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Line 18: Line 18:
{{Mapping|legend=1| 1 0 2 | 0 5 1 }}
{{Mapping|legend=1| 1 0 2 | 0 5 1 }}


: Mapping generators: ~2, ~5/4
: mapping generators: ~2, ~5/4


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~5/4 = 380.4994
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~5/4 = 380.4994
* [[POTE]]: ~2 = 1\1, ~5/4 = 380.058


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 65: Line 67:
{{Multival|legend=1| 5 1 12 -10 5 25 }}
{{Multival|legend=1| 5 1 12 -10 5 25 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~5/4 = 380.6512
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~5/4 = 380.6512
* [[POTE]]: ~2 = 1\1, ~5/4 = 380.352


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 91: Line 95:
Mapping: {{mapping| 1 0 2 -1 6 | 0 5 1 12 -8 }}
Mapping: {{mapping| 1 0 2 -1 6 | 0 5 1 12 -8 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.7200
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.7200
* POTE: ~2 = 1\1, ~5/4 = 380.696


Minimax tuning:  
Minimax tuning:  
Line 113: Line 119:
Mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 1 12 -8 18 }}
Mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 1 12 -8 18 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.4354
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.4354
* POTE: ~2 = 1\1, ~5/4 = 380.427


Tuning ranges:  
Tuning ranges:  
Line 131: Line 139:
Mapping: {{mapping| 1 0 2 -1 6 -2 6 | 0 5 1 12 -8 18 -6 }}
Mapping: {{mapping| 1 0 2 -1 6 -2 6 | 0 5 1 12 -8 18 -6 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.5103
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.5103
* POTE: ~2 = 1\1, ~5/4 = 380.604


Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }}
Line 144: Line 154:
Mapping: {{mapping| 1 0 2 -1 6 -2 6 9 | 0 5 1 12 -8 18 -6 -15 }}
Mapping: {{mapping| 1 0 2 -1 6 -2 6 9 | 0 5 1 12 -8 18 -6 -15 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.4507
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.4507


Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }}
Line 157: Line 168:
Mapping: {{mapping| 1 0 2 -1 6 -2 6 -4 | 0 5 1 12 -8 18 -6 26 }}
Mapping: {{mapping| 1 0 2 -1 6 -2 6 -4 | 0 5 1 12 -8 18 -6 26 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.5733
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.5733


Optimal ET sequence: {{Optimal ET sequence| 19h, 22fh, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 19h, 22fh, 41 }}
Line 170: Line 182:
Mapping: {{mapping| 1 0 2 -1 6 -2 -7 | 0 5 1 12 -8 18 35 }}
Mapping: {{mapping| 1 0 2 -1 6 -2 -7 | 0 5 1 12 -8 18 35 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.2706
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.2706


Optimal ET sequence: {{Optimal ET sequence| 19g, 41, 101cde, 142cdefg }}
Optimal ET sequence: {{Optimal ET sequence| 19g, 41, 101cde, 142cdefg }}
Line 183: Line 196:
Mapping: {{mapping| 1 0 2 -1 6 -2 -7 -4 | 0 5 1 12 -8 18 35 26 }}
Mapping: {{mapping| 1 0 2 -1 6 -2 -7 -4 | 0 5 1 12 -8 18 35 26 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.3604
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.3604


Optimal ET sequence: {{Optimal ET sequence| 19g, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 19g, 41 }}
Line 198: Line 212:
Sval mapping: {{mapping| 1 0 2 -1 6 -2 2 4 | 0 5 1 12 -8 18 9 3 }}
Sval mapping: {{mapping| 1 0 2 -1 6 -2 2 4 | 0 5 1 12 -8 18 9 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 380.416
Optimal tunings:
* POTE: ~2 = 1\1, ~5/4 = 380.416


Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }}
Line 209: Line 224:
Mapping: {{mapping| 1 0 2 -1 6 4 | 0 5 1 12 -8 -1 }}
Mapping: {{mapping| 1 0 2 -1 6 4 | 0 5 1 12 -8 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.6741
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.6741
* POTE: ~2 = 1\1, ~5/4 = 380.477


Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41f }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41f }}
Line 222: Line 239:
Mapping: {{mapping| 1 0 2 -1 6 4 6 | 0 5 1 12 -8 -1 -6 }}
Mapping: {{mapping| 1 0 2 -1 6 4 6 | 0 5 1 12 -8 -1 -6 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.7839
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.7839
* POTE: ~2 = 1\1, ~5/4 = 380.729


Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41f }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41f }}
Line 235: Line 254:
Mapping: {{mapping| 1 0 2 -1 6 4 6 9 | 0 5 1 12 -8 -1 -6 -15 }}
Mapping: {{mapping| 1 0 2 -1 6 4 6 9 | 0 5 1 12 -8 -1 -6 -15 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.6248
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.6248


Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41f }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41f }}
Line 248: Line 268:
Mapping: {{mapping| 1 0 2 -1 6 11 | 0 5 1 12 -8 -23 }}
Mapping: {{mapping| 1 0 2 -1 6 11 | 0 5 1 12 -8 -23 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.7876
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.7876
* POTE: ~2 = 1\1, ~5/4 = 380.787


Optimal ET sequence: {{Optimal ET sequence| 19f, 22, 41, 63, 104 }}
Optimal ET sequence: {{Optimal ET sequence| 19f, 22, 41, 63, 104 }}
Line 261: Line 283:
Mapping: {{mapping| 1 0 2 -1 6 11 6 | 0 5 1 12 -8 -23 -6 }}
Mapping: {{mapping| 1 0 2 -1 6 11 6 | 0 5 1 12 -8 -23 -6 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.8373
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.8373
* POTE: ~2 = 1\1, ~5/4 = 380.827


Optimal ET sequence: {{Optimal ET sequence| 19f, 22, 41, 63, 104g }}
Optimal ET sequence: {{Optimal ET sequence| 19f, 22, 41, 63, 104g }}
Line 274: Line 298:
Mapping: {{mapping| 1 0 2 -1 6 11 6 9 | 0 5 1 12 -8 -23 -6 -15 }}
Mapping: {{mapping| 1 0 2 -1 6 11 6 9 | 0 5 1 12 -8 -23 -6 -15 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.7411
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.7411


Optimal ET sequence: {{Optimal ET sequence| 19f, 22, 41, 63h, 104gh }}
Optimal ET sequence: {{Optimal ET sequence| 19f, 22, 41, 63h, 104gh }}
Line 287: Line 312:
Mapping: {{mapping| 2 0 4 -2 12 15 | 0 5 1 12 -8 -12 }}
Mapping: {{mapping| 2 0 4 -2 12 15 | 0 5 1 12 -8 -12 }}


Optimal tuning (CTE): ~55/39 = 1\2, ~5/4 = 380.5385
Optimal tunings:
* CTE: ~55/39 = 1\2, ~5/4 = 380.5385
* POTE: ~55/39 = 1\2, ~5/4 = 380.508


Optimal ET sequence: {{Optimal ET sequence| 22, 60, 82 }}
Optimal ET sequence: {{Optimal ET sequence| 22, 60, 82 }}
Line 300: Line 327:
Mapping: {{mapping| 2 0 4 -2 12 15 5 | 0 5 1 12 -8 -12 5 }}
Mapping: {{mapping| 2 0 4 -2 12 15 5 | 0 5 1 12 -8 -12 5 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~5/4 = 380.5533
Optimal tunings:
* CTE: ~17/12 = 1\2, ~5/4 = 380.5533
* POTE: ~17/12 = 1\2, ~5/4 = 380.508


Optimal ET sequence: {{Optimal ET sequence| 22, 60, 82 }}
Optimal ET sequence: {{Optimal ET sequence| 22, 60, 82 }}
Line 313: Line 342:
Mapping: {{mapping| 2 0 4 -2 12 15 5 18 | 0 5 1 12 -8 -12 5 -15 }}
Mapping: {{mapping| 2 0 4 -2 12 15 5 18 | 0 5 1 12 -8 -12 5 -15 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~5/4 = 380.4704
Optimal tunings:
* CTE: ~17/12 = 1\2, ~5/4 = 380.4704


Optimal ET sequence: {{Optimal ET sequence| 22, 60, 82 }}
Optimal ET sequence: {{Optimal ET sequence| 22, 60, 82 }}
Line 326: Line 356:
Mapping: {{mapping| 1 0 2 -1 -1 | 0 5 1 12 14 }}
Mapping: {{mapping| 1 0 2 -1 -1 | 0 5 1 12 14 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 381.2311
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 381.2311
* POTE: ~2 = 1\1, ~5/4 = 381.019


