Breed family: Difference between revisions

m Lif: clarify
Xenllium (talk | contribs)
No edit summary
Line 18: Line 18:
[[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 }}
Line 40: Line 42:
[[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 }}
Line 58: Line 62:
* 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|legend=1| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}
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>
Line 72: Line 78:
* 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|legend=1| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}
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 ===
Line 83: Line 115:
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|legend=1| 27e, 31, 41, 58, 99ef, 157eff }}
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>
Line 94: Line 128:
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|legend=1| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
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>
Line 115: Line 151:
: [{{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 }}
Line 127: Line 165:
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|legend=1| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}
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>