Xenharmonic Wiki

Magic family: Difference between revisions

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Unify to 3 decimal places. Re-adopt template: Optimal ET sequence for all the sections. Misc cleanup
Spell 1\1 in decimal; note the badness metric being used; misc. cleanup
Line 21: Line 21:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 380.499
* [[CTE]]: ~2 = 1200.000, ~5/4 = 380.499
* [[POTE]]: ~2 = 1\1, ~5/4 = 380.058
* [[POTE]]: ~2 = 1200.000, ~5/4 = 380.058


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 36: Line 36:
{{Optimal ET sequence|legend=1| 3, 13b, 16, 19, 22, 41 }}
{{Optimal ET sequence|legend=1| 3, 13b, 16, 19, 22, 41 }}


[[Badness]]: 0.039163
[[Badness]] (Smith): 0.039163


=== Overview to extensions ===
=== Overview to extensions ===
Line 67: Line 67:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 380.651
* [[CTE]]: ~2 = 1200.000, ~5/4 = 380.651
* [[POTE]]: ~2 = 1\1, ~5/4 = 380.352
* [[POTE]]: ~2 = 1200.000, ~5/4 = 380.352


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 82: Line 82:
{{Optimal ET sequence|legend=1| 19, 22, 41, 104, 145c, 186c }}
{{Optimal ET sequence|legend=1| 19, 22, 41, 104, 145c, 186c }}


[[Badness]]: 0.018918
[[Badness]] (Smith): 0.018918


=== 11-limit ===
=== 11-limit ===
Line 96: Line 96:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.720
* CTE: ~2 = 1200.000, ~5/4 = 380.720
* POTE: ~2 = 1\1, ~5/4 = 380.696
* POTE: ~2 = 1200.000, ~5/4 = 380.696


Minimax tuning:  
Minimax tuning:  
Line 109: Line 109:
{{Optimal ET sequence|legend=0| 19, 22, 41, 104, 145c, 249cce }}
{{Optimal ET sequence|legend=0| 19, 22, 41, 104, 145c, 249cce }}


Badness: 0.020352
Badness (Smith): 0.020352


==== 13-limit ====
==== 13-limit ====
Line 121: Line 121:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.435
* CTE: ~2 = 1200.000, ~5/4 = 380.435
* POTE: ~2 = 1\1, ~5/4 = 380.427
* POTE: ~2 = 1200.000, ~5/4 = 380.427


Tuning ranges:  
Tuning ranges:  
Line 130: Line 130:
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}


Badness: 0.021509
Badness (Smith): 0.021509


===== Magical =====
===== Magical =====
Line 140: Line 140:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.510
* CTE: ~2 = 1200.000, ~5/4 = 380.510
* POTE: ~2 = 1\1, ~5/4 = 380.604
* POTE: ~2 = 1200.000, ~5/4 = 380.604


{{Optimal ET sequence|legend=0| 19, 22f, 41 }}
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}


Badness: 0.020633
Badness (Smith): 0.020633


====== 19-limit ======
====== 19-limit ======
Line 155: Line 155:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.451
* CTE: ~2 = 1200.000, ~5/4 = 380.451


{{Optimal ET sequence|legend=0| 19, 22f, 41 }}
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}


Badness: 0.020881
Badness (Smith): 0.020881


====== Magica ======
====== Magica ======
Line 169: Line 169:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.573
* CTE: ~2 = 1200.000, ~5/4 = 380.573


{{Optimal ET sequence|legend=0| 19h, 22fh, 41 }}
{{Optimal ET sequence|legend=0| 19h, 22fh, 41 }}


Badness: 0.019945
Badness (Smith): 0.019945


===== Magia =====
===== Magia =====
Line 183: Line 183:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.271
* CTE: ~2 = 1200.000, ~5/4 = 380.271


{{Optimal ET sequence|legend=0| 19g, 41, 101cde, 142cdefg }}
{{Optimal ET sequence|legend=0| 19g, 41, 101cde, 142cdefg }}