Optimal ET sequence: {{Optimal ET sequence| 19e, 22, 63e, 85ee }}
Optimal ET sequence: {{Optimal ET sequence| 19e, 22, 63e, 85ee }}
Line 339: Line 371:
Mapping: {{mapping| 1 0 2 -1 -1 4 | 0 5 1 12 14 -1 }}
Mapping: {{mapping| 1 0 2 -1 -1 4 | 0 5 1 12 14 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 381.1957
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 381.1957
* POTE: ~2 = 1\1, ~5/4 = 380.520


Optimal ET sequence: {{Optimal ET sequence| 19e, 22, 63eff }}
Optimal ET sequence: {{Optimal ET sequence| 19e, 22, 63eff }}
Line 352: Line 386:
Mapping: {{mapping| 1 0 2 -1 -1 4 -1 | 0 5 1 12 14 -1 16 }}
Mapping: {{mapping| 1 0 2 -1 -1 4 -1 | 0 5 1 12 14 -1 16 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 381.2884
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 381.2884
* POTE: ~2 = 1\1, ~5/4 = 380.619


Optimal ET sequence: {{Optimal ET sequence| 19eg, 22, 63effg }}
Optimal ET sequence: {{Optimal ET sequence| 19eg, 22, 63effg }}
Line 365: Line 401:
Mapping: {{mapping| 1 0 2 -1 -1 4 -1 2 | 0 5 1 12 14 -1 16 7 }}
Mapping: {{mapping| 1 0 2 -1 -1 4 -1 2 | 0 5 1 12 14 -1 16 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 381.4641
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 381.4641


Optimal ET sequence: {{Optimal ET sequence| 19egh, 22 }}
Optimal ET sequence: {{Optimal ET sequence| 19egh, 22 }}
Line 378: Line 415:
Mapping: {{mapping| 1 0 2 -1 -1 -2 | 0 5 1 12 14 18 }}
Mapping: {{mapping| 1 0 2 -1 -1 -2 | 0 5 1 12 14 18 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.8157
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.8157
* POTE: ~2 = 1\1, ~5/4 = 380.483


Optimal ET sequence: {{Optimal ET sequence| 19e, 22f, 41e, 63ef }}
Optimal ET sequence: {{Optimal ET sequence| 19e, 22f, 41e, 63ef }}
Line 391: Line 430:
Mapping: {{mapping| 1 0 2 -1 -1 -2 -1 | 0 5 1 12 14 18 16 }}
Mapping: {{mapping| 1 0 2 -1 -1 -2 -1 | 0 5 1 12 14 18 16 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.9518
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.9518
* POTE: ~2 = 1\1, ~5/4 = 380.604


Optimal ET sequence: {{Optimal ET sequence| 19eg, 22f, 41eg, 63efg }}
Optimal ET sequence: {{Optimal ET sequence| 19eg, 22f, 41eg, 63efg }}
Line 404: Line 445:
Mapping: {{mapping| 1 0 2 -1 -1 -2 -1 -4 | 0 5 1 12 14 18 16 26 }}
Mapping: {{mapping| 1 0 2 -1 -1 -2 -1 -4 | 0 5 1 12 14 18 16 26 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.8658
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.8658


Optimal ET sequence: {{Optimal ET sequence| 19egh, 22fh, 41eg, 63efg }}
Optimal ET sequence: {{Optimal ET sequence| 19egh, 22fh, 41eg, 63efg }}
Line 417: Line 459:
Mapping: {{mapping| 1 0 2 -1 0 | 0 5 1 12 11 }}
Mapping: {{mapping| 1 0 2 -1 0 | 0 5 1 12 11 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 379.7959
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 379.7959
* POTE: ~2 = 1\1, ~5/4 = 379.642


Optimal ET sequence: {{Optimal ET sequence| 3de, …, 16d, 19, 41ee, 60ee }}
Optimal ET sequence: {{Optimal ET sequence| 3de, …, 16d, 19, 41ee, 60ee }}
Line 423: Line 467:
Badness: 0.039282
Badness: 0.039282


==== Tridecimal horcrux ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 430: Line 474:
Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 11 18 }}
Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 11 18 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 379.8847
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 379.8847
* POTE: ~2 = 1\1, ~5/4 = 379.791


