Schismatic family: Difference between revisions
m Text replacement - "Eigenmonzo (unchanged-interval)" to "Unchanged-interval (eigenmonzo)" |
m Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) " |
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* [[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 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 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 }} | ||
: | : 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 }} | ||
: | : 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 }} | ||
: | : 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 }} | ||
: | : 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 }} | ||
: | : 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 }} | ||
: | : 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 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 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 }} | ||
: | : 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 }} | ||
: | : 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 }} | ||
: | : 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 }} | ||
: | : 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 }} | ||
: | : 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 }} | ||
: | : 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]] | * [[7-odd-limit]] unchanged-interval (eigenmonzo) basis: 2.7/3 | ||
* [[9-odd-limit]] | * [[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]] | * [[7-odd-limit]] unchanged-interval (eigenmonzo) basis: 2.7/3 | ||
* [[9-odd-limit]] | * [[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| | * [[7-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis)]]: 2.5/3 | ||
* [[9-odd-limit]] | * [[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| | * [[7-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3 | ||
* [[9-odd-limit]] | * [[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 }} | ||