Badness: 0.026232
Badness (Smith): 0.026232


====== 19-limit ======
====== 19-limit ======
Line 197: Line 197:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.360
* CTE: ~2 = 1200.000, ~5/4 = 380.360


{{Optimal ET sequence|legend=0| 19g, 41 }}
{{Optimal ET sequence|legend=0| 19g, 41 }}


Badness: 0.023709
Badness (Smith): 0.023709


===== Evening =====
===== Evening =====
Line 213: Line 213:


Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1\1, ~5/4 = 380.416
* POTE: ~2 = 1200.000, ~5/4 = 380.416


{{Optimal ET sequence|legend=0| 19, 22f, 41 }}
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}
Line 225: Line 225:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.674
* CTE: ~2 = 1200.000, ~5/4 = 380.674
* POTE: ~2 = 1\1, ~5/4 = 380.477
* POTE: ~2 = 1200.000, ~5/4 = 380.477


{{Optimal ET sequence|legend=0| 19, 22, 41f }}
{{Optimal ET sequence|legend=0| 19, 22, 41f }}


Badness: 0.025829
Badness (Smith): 0.025829


===== 17-limit =====
===== 17-limit =====
Line 240: Line 240:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.784
* CTE: ~2 = 1200.000, ~5/4 = 380.784
* POTE: ~2 = 1\1, ~5/4 = 380.729
* POTE: ~2 = 1200.000, ~5/4 = 380.729


{{Optimal ET sequence|legend=0| 19, 22, 41f }}
{{Optimal ET sequence|legend=0| 19, 22, 41f }}


Badness: 0.023768
Badness (Smith): 0.023768


===== 19-limit =====
===== 19-limit =====
Line 255: Line 255:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.625
* CTE: ~2 = 1200.000, ~5/4 = 380.625


{{Optimal ET sequence|legend=0| 19, 22, 41f }}
{{Optimal ET sequence|legend=0| 19, 22, 41f }}


Badness: 0.023232
Badness (Smith): 0.023232


==== Necromancy ====
==== Necromancy ====
Line 269: Line 269:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.788
* CTE: ~2 = 1200.000, ~5/4 = 380.788
* POTE: ~2 = 1\1, ~5/4 = 380.787
* POTE: ~2 = 1200.000, ~5/4 = 380.787


{{Optimal ET sequence|legend=0| 19f, 22, 41, 63, 104 }}
{{Optimal ET sequence|legend=0| 19f, 22, 41, 63, 104 }}


Badness: 0.025275
Badness (Smith): 0.025275


===== 17-limit =====
===== 17-limit =====
Line 284: Line 284:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.837
* CTE: ~2 = 1200.000, ~5/4 = 380.837
* POTE: ~2 = 1\1, ~5/4 = 380.827
* POTE: ~2 = 1200.000, ~5/4 = 380.827


{{Optimal ET sequence|legend=0| 19f, 22, 41, 63, 104g }}
{{Optimal ET sequence|legend=0| 19f, 22, 41, 63, 104g }}


Badness: 0.022032
Badness (Smith): 0.022032


===== 19-limit =====
===== 19-limit =====
Line 299: Line 299:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.741
* CTE: ~2 = 1200.000, ~5/4 = 380.741


{{Optimal ET sequence|legend=0| 19f, 22, 41, 63h, 104gh }}
{{Optimal ET sequence|legend=0| 19f, 22, 41, 63h, 104gh }}


Badness: 0.021101
Badness (Smith): 0.021101


==== Soothsaying ====
==== Soothsaying ====
Line 313: Line 313:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 1\2, ~5/4 = 380.539
* CTE: ~55/39 = 600.000, ~5/4 = 380.539
* POTE: ~55/39 = 1\2, ~5/4 = 380.508
* POTE: ~55/39 = 600.000, ~5/4 = 380.508