Optimal ET sequence: {{Optimal ET sequence| 3def, …, 19, 41ee, 60ee }}
Optimal ET sequence: {{Optimal ET sequence| 3def, …, 19, 41ee, 60ee }}
Line 443: Line 489:
Mapping: {{mapping| 1 0 2 -1 0 -2 0 | 0 5 1 12 11 18 16 }}
Mapping: {{mapping| 1 0 2 -1 0 -2 0 | 0 5 1 12 11 18 16 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.2159
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.2159


Optimal ET sequence: {{Optimal ET sequence| 3defg, …, 19g, 41eeg }}
Optimal ET sequence: {{Optimal ET sequence| 3defg, …, 19g, 41eeg }}
Line 456: Line 503:
Mapping: {{mapping| 1 0 2 -1 0 -2 0 | 0 5 1 12 11 18 13 }}
Mapping: {{mapping| 1 0 2 -1 0 -2 0 | 0 5 1 12 11 18 13 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 379.5237
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 379.5237


Optimal ET sequence: {{Optimal ET sequence| 3defg, …, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 3defg, …, 19 }}
Line 469: Line 517:
Mapping: {{mapping| 1 0 2 -1 0 4 | 0 5 1 12 11 -1 }}
Mapping: {{mapping| 1 0 2 -1 0 4 | 0 5 1 12 11 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 379.7574
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 379.7574
* POTE: ~2 = 1\1, ~5/4 = 379.116


Optimal ET sequence: {{Optimal ET sequence| 3de, …, 16d, 19, 41eef, 60eeff }}
Optimal ET sequence: {{Optimal ET sequence| 3de, …, 16d, 19, 41eef, 60eeff }}
Line 482: Line 532:
Mapping: {{mapping| 1 0 2 -1 -7 | 0 5 1 12 33 }}
Mapping: {{mapping| 1 0 2 -1 -7 | 0 5 1 12 33 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.4163
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.4163
* POTE: ~2 = 1\1, ~5/4 = 380.232


Optimal ET sequence: {{Optimal ET sequence| 19e, 22e, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 19e, 22e, 41 }}
Line 495: Line 547:
Mapping: {{mapping| 1 0 2 -1 -7 -2 | 0 5 1 12 33 18 }}
Mapping: {{mapping| 1 0 2 -1 -7 -2 | 0 5 1 12 33 18 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.3523
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.3523
* POTE: ~2 = 1\1, ~5/4 = 380.189


Optimal ET sequence: {{Optimal ET sequence| 19e, 41, 142cdf }}
Optimal ET sequence: {{Optimal ET sequence| 19e, 41, 142cdf }}
Line 508: Line 562:
Mapping: {{mapping| 1 0 2 -1 -7 -2 -7 | 0 5 1 12 33 18 35 }}
Mapping: {{mapping| 1 0 2 -1 -7 -2 -7 | 0 5 1 12 33 18 35 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.2809
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.2809
* POTE: ~2 = 1\1, ~5/4 = 380.114


Optimal ET sequence: {{Optimal ET sequence| 19eg, 41, 101cd, 142cdfg }}
Optimal ET sequence: {{Optimal ET sequence| 19eg, 41, 101cd, 142cdfg }}
Line 521: Line 577:
Mapping: {{mapping| 1 0 2 -1 -7 -2 -7 -4 | 0 5 1 12 33 18 35 26 }}
Mapping: {{mapping| 1 0 2 -1 -7 -2 -7 -4 | 0 5 1 12 33 18 35 26 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.3389
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 380.3389


Optimal ET sequence: {{Optimal ET sequence| 19egh, 41, 101cdhh, 142cdfghh }}
Optimal ET sequence: {{Optimal ET sequence| 19egh, 41, 101cdhh, 142cdfghh }}
Line 534: Line 591:
Mapping: {{mapping| 2 0 4 -2 5 | 0 5 1 12 3 }}
Mapping: {{mapping| 2 0 4 -2 5 | 0 5 1 12 3 }}


Optimal tuning (CTE): ~99/70 = 1\2, ~5/4 = 380.7317
Optimal tunings:
* CTE: ~99/70 = 1\2, ~5/4 = 380.7317
* POTE: ~99/70 = 1\2, ~5/4 = 380.223


