Breed family: Difference between revisions
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.5 | * [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.5 | ||
[[Optimal tuning]] (POTE): ~2 = 1\1, ~49/40 = 350.9664, ~10/7 = 617.6720 | |||
{{Optimal ET sequence|legend=1| 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d }} | {{Optimal ET sequence|legend=1| 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d }} | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5.11 | * [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5.11 | ||
[[Optimal tuning]] (POTE): ~2 = 1\1, ~11/9 = 350.5034, ~10/7 = 617.8275 | |||
{{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }} | {{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }} | ||
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* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7/5.15/13 | * 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7/5.15/13 | ||
{{Optimal ET sequence | Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.7179, ~10/7 = 617.8286 | ||
Optimal ET sequence: {{Optimal ET sequence| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }} | |||
Badness: 0.624 × 10<sup>-3</sup> | Badness: 0.624 × 10<sup>-3</sup> | ||
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* 17-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.17/9 | * 17-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.17/9 | ||
{{Optimal ET sequence | Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.6947, ~10/7 = 617.5315 | ||
Optimal ET sequence: {{Optimal ET sequence| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }} | |||
Badness: 0.741 × 10<sup>-3</sup> | Badness: 0.741 × 10<sup>-3</sup> | ||
==== Heartlandia ==== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 243/242, 364/363, 441/440, 1452/1445 | |||
Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 4 0 1 10 23 12 | 0 0 2 1 0 -1 -1 }} | |||
: mapping generators: ~2, ~119/108, ~27/17 | |||
Optimal tuning (POTE): ~2 = 1\1, ~119/108 = 175.4177, ~27/17 = 793.9762 | |||
Optimal ET sequence: {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }} | |||
===== 19-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 171/170, 243/242, 324/323, 364/363, 441/440 | |||
Mapping: {{mapping| 1 1 1 2 2 1 3 3 | 0 4 0 1 10 23 12 4 | 0 0 2 1 0 -1 -1 1 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 175.3862, ~19/12 = 793.9558 | |||
Optimal ET sequence: {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }} | |||
=== Jofur === | === Jofur === | ||
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Mapping: {{mapping| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }} | Mapping: {{mapping| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }} | ||
{{Optimal ET sequence | Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.4477, ~10/7 = 618.8891 | ||
Optimal ET sequence: {{Optimal ET sequence| 27e, 31, 41, 58, 99ef, 157eff }} | |||
Badness: 0.749 × 10<sup>-3</sup> | Badness: 0.749 × 10<sup>-3</sup> | ||
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Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }} | Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }} | ||
{{Optimal ET sequence | Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.3935, ~10/7 = 618.1036 | ||
Optimal ET sequence: {{Optimal ET sequence| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }} | |||
Badness: 0.542 × 10<sup>-3</sup> | Badness: 0.542 × 10<sup>-3</sup> | ||
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: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 23/10 3/10 2/5 0 -2/5 }}, {{monzo| 12/5 2/5 1/5 0 -1/5 }}, {{monzo| 23/10 3/10 -3/5 0 3/5 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 23/10 3/10 2/5 0 -2/5 }}, {{monzo| 12/5 2/5 1/5 0 -1/5 }}, {{monzo| 23/10 3/10 -3/5 0 3/5 }}] | ||
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.11/5 | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.11/5 | ||
[[Optimal tuning]] (POTE): ~2 = 1\1, ~49/40 = 350.7145, ~10/7 = 617.0044 | |||
{{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }} | {{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }} | ||
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Mapping: {{mapping| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }} | Mapping: {{mapping| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }} | ||
{{Optimal ET sequence | Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 350.6803, ~10/7 = 617.1448 | ||
Optimal ET sequence: {{Optimal ET sequence| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }} | |||
Badness: 0.923 × 10<sup>-3</sup> | Badness: 0.923 × 10<sup>-3</sup> | ||