{{Optimal ET sequence|legend=0| 22, 60, 82 }}
{{Optimal ET sequence|legend=0| 22, 60, 82 }}


Badness: 0.055443
Badness (Smith): 0.055443


===== 17-limit =====
===== 17-limit =====
Line 328: Line 328:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 1\2, ~5/4 = 380.553
* CTE: ~17/12 = 600.000, ~5/4 = 380.553
* POTE: ~17/12 = 1\2, ~5/4 = 380.508
* POTE: ~17/12 = 600.000, ~5/4 = 380.508


{{Optimal ET sequence|legend=0| 22, 60, 82 }}
{{Optimal ET sequence|legend=0| 22, 60, 82 }}


Badness: 0.035654
Badness (Smith): 0.035654


===== 19-limit =====
===== 19-limit =====
Line 343: Line 343:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 1\2, ~5/4 = 380.470
* CTE: ~17/12 = 600.000, ~5/4 = 380.470


{{Optimal ET sequence|legend=0| 22, 60, 82 }}
{{Optimal ET sequence|legend=0| 22, 60, 82 }}


Badness: 0.031291
Badness (Smith): 0.031291


=== Telepathy ===
=== Telepathy ===
Line 359: Line 359:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 381.231
* CTE: ~2 = 1200.000, ~5/4 = 381.231
* POTE: ~2 = 1\1, ~5/4 = 381.019
* POTE: ~2 = 1200.000, ~5/4 = 381.019


{{Optimal ET sequence|legend=0| 19e, 22, 63e, 85ee }}
{{Optimal ET sequence|legend=0| 19e, 22, 63e, 85ee }}


Badness: 0.027109
Badness (Smith): 0.027109


==== 13-limit ====
==== 13-limit ====
Line 374: Line 374:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 381.196
* CTE: ~2 = 1200.000, ~5/4 = 381.196
* POTE: ~2 = 1\1, ~5/4 = 380.520
* POTE: ~2 = 1200.000, ~5/4 = 380.520


{{Optimal ET sequence|legend=0| 19e, 22, 63eff }}
{{Optimal ET sequence|legend=0| 19e, 22, 63eff }}


Badness: 0.025522
Badness (Smith): 0.025522


===== 17-limit =====
===== 17-limit =====
Line 389: Line 389:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 381.288
* CTE: ~2 = 1200.000, ~5/4 = 381.288
* POTE: ~2 = 1\1, ~5/4 = 380.619
* POTE: ~2 = 1200.000, ~5/4 = 380.619


{{Optimal ET sequence|legend=0| 19eg, 22, 63effg }}
{{Optimal ET sequence|legend=0| 19eg, 22, 63effg }}


Badness: 0.020201
Badness (Smith): 0.020201


===== 19-limit =====
===== 19-limit =====
Line 404: Line 404:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 381.464
* CTE: ~2 = 1200.000, ~5/4 = 381.464


{{Optimal ET sequence|legend=0| 19egh, 22 }}
{{Optimal ET sequence|legend=0| 19egh, 22 }}


Badness: 0.019004
Badness (Smith): 0.019004


==== Intuition ====
==== Intuition ====
Line 418: Line 418:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.816
* CTE: ~2 = 1200.000, ~5/4 = 380.816
* POTE: ~2 = 1\1, ~5/4 = 380.483
* POTE: ~2 = 1200.000, ~5/4 = 380.483


{{Optimal ET sequence|legend=0| 19e, 22f, 41e, 63ef }}
{{Optimal ET sequence|legend=0| 19e, 22f, 41e, 63ef }}


Badness: 0.026089
Badness (Smith): 0.026089


===== 17-limit =====
===== 17-limit =====
Line 433: Line 433:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.952
* CTE: ~2 = 1200.000, ~5/4 = 380.952
* POTE: ~2 = 1\1, ~5/4 = 380.604
* POTE: ~2 = 1200.000, ~5/4 = 380.604