Optimal ET sequence: {{Optimal ET sequence| 22, 60e, 82e, 104e }}
Optimal ET sequence: {{Optimal ET sequence| 22, 60e, 82e, 104e }}
Line 547: Line 606:
Mapping: {{mapping| 2 0 4 -2 5 -4 | 0 5 1 12 3 18 }}
Mapping: {{mapping| 2 0 4 -2 5 -4 | 0 5 1 12 3 18 }}


Optimal tuning (CTE): ~99/70 = 1\2, ~5/4 = 380.4171
Optimal tunings:
* CTE: ~99/70 = 1\2, ~5/4 = 380.4171
* POTE: ~99/70 = 1\2, ~5/4 = 379.920


Optimal ET sequence: {{Optimal ET sequence| 22f, 60e, 82ef }}
Optimal ET sequence: {{Optimal ET sequence| 22f, 60e, 82ef }}
Line 560: Line 621:
Mapping: {{mapping| 2 0 4 -2 5 -4 5 | 0 5 1 12 3 18 5 }}
Mapping: {{mapping| 2 0 4 -2 5 -4 5 | 0 5 1 12 3 18 5 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~5/4 = 380.4329
Optimal tunings:
* CTE: ~17/12 = 1\2, ~5/4 = 380.4329


Optimal ET sequence: {{Optimal ET sequence| 22f, 60e, 82ef }}
Optimal ET sequence: {{Optimal ET sequence| 22f, 60e, 82ef }}
Line 573: Line 635:
Mapping: {{mapping| 1 5 3 11 12 | 0 -10 -2 -24 -25 }}
Mapping: {{mapping| 1 5 3 11 12 | 0 -10 -2 -24 -25 }}


Optimal tuning (CTE): ~2 = 1\1, ~14/11 = 409.7603
Optimal tunings:
* CTE: ~2 = 1\1, ~14/11 = 409.7603
* POTE: ~2 = 1\1, ~14/11 = 409.910


Optimal ET sequence: {{Optimal ET sequence| 38d, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 38d, 41 }}
Line 586: Line 650:
Mapping: {{mapping| 1 5 3 11 12 16 | 0 -10 -2 -24 -25 -36 }}
Mapping: {{mapping| 1 5 3 11 12 16 | 0 -10 -2 -24 -25 -36 }}


Optimal tuning (CTE): ~2 = 1\1, ~14/11 = 409.8421
Optimal tunings:
* CTE: ~2 = 1\1, ~14/11 = 409.8421
* POTE: ~2 = 1\1, ~14/11 = 410.004


Optimal ET sequence: {{Optimal ET sequence| 38df, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 38df, 41 }}
Line 599: Line 665:
Mapping: {{mapping| 1 5 3 11 12 16 14 | 0 -10 -2 -24 -25 -36 -29 }}
Mapping: {{mapping| 1 5 3 11 12 16 14 | 0 -10 -2 -24 -25 -36 -29 }}


Optimal tuning (CTE): ~2 = 1\1, ~14/11 = 409.8958
Optimal tunings:
* CTE: ~2 = 1\1, ~14/11 = 409.8958


Optimal ET sequence: {{Optimal ET sequence| 38df, 41, 120cdg, 161cdg, 202ccddfgg }}
Optimal ET sequence: {{Optimal ET sequence| 38df, 41, 120cdg, 161cdg, 202ccddfgg }}
Line 612: Line 679:
Mapping: {{mapping| 1 5 3 11 12 16 14 8 | 0 -10 -2 -24 -25 -36 -29 -11 }}
Mapping: {{mapping| 1 5 3 11 12 16 14 8 | 0 -10 -2 -24 -25 -36 -29 -11 }}


Optimal tuning (CTE): ~2 = 1\1, ~14/11 = 409.8836
Optimal tunings:
* CTE: ~2 = 1\1, ~14/11 = 409.8836


Optimal ET sequence: {{Optimal ET sequence| 38df, 41, 120cdgh, 161cdgh, 202ccddfgghh }}
Optimal ET sequence: {{Optimal ET sequence| 38df, 41, 120cdgh, 161cdgh, 202ccddfgghh }}
Line 631: Line 699:
{{Multival|legend=1| 5 1 -7 -10 -25 -19 }}
{{Multival|legend=1| 5 1 -7 -10 -25 -19 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~5/4 = 378.744
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~5/4 = 378.744
* [[POTE]]: ~2 = 1\1, ~5/4 = 378.479


