Schismatic family: Difference between revisions

Lériendil (talk | contribs)
m Text replacement - "Eigenmonzo (unchanged-interval)" to "Unchanged-interval (eigenmonzo)"
Lériendil (talk | contribs)
m Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) "
Line 74: Line 74:
* [[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 list| 1 0 0 0 | 5/3 1/15 0 -1/15 | 5/3 -8/15 0 8/15 | 5/3 -14/15 0 14/15 }}
: {{monzo list| 1 0 0 0 | 5/3 1/15 0 -1/15 | 5/3 -8/15 0 8/15 | 5/3 -14/15 0 14/15 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) 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 list| 1 0 0 0 | 25/16 1/8 0 -1/16 | 5/2 -1 0 1/2 | 25/8 -7/4 0 7/8 }}
: {{monzo list| 1 0 0 0 | 25/16 1/8 0 -1/16 | 5/2 -1 0 1/2 | 25/8 -7/4 0 7/8 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7


[[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 (unchanged-interval) basis: 2.9/7
: unchanged-interval (eigenmonzo) basis: 2.9/7


Tuning ranges:  
Tuning ranges:  
Line 121: Line 121:
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 (unchanged-interval) basis: 2.13/7
: unchanged-interval (eigenmonzo) basis: 2.13/7


Tuning ranges:  
Tuning ranges:  
Line 240: Line 240:
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 (unchanged-interval) basis: 2.11/9
: unchanged-interval (eigenmonzo) basis: 2.11/9


Tuning ranges:  
Tuning ranges:  
Line 261: Line 261:
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 (unchanged-interval) basis: 2.13/9
: unchanged-interval (eigenmonzo) basis: 2.13/9


Tuning ranges:  
Tuning ranges:  
Line 361: Line 361:
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 (unchanged-interval) basis: 2.11/9
: unchanged-interval (eigenmonzo) basis: 2.11/9


{{Optimal ET sequence|legend=1| 12, 41e, 53, 118d, 171de }}
{{Optimal ET sequence|legend=1| 12, 41e, 53, 118d, 171de }}
Line 378: Line 378:
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 (unchanged-interval) basis: 2.11/9
: unchanged-interval (eigenmonzo) basis: 2.11/9


{{Optimal ET sequence|legend=1| 12f, 41ef, 53, 118d, 171de }}
{{Optimal ET sequence|legend=1| 12f, 41ef, 53, 118d, 171de }}
Line 517: Line 517:
* [[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|eigenmonzo (unchanged-interval) basis]]: 2.7/5
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) 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|eigenmonzo (unchanged-interval) basis]]: 2.9/5
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 544: Line 544:
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 }}
: eigenmonzo (unchanged-interval) basis: 2.11/7
: unchanged-interval (eigenmonzo) basis: 2.11/7


{{Optimal ET sequence|legend=1| 53, 118, 289e, 407de }}
{{Optimal ET sequence|legend=1| 53, 118, 289e, 407de }}
Line 561: Line 561:
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 (unchanged-interval) basis: 2.13/7
: unchanged-interval (eigenmonzo) basis: 2.13/7


{{Optimal ET sequence|legend=1| 53, 118, 171e }}
{{Optimal ET sequence|legend=1| 53, 118, 171e }}
Line 578: Line 578:
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 (unchanged-interval) basis: 2.17/13
: unchanged-interval (eigenmonzo) basis: 2.17/13


{{Optimal ET sequence|legend=1| 53, 118, 171e, 289ef, 460eef }}
{{Optimal ET sequence|legend=1| 53, 118, 171e, 289ef, 460eef }}
Line 636: Line 636:
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 (unchanged-interval) basis: 2.11/7
: unchanged-interval (eigenmonzo) basis: 2.11/7


{{Optimal ET sequence|legend=1| 53, 171, 224, 1291cde, 1515cde, 1739cddee, 1963cddee, 2187ccddee }}
{{Optimal ET sequence|legend=1| 53, 171, 224, 1291cde, 1515cde, 1739cddee, 1963cddee, 2187ccddee }}
Line 689: Line 689:
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 (unchanged-interval) basis: 2.11
: unchanged-interval (eigenmonzo) basis: 2.11


{{Optimal ET sequence|legend=1| 53e, 118, 289, 407d, 696d }}
{{Optimal ET sequence|legend=1| 53e, 118, 289, 407d, 696d }}
Line 706: Line 706:
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 (unchanged-interval) basis: 2.13/11
: unchanged-interval (eigenmonzo) basis: 2.13/11


{{Optimal ET sequence|legend=1| 53e, 118, 171, 289f, 460ef }}
{{Optimal ET sequence|legend=1| 53e, 118, 171, 289f, 460ef }}
Line 868: Line 868:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]] eigenmonzo (unchanged-interval) basis: 2.7/3
* [[7-odd-limit]] unchanged-interval (eigenmonzo) basis: 2.7/3
* [[9-odd-limit]] eigenmonzo (unchanged-interval) basis: 2.9/7
* [[9-odd-limit]] unchanged-interval (eigenmonzo) basis: 2.9/7


{{Optimal ET sequence|legend=1| 12, 53d, 65, 77, 166c, 243c }}
{{Optimal ET sequence|legend=1| 12, 53d, 65, 77, 166c, 243c }}
Line 991: Line 991:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]] eigenmonzo (unchanged-interval) basis: 2.7/3
* [[7-odd-limit]] unchanged-interval (eigenmonzo) basis: 2.7/3
* [[9-odd-limit]] eigenmonzo (unchanged-interval) basis: 2.9/7
* [[9-odd-limit]] unchanged-interval (eigenmonzo) basis: 2.9/7


{{Optimal ET sequence|legend=1| 12, 106d, 118, 130, 248, 378 }}
{{Optimal ET sequence|legend=1| 12, 106d, 118, 130, 248, 378 }}
Line 1,436: Line 1,436:


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


{{Optimal ET sequence|legend=1| 12, 147d, 159, 171, 867, 1038, 1209, 1380, 1551, 1722 }}
{{Optimal ET sequence|legend=1| 12, 147d, 159, 171, 867, 1038, 1209, 1380, 1551, 1722 }}
Line 1,649: Line 1,649:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3
* [[7-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3
* [[9-odd-limit]] eigenmonzo (unchanged-interval) basis: 2.9/7
* [[9-odd-limit]] unchanged-interval (eigenmonzo) basis: 2.9/7


{{Optimal ET sequence|legend=1| 41, 89, 130, 171, 814, 985, 1156, 1327, 1498, 2825bd }}
{{Optimal ET sequence|legend=1| 41, 89, 130, 171, 814, 985, 1156, 1327, 1498, 2825bd }}