{{Optimal ET sequence|legend=0| 19eg, 22f, 41eg, 63efg }}
{{Optimal ET sequence|legend=0| 19eg, 22f, 41eg, 63efg }}


Badness: 0.020274
Badness (Smith): 0.020274


===== 19-limit =====
===== 19-limit =====
Line 448: Line 448:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.866
* CTE: ~2 = 1200.000, ~5/4 = 380.866


{{Optimal ET sequence|legend=0| 19egh, 22fh, 41eg, 63efg }}
{{Optimal ET sequence|legend=0| 19egh, 22fh, 41eg, 63efg }}


Badness: 0.019518
Badness (Smith): 0.019518


=== Horcrux ===
=== Horcrux ===
Line 462: Line 462:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 379.796
* CTE: ~2 = 1200.000, ~5/4 = 379.796
* POTE: ~2 = 1\1, ~5/4 = 379.642
* POTE: ~2 = 1200.000, ~5/4 = 379.642


{{Optimal ET sequence|legend=0| 3de, …, 16d, 19, 41ee, 60ee }}
{{Optimal ET sequence|legend=0| 3de, …, 16d, 19, 41ee, 60ee }}


Badness: 0.039282
Badness (Smith): 0.039282


==== 13-limit ====
==== 13-limit ====
Line 477: Line 477:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 379.885
* CTE: ~2 = 1200.000, ~5/4 = 379.885
* POTE: ~2 = 1\1, ~5/4 = 379.791
* POTE: ~2 = 1200.000, ~5/4 = 379.791


{{Optimal ET sequence|legend=0| 3def, …, 19, 41ee, 60ee }}
{{Optimal ET sequence|legend=0| 3def, …, 19, 41ee, 60ee }}


Badness: 0.031938
Badness (Smith): 0.031938


===== 17-limit =====
===== 17-limit =====
Line 492: Line 492:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.216
* CTE: ~2 = 1200.000, ~5/4 = 380.216


{{Optimal ET sequence|legend=0| 3defg, …, 19g, 41eeg }}
{{Optimal ET sequence|legend=0| 3defg, …, 19g, 41eeg }}


Badness: 0.028074
Badness (Smith): 0.028074


===== Horcruxic =====
===== Horcruxic =====
Line 506: Line 506:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 379.524
* CTE: ~2 = 1200.000, ~5/4 = 379.524


{{Optimal ET sequence|legend=0| 3defg, …, 19 }}
{{Optimal ET sequence|legend=0| 3defg, …, 19 }}


Badness: 0.029556
Badness (Smith): 0.029556


==== Glamour ====
==== Glamour ====
Line 520: Line 520:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 379.757
* CTE: ~2 = 1200.000, ~5/4 = 379.757
* POTE: ~2 = 1\1, ~5/4 = 379.116
* POTE: ~2 = 1200.000, ~5/4 = 379.116


{{Optimal ET sequence|legend=0| 3de, …, 16d, 19, 41eef, 60eeff }}
{{Optimal ET sequence|legend=0| 3de, …, 16d, 19, 41eef, 60eeff }}


Badness: 0.033317
Badness (Smith): 0.033317


=== Witchcraft ===
=== Witchcraft ===
Line 535: Line 535:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.416
* CTE: ~2 = 1200.000, ~5/4 = 380.416
* POTE: ~2 = 1\1, ~5/4 = 380.232
* POTE: ~2 = 1200.000, ~5/4 = 380.232


{{Optimal ET sequence|legend=0| 19e, 22e, 41 }}
{{Optimal ET sequence|legend=0| 19e, 22e, 41 }}


Badness: 0.030706
Badness (Smith): 0.030706


==== 13-limit ====
==== 13-limit ====
Line 550: Line 550:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.352
* CTE: ~2 = 1200.000, ~5/4 = 380.352
* POTE: ~2 = 1\1, ~5/4 = 380.189
* POTE: ~2 = 1200.000, ~5/4 = 380.189