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 640: Line 710:
* 9-odd-limit diamond monotone and tradeoff: ~5/4 = 378.947
* 9-odd-limit diamond monotone and tradeoff: ~5/4 = 378.947


{{Optimal ET sequence|legend=1| 16, 19 }}
{{Optimal ET sequence|legend=1| 16, 19, 73bcd, 92bcdd, 111bcddd }}


[[Badness]]: 0.056206
[[Badness]]: 0.056206
Line 651: Line 721:
Mapping: {{mapping| 1 0 2 5 0 | 0 5 1 -7 11 }}
Mapping: {{mapping| 1 0 2 5 0 | 0 5 1 -7 11 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 378.228
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 378.228
* POTE: ~2 = 1\1, ~5/4 = 377.724


Tuning ranges:  
Tuning ranges:  
Line 658: Line 730:
* 11-odd-limit diamond monotone and tradeoff: ~5/4 = 378.947
* 11-odd-limit diamond monotone and tradeoff: ~5/4 = 378.947


Optimal ET sequence: {{Optimal ET sequence| 16, 19, 54bd, 73bcd, 92bcdde }}
Optimal ET sequence: {{Optimal ET sequence| 16, 19, 54bd }}


Badness: 0.048038
Badness: 0.048038
Line 669: Line 741:
Mapping: {{mapping| 1 0 2 5 0 4 | 0 5 1 -7 11 -1 }}
Mapping: {{mapping| 1 0 2 5 0 4 | 0 5 1 -7 11 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 377.653
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 378.1761
* POTE: ~2 = 1\1, ~5/4 = 377.653


Optimal ET sequence: {{Optimal ET sequence| 16, 19, 54bdf, 73bcdff, 92bcddeff }}
Optimal ET sequence: {{Optimal ET sequence| 16, 19, 54bdf }}


Badness: 0.030386
Badness: 0.030386
Line 682: Line 756:
Mapping: {{mapping| 1 0 2 5 5 | 0 5 1 -7 -5 }}
Mapping: {{mapping| 1 0 2 5 5 | 0 5 1 -7 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 377.724
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 377.724
* POTE: ~2 = 1\1, ~5/4 = 377.832


Optimal ET sequence: {{Optimal ET sequence| 3, 10bd, 13bd, 16, 19e, 35ee }}
Optimal ET sequence: {{Optimal ET sequence| 3, 10bd, 13bd, 16, 19e, 35ee }}
Line 695: Line 771:
Mapping: {{mapping| 1 0 2 5 5 4 | 0 5 1 -7 -5 -1 }}
Mapping: {{mapping| 1 0 2 5 5 4 | 0 5 1 -7 -5 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 377.652
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 377.652
* POTE: ~2 = 1\1, ~5/4 = 377.838


Optimal ET sequence: {{Optimal ET sequence| 3, 10bd, 13bd, 16, 19e, 35eef }}
Optimal ET sequence: {{Optimal ET sequence| 3, 10bd, 13bd, 16, 19e, 35eef }}
Line 712: Line 790:
{{Multival|legend=1| 5 1 9 -10 0 18 }}
{{Multival|legend=1| 5 1 9 -10 0 18 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~5/4 = 377.385
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~5/4 = 377.385


{{Optimal ET sequence|legend=1| 3d, …, 13b, 16, 19d, 35d }}
{{Optimal ET sequence|legend=1| 3d, …, 13b, 16, 19d, 35d }}
Line 725: Line 804:
Mapping: {{mapping| 1 0 2 0 0 | 0 5 1 9 11 }}
Mapping: {{mapping| 1 0 2 0 0 | 0 5 1 9 11 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 377.388
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 377.388


Optimal ET sequence: {{Optimal ET sequence| 3de, …, 13be, 16, 19d, 35d }}
Optimal ET sequence: {{Optimal ET sequence| 3de, …, 13be, 16, 19d, 35d }}
Line 738: Line 818:
Mapping: {{mapping| 1 0 2 0 0 -1 | 0 5 1 9 11 15 }}
Mapping: {{mapping| 1 0 2 0 0 -1 | 0 5 1 9 11 15 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 376.914
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 376.914


