/2 = {{monzo| 6/11 0 0 0 1/88 }}
* 11-odd-limit: ~3/2 = {{monzo| 6/11 0 0 0 1/88 }}
: Eigenmonzo basis: 2.11
: Eigenmonzo basis (unchanged-interval basis): 2.11


Optimal GPV sequence: {{Val list| 53e, 118, 289, 407d, 696d }}
Optimal GPV sequence: {{Val list| 53e, 118, 289, 407d, 696d }}
Line 734: Line 734:
Minimax tuning:  
Minimax tuning:  
* 13 and 15-odd-limit: ~3/2 = {{monzo| 71/121 0 0 0 1/121 -1/121 }}
* 13 and 15-odd-limit: ~3/2 = {{monzo| 71/121 0 0 0 1/121 -1/121 }}
: Eigenmonzo basis: 2.13/11
: Eigenmonzo basis (unchanged-interval basis): 2.13/11


Optimal GPV sequence: {{Val list| 53e, 118, 171, 289f, 460ef }}
Optimal GPV sequence: {{Val list| 53e, 118, 171, 289f, 460ef }}
Line 751: Line 751:
Minimax tuning:  
Minimax tuning:  
* 17-odd-limit: ~3/2 = {{monzo| 71/121 0 0 0 1/121 -1/121 }}
* 17-odd-limit: ~3/2 = {{monzo| 71/121 0 0 0 1/121 -1/121 }}
: Eigenmonzo basis: 2.13/11
: Eigenmonzo basis (unchanged-interval basis): 2.13/11


Optimal GPV sequence: {{Val list| 53e, 118, 171, 289f, 460ef }}
Optimal GPV sequence: {{Val list| 53e, 118, 171, 289f, 460ef }}
Line 898: Line 898:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]] eigenmonzos (unchanged intervals): 2, 7/6
* [[7-odd-limit]] eigenmonzos (unchanged-intervals): 2, 7/6
* [[9-odd-limit]] eigenmonzos (unchanged intervals): 2, 9/7
* [[9-odd-limit]] eigenmonzos (unchanged-intervals): 2, 9/7


{{Val list|legend=1| 12, 53d, 65, 77, 166c, 243c }}
{{Val list|legend=1| 12, 53d, 65, 77, 166c, 243c }}
Line 1,023: Line 1,023:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]] eigenmonzos (unchanged intervals): 2, 7/6
* [[7-odd-limit]] eigenmonzos (unchanged-intervals): 2, 7/6
* [[9-odd-limit]] eigenmonzos (unchanged intervals): 2, 9/7
* [[9-odd-limit]] eigenmonzos (unchanged-intervals): 2, 9/7


{{Val list|legend=1| 12, 106d, 118, 130, 248, 378, 508 }}
{{Val list|legend=1| 12, 106d, 118, 130, 248, 378, 508 }}
Line 1,378: Line 1,378:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]] [[eigenmonzo basis]]: 2.5/3
* [[7-odd-limit]] [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.5/3
* [[9-odd-limit]] eigenmonzo basis: 2.9/7
* [[9-odd-limit]] Eigenmonzo basis (unchanged-interval basis): 2.9/7


{{Val list|legend=1| 12, 147d, 159, 171, 867, 1038, 1209, 1380, 1551, 1722 }}
{{Val list|legend=1| 12, 147d, 159, 171, 867, 1038, 1209, 1380, 1551, 1722 }}
Line 1,580: Line 1,580:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]] eigenmonzos (unchanged intervals): 2, 7/6
* [[7-odd-limit]] eigenmonzos (unchanged-intervals): 2, 7/6
* [[9-odd-limit]] eigenmonzos (unchanged intervals): 2, 9/7
* [[9-odd-limit]] eigenmonzos (unchanged-intervals): 2, 9/7


{{Val list|legend=1| 41, 89, 130, 171, 814, 985, 1156, 1327, 1498, 2825bd }}
{{Val list|legend=1| 41, 89, 130, 171, 814, 985, 1156, 1327, 1498, 2825bd }}
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