{{Optimal ET sequence|legend=0| 19e, 41, 142cdf }}
{{Optimal ET sequence|legend=0| 19e, 41, 142cdf }}


Badness: 0.023547
Badness (Smith): 0.023547


==== 17-limit ====
==== 17-limit ====
Line 565: Line 565:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.281
* CTE: ~2 = 1200.000, ~5/4 = 380.281
* POTE: ~2 = 1\1, ~5/4 = 380.114
* POTE: ~2 = 1200.000, ~5/4 = 380.114


{{Optimal ET sequence|legend=0| 19eg, 41, 101cd, 142cdfg }}
{{Optimal ET sequence|legend=0| 19eg, 41, 101cd, 142cdfg }}


Badness: 0.020756
Badness (Smith): 0.020756


==== 19-limit ====
==== 19-limit ====
Line 580: Line 580:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.339
* CTE: ~2 = 1200.000, ~5/4 = 380.339


{{Optimal ET sequence|legend=0| 19egh, 41, 101cdhh, 142cdfghh }}
{{Optimal ET sequence|legend=0| 19egh, 41, 101cdhh, 142cdfghh }}


Badness: 0.018625
Badness (Smith): 0.018625


=== Divination ===
=== Divination ===
Line 594: Line 594:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~5/4 = 380.732
* CTE: ~99/70 = 600.000, ~5/4 = 380.732
* POTE: ~99/70 = 1\2, ~5/4 = 380.223
* POTE: ~99/70 = 600.000, ~5/4 = 380.223


{{Optimal ET sequence|legend=0| 22, 60e, 82e, 104e }}
{{Optimal ET sequence|legend=0| 22, 60e, 82e, 104e }}


Badness: 0.035864
Badness (Smith): 0.035864


==== 13-limit ====
==== 13-limit ====
Line 609: Line 609:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~5/4 = 380.417
* CTE: ~99/70 = 600.000, ~5/4 = 380.417
* POTE: ~99/70 = 1\2, ~5/4 = 379.920
* POTE: ~99/70 = 600.000, ~5/4 = 379.920


{{Optimal ET sequence|legend=0| 22f, 60e, 82ef }}
{{Optimal ET sequence|legend=0| 22f, 60e, 82ef }}


Badness: 0.034551
Badness (Smith): 0.034551


==== 17-limit ====
==== 17-limit ====
Line 624: Line 624:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 1\2, ~5/4 = 380.433
* CTE: ~17/12 = 600.000, ~5/4 = 380.433


{{Optimal ET sequence|legend=0| 22f, 60e, 82ef }}
{{Optimal ET sequence|legend=0| 22f, 60e, 82ef }}


Badness: 0.023775
Badness (Smith): 0.023775


=== Hocus ===
=== Hocus ===
Line 638: Line 638:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/11 = 409.760
* CTE: ~2 = 1200.000, ~14/11 = 409.760
* POTE: ~2 = 1\1, ~14/11 = 409.910
* POTE: ~2 = 1200.000, ~14/11 = 409.910


{{Optimal ET sequence|legend=0| 38d, 41 }}
{{Optimal ET sequence|legend=0| 38d, 41 }}


Badness: 0.038519
Badness (Smith): 0.038519


==== 13-limit ====
==== 13-limit ====
Line 653: Line 653:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/11 = 409.842
* CTE: ~2 = 1200.000, ~14/11 = 409.842
* POTE: ~2 = 1\1, ~14/11 = 410.004
* POTE: ~2 = 1200.000, ~14/11 = 410.004


{{Optimal ET sequence|legend=0| 38df, 41 }}
{{Optimal ET sequence|legend=0| 38df, 41 }}


Badness: 0.030280
Badness (Smith): 0.030280


==== 17-limit ====
==== 17-limit ====
Line 668: Line 668:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/11 = 409.896
* CTE: ~2 = 1200.000, ~14/11 = 409.896