Optimal ET sequence: {{Optimal ET sequence| 3def, …, 16, 35d }}
Optimal ET sequence: {{Optimal ET sequence| 3def, …, 16, 35d }}
Line 745: Line 826:


== Brightstone ==
== Brightstone ==
{{see also| Archytas clan }}
{{See also| Archytas clan }}


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 755: Line 836:
{{Multival|legend=1| 5 1 -10 -10 -30 -26 }}
{{Multival|legend=1| 5 1 -10 -10 -30 -26 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~5/4 = 381.955
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~5/4 = 381.955


{{Optimal ET sequence|legend=1| 3, …, 19d, 22 }}
{{Optimal ET sequence|legend=1| 3, …, 19d, 22 }}
Line 768: Line 850:
Mapping: {{mapping| 1 0 2 6 6 | 0 5 1 -10 -8 }}
Mapping: {{mapping| 1 0 2 6 6 | 0 5 1 -10 -8 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 381.790
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 381.790


Optimal ET sequence: {{Optimal ET sequence| 3, …, 19d, 22 }}
Optimal ET sequence: {{Optimal ET sequence| 3, …, 19d, 22 }}
Line 781: Line 864:
Mapping: {{mapping| 1 0 2 6 6 4 | 0 5 1 -10 -8 -1 }}
Mapping: {{mapping| 1 0 2 6 6 4 | 0 5 1 -10 -8 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 381.732
Optimal tunings:
* CTE: ~2 = 1\1, ~5/4 = 381.732


Optimal ET sequence: {{Optimal ET sequence| 3, …, 19d, 22 }}
Optimal ET sequence: {{Optimal ET sequence| 3, …, 19d, 22 }}
Line 794: Line 878:
{{Mapping|legend=1| 1 5 3 -3 | 0 -10 -2 17 }}
{{Mapping|legend=1| 1 5 3 -3 | 0 -10 -2 17 }}


: Mapping generators: ~2, ~63/50
: mapping generators: ~2, ~63/50


{{Multival|legend=1| 10 2 -17 -20 -55 -45 }}
{{Multival|legend=1| 10 2 -17 -20 -55 -45 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~63/50 = 409.836
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~63/50 = 409.836
* [[POTE]]: ~2 = 1\1, ~63/50 = 410.108


{{Optimal ET sequence|legend=1| 3, …, 35d, 38, 41, 202cc, 243cc, 284cc }}
{{Optimal ET sequence|legend=1| 3, …, 35d, 38, 41, 202cc, 243cc, 284cc }}
Line 811: Line 897:
{{Mapping|legend=1| 1 10 4 0 | 0 -15 -3 5 }}
{{Mapping|legend=1| 1 10 4 0 | 0 -15 -3 5 }}


: Mapping generators: ~2, ~147/100
: mapping generators: ~2, ~147/100


{{Multival|legend=1| 15 3 -5 -30 -50 -20 }}
{{Multival|legend=1| 15 3 -5 -30 -50 -20 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~147/100 = 673.187
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~147/100 = 673.187
* [[POTE]]: ~2 = 1\1, ~147/100 = 673.290


{{Optimal ET sequence|legend=1| 16, 25, 41 }}
{{Optimal ET sequence|legend=1| 16, 25, 41 }}
Line 828: Line 916:
Mapping: {{mapping| 1 10 4 0 13 | 0 -15 -3 5 -17 }}
Mapping: {{mapping| 1 10 4 0 13 | 0 -15 -3 5 -17 }}


Optimal tuning (CTE): ~2 = 1\1, ~22/15 = 673.241
Optimal tunings:
* CTE: ~2 = 1\1, ~22/15 = 673.241
* POTE: ~2 = 1\1, ~22/15 = 673.340


Optimal ET sequence: {{Optimal ET sequence| 16, 25e, 41, 221cc, 262ccde }}
Optimal ET sequence: {{Optimal ET sequence| 16, 25e, 41, 221cc, 262ccde }}
Line 841: Line 931:
Mapping: {{mapping| 1 10 4 0 13 11 | 0 -15 -3 5 -17 -13 }}
Mapping: {{mapping| 1 10 4 0 13 11 | 0 -15 -3 5 -17 -13 }}


Optimal tuning (CTE): ~2 = 1\1, ~22/15 = 673.294
Optimal tunings:
* CTE: ~2 = 1\1, ~22/15 = 673.294
* POTE: ~2 = 1\1, ~22/15 = 673.359