{{Optimal ET sequence|legend=0| 38df, 41, 120cdg, 161cdg, 202ccddfgg }}
{{Optimal ET sequence|legend=0| 38df, 41, 120cdg, 161cdg, 202ccddfgg }}


Badness: 0.025491
Badness (Smith): 0.025491


==== 19-limit ====
==== 19-limit ====
Line 682: Line 682:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/11 = 409.884
* CTE: ~2 = 1200.000, ~14/11 = 409.884


{{Optimal ET sequence|legend=0| 38df, 41, 120cdgh, 161cdgh, 202ccddfgghh }}
{{Optimal ET sequence|legend=0| 38df, 41, 120cdgh, 161cdgh, 202ccddfgghh }}


Badness: 0.020277
Badness (Smith): 0.020277


== Muggles ==
== Muggles ==
Line 702: Line 702:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 378.744
* [[CTE]]: ~2 = 1200.000, ~5/4 = 378.744
* [[POTE]]: ~2 = 1\1, ~5/4 = 378.479
* [[POTE]]: ~2 = 1200.000, ~5/4 = 378.479


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 712: Line 712:
{{Optimal ET sequence|legend=1| 16, 19, 73bcd, 92bcdd, 111bcddd }}
{{Optimal ET sequence|legend=1| 16, 19, 73bcd, 92bcdd, 111bcddd }}


[[Badness]]: 0.056206
[[Badness]] (Smith): 0.056206


=== 11-limit ===
=== 11-limit ===
Line 722: Line 722:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 378.228
* CTE: ~2 = 1200.000, ~5/4 = 378.228
* POTE: ~2 = 1\1, ~5/4 = 377.724
* POTE: ~2 = 1200.000, ~5/4 = 377.724


Tuning ranges:  
Tuning ranges:  
Line 731: Line 731:
{{Optimal ET sequence|legend=0| 16, 19, 54bd }}
{{Optimal ET sequence|legend=0| 16, 19, 54bd }}


Badness: 0.048038
Badness (Smith): 0.048038


==== 13-limit ====
==== 13-limit ====
Line 741: Line 741:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 378.176
* CTE: ~2 = 1200.000, ~5/4 = 378.176
* POTE: ~2 = 1\1, ~5/4 = 377.653
* POTE: ~2 = 1200.000, ~5/4 = 377.653


{{Optimal ET sequence|legend=0| 16, 19, 54bdf }}
{{Optimal ET sequence|legend=0| 16, 19, 54bdf }}


Badness: 0.030386
Badness (Smith): 0.030386


=== Muggloid ===
=== Muggloid ===
Line 756: Line 756:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 377.724
* CTE: ~2 = 1200.000, ~5/4 = 377.724
* POTE: ~2 = 1\1, ~5/4 = 377.832
* POTE: ~2 = 1200.000, ~5/4 = 377.832


{{Optimal ET sequence|legend=0| 3, 10bd, 13bd, 16, 19e, 35ee }}
{{Optimal ET sequence|legend=0| 3, 10bd, 13bd, 16, 19e, 35ee }}


Badness: 0.046970
Badness (Smith): 0.046970


==== 13-limit ====
==== 13-limit ====
Line 771: Line 771:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 377.652
* CTE: ~2 = 1200.000, ~5/4 = 377.652
* POTE: ~2 = 1\1, ~5/4 = 377.838
* POTE: ~2 = 1200.000, ~5/4 = 377.838


{{Optimal ET sequence|legend=0| 3, 10bd, 13bd, 16, 19e, 35eef }}
{{Optimal ET sequence|legend=0| 3, 10bd, 13bd, 16, 19e, 35eef }}


Badness: 0.028732
Badness (Smith): 0.028732


== Darkstone ==
== Darkstone ==
Line 790: Line 790:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 377.385
* [[CTE]]: ~2 = 1200.000, ~5/4 = 377.385


{{Optimal ET sequence|legend=1| 3d, …, 13b, 16, 19d, 35d }}
{{Optimal ET sequence|legend=1| 3d, …, 13b, 16, 19d, 35d }}


[[Badness]]: 0.084213
[[Badness]] (Smith): 0.084213


=== 11-limit ===
=== 11-limit ===
Line 804: Line 804:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 377.388
* CTE: ~2 = 1200.000, ~5/4 = 377.388


{{Optimal ET sequence|legend=0| 3de, …, 13be, 16, 19d, 35d }}
{{Optimal ET sequence|legend=0| 3de, …, 13be, 16, 19d, 35d }}


Badness: 0.046775
Badness (Smith): 0.046775


=== 13-limit ===
=== 13-limit ===
Line 818: Line 818:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 376.914
* CTE: ~2 = 1200.000, ~5/4 = 376.914


{{Optimal ET sequence|legend=0| 3def, …, 16, 35d }}
{{Optimal ET sequence|legend=0| 3def, …, 16, 35d }}


Badness: 0.038328
Badness (Smith): 0.038328


== Brightstone ==
== Brightstone ==
Line 834: Line 834:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 381.955
* [[CTE]]: ~2 = 1200.000, ~5/4 = 381.955


{{Optimal ET sequence|legend=1| 3, …, 19d, 22 }}
{{Optimal ET sequence|legend=1| 3, …, 19d, 22 }}


[[Badness]]: 0.088072
[[Badness]] (Smith): 0.088072


=== 11-limit ===
=== 11-limit ===
Line 848: Line 848:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 381.790
* CTE: ~2 = 1200.000, ~5/4 = 381.790


{{Optimal ET sequence|legend=0| 3, …, 19d, 22 }}
{{Optimal ET sequence|legend=0| 3, …, 19d, 22 }}


Badness: 0.047379
Badness (Smith): 0.047379


=== 13-limit ===
=== 13-limit ===
Line 862: Line 862:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 381.732
* CTE: ~2 = 1200.000, ~5/4 = 381.732


{{Optimal ET sequence|legend=0| 3, …, 19d, 22 }}
{{Optimal ET sequence|legend=0| 3, …, 19d, 22 }}


Badness: 0.039703
Badness (Smith): 0.039703


== Hocum ==
== Hocum ==
Line 880: Line 880:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~63/50 = 409.836
* [[CTE]]: ~2 = 1200.000, ~63/50 = 409.836
* [[POTE]]: ~2 = 1\1, ~63/50 = 410.108
* [[POTE]]: ~2 = 1200.000, ~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 }}


[[Badness]]: 0.107115
[[Badness]] (Smith): 0.107115


== Trismegistus ==
== Trismegistus ==
Line 901: Line 901:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~147/100 = 673.187
* [[CTE]]: ~2 = 1200.000, ~147/100 = 673.187
* [[POTE]]: ~2 = 1\1, ~147/100 = 673.290
* [[POTE]]: ~2 = 1200.000, ~147/100 = 673.290


{{Optimal ET sequence|legend=1| 16, 25, 41 }}
{{Optimal ET sequence|legend=1| 16, 25, 41 }}


[[Badness]]: 0.098334
[[Badness]] (Smith): 0.098334


=== 11-limit ===
=== 11-limit ===
Line 916: Line 916:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~22/15 = 673.241
* CTE: ~2 = 1200.000, ~22/15 = 673.241
* POTE: ~2 = 1\1, ~22/15 = 673.340
* POTE: ~2 = 1200.000, ~22/15 = 673.340


{{Optimal ET sequence|legend=0| 16, 25e, 41, 221cc, 262ccde }}
{{Optimal ET sequence|legend=0| 16, 25e, 41, 221cc, 262ccde }}


Badness: 0.045623
Badness (Smith): 0.045623


=== 13-limit ===
=== 13-limit ===
Line 931: Line 931:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~22/15 = 673.294
* CTE: ~2 = 1200.000, ~22/15 = 673.294
* POTE: ~2 = 1\1, ~22/15 = 673.359
* POTE: ~2 = 1200.000, ~22/15 = 673.359