Optimal ET sequence: {{Optimal ET sequence| 16, 25e, 41, 139cf, 180cf, 221ccf }}
Optimal ET sequence: {{Optimal ET sequence| 16, 25e, 41, 139cf, 180cf, 221ccf }}
Line 858: Line 950:
{{Multival|legend=1| 20 4 7 -40 -45 5 }}
{{Multival|legend=1| 20 4 7 -40 -45 5 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~28/25 = 204.860
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~28/25 = 204.860
* [[POTE]]: ~2 = 1\1, ~28/25 = 204.987


{{Optimal ET sequence|legend=1| 6, …, 29b, 35, 41 }}
{{Optimal ET sequence|legend=1| 6, …, 29b, 35, 41 }}
Line 871: Line 965:
Mapping: {{mapping| 1 5 3 4 5 | 0 -20 -4 -7 -9 }}
Mapping: {{mapping| 1 5 3 4 5 | 0 -20 -4 -7 -9 }}


Optimal tuning (CTE): ~2 = 1\1, ~28/25 = 204.881
Optimal tunings:
* CTE: ~2 = 1\1, ~28/25 = 204.881
* POTE: ~2 = 1\1, ~28/25 = 204.956


Optimal ET sequence: {{Optimal ET sequence| 6, …, 29b, 35, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 6, …, 29b, 35, 41 }}
Line 884: Line 980:
Mapping: {{mapping| 1 5 3 4 5 9 | 0 -20 -4 -7 -9 -31 }}
Mapping: {{mapping| 1 5 3 4 5 9 | 0 -20 -4 -7 -9 -31 }}


Optimal tuning (CTE): ~2 = 1\1, ~28/25 = 204.956
Optimal tunings:
* CTE: ~2 = 1\1, ~28/25 = 204.956
* POTE: ~2 = 1\1, ~28/25 = 205.028


Optimal ET sequence: {{Optimal ET sequence| 35f, 41, 199ccdef, 240ccdef, 281ccdeff }}
Optimal ET sequence: {{Optimal ET sequence| 35f, 41, 199ccdef, 240ccdef, 281ccdeff }}
Line 899: Line 997:
{{Multival|legend=1| 25 5 19 -50 -40 30 }}
{{Multival|legend=1| 25 5 19 -50 -40 30 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~48/35 = 556.123
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~48/35 = 556.123


{{Optimal ET sequence|legend=1| 13b, 28b, 41 }}
{{Optimal ET sequence|legend=1| 13b, 28b, 41 }}
Line 912: Line 1,011:
Mapping: {{mapping| 1 -10 0 -6 3 | 0 25 5 19 1 }}
Mapping: {{mapping| 1 -10 0 -6 3 | 0 25 5 19 1 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/8 = 556.122
Optimal tunings:
* CTE: ~2 = 1\1, ~11/8 = 556.122


Optimal ET sequence: {{Optimal ET sequence| 13b, 28b, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 13b, 28b, 41 }}
Line 925: Line 1,025:
Mapping: {{mapping| 1 -10 0 -6 3 0 | 0 25 5 19 1 8 }}
Mapping: {{mapping| 1 -10 0 -6 3 0 | 0 25 5 19 1 8 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/8 = 556.106
Optimal tunings:
* CTE: ~2 = 1\1, ~11/8 = 556.106


Optimal ET sequence: {{Optimal ET sequence| 13b, 28b, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 13b, 28b, 41 }}
Line 938: Line 1,039:
{{Mapping|legend=1| 5 0 10 14 | 0 5 1 0 }}
{{Mapping|legend=1| 5 0 10 14 | 0 5 1 0 }}


: Mapping generators: ~8/7, ~5/4
: mapping generators: ~8/7, ~5/4


[[Optimal tuning]] ([[CTE]]): ~8/7 = 1\5, ~5/4 = 380.499
[[Optimal tuning]]s:
* [[CTE]]: ~8/7 = 1\5, ~5/4 = 380.499
* [[POTE]]: ~8/7 = 1\5, ~5/4 = 379.7131


{{Optimal ET sequence|legend=1| 25, 35, 60 }}
{{Optimal ET sequence|legend=1| 25, 35, 60 }}
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