{{Optimal ET sequence|legend=0| 16, 25e, 41, 139cf, 180cf, 221ccf }}
{{Optimal ET sequence|legend=0| 16, 25e, 41, 139cf, 180cf, 221ccf }}


Badness: 0.033081
Badness (Smith): 0.033081


== Quadrimage ==
== Quadrimage ==
Line 950: Line 950:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~28/25 = 204.860
* [[CTE]]: ~2 = 1200.000, ~28/25 = 204.860
* [[POTE]]: ~2 = 1\1, ~28/25 = 204.987
* [[POTE]]: ~2 = 1200.000, ~28/25 = 204.987


{{Optimal ET sequence|legend=1| 6, …, 29b, 35, 41 }}
{{Optimal ET sequence|legend=1| 6, …, 29b, 35, 41 }}


[[Badness]]: 0.127422
[[Badness]] (Smith): 0.127422


=== 11-limit ===
=== 11-limit ===
Line 965: Line 965:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~28/25 = 204.881
* CTE: ~2 = 1200.000, ~28/25 = 204.881
* POTE: ~2 = 1\1, ~28/25 = 204.956
* POTE: ~2 = 1200.000, ~28/25 = 204.956


{{Optimal ET sequence|legend=0| 6, …, 29b, 35, 41 }}
{{Optimal ET sequence|legend=0| 6, …, 29b, 35, 41 }}


Badness: 0.061572
Badness (Smith): 0.061572


=== 13-limit ===
=== 13-limit ===
Line 980: Line 980:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~28/25 = 204.956
* CTE: ~2 = 1200.000, ~28/25 = 204.956
* POTE: ~2 = 1\1, ~28/25 = 205.028
* POTE: ~2 = 1200.000, ~28/25 = 205.028


{{Optimal ET sequence|legend=0| 35f, 41, 199ccdef, 240ccdef, 281ccdeff }}
{{Optimal ET sequence|legend=0| 35f, 41, 199ccdef, 240ccdef, 281ccdeff }}


Badness: 0.044047
Badness (Smith): 0.044047


== Quinmage ==
== Quinmage ==
Line 997: Line 997:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~48/35 = 556.123
* [[CTE]]: ~2 = 1200.000, ~48/35 = 556.123


{{Optimal ET sequence|legend=1| 13b, 28b, 41 }}
{{Optimal ET sequence|legend=1| 13b, 28b, 41 }}


[[Badness]]: 0.194548
[[Badness]] (Smith): 0.194548


=== 11-limit ===
=== 11-limit ===
Line 1,011: Line 1,011:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/8 = 556.122
* CTE: ~2 = 1200.000, ~11/8 = 556.122


{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}
{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}


Badness: 0.101724
Badness (Smith): 0.101724


=== 13-limit ===
=== 13-limit ===
Line 1,025: Line 1,025:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/8 = 556.106
* CTE: ~2 = 1200.000, ~11/8 = 556.106


{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}
{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}


Badness: 0.067742
Badness (Smith): 0.067742


== Warlock ==
== Warlock ==
Line 1,041: Line 1,041:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~8/7 = 1\5, ~5/4 = 380.499 (~256/245 = 99.501)
* [[CTE]]: ~8/7 = 240.000, ~5/4 = 380.499 (~256/245 = 99.501)
* [[POTE]]: ~8/7 = 1\5, ~5/4 = 379.713 (~256/245 = 100.287)
* [[POTE]]: ~8/7 = 240.000, ~5/4 = 379.713 (~256/245 = 100.287)


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


[[Badness]]: 0.287190
[[Badness]] (Smith): 0.287190


[[Category:Temperament families]]
[[Category:Temperament families]]
Retrieved from "https://en.xen.wiki/w/Magic_family"