Xenharmonic Wiki

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VisualWikitext
-diamond monotone and tradeoff range (trivial and lack of significance)
Unify to 3 decimal places. Re-adopt template: Optimal ET sequence for all the sections. Misc cleanup
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 380.4994
* [[CTE]]: ~2 = 1\1, ~5/4 = 380.499
* [[POTE]]: ~2 = 1\1, ~5/4 = 380.058
* [[POTE]]: ~2 = 1\1, ~5/4 = 380.058


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[5-odd-limit]]: ~5/4 = {{monzo| 0 1/5 0 }}
* [[5-odd-limit]]: ~5/4 = {{monzo| 0 1/5 0 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 62: Line 62:
{{Mapping|legend=1| 1 0 2 -1 | 0 5 1 12 }}
{{Mapping|legend=1| 1 0 2 -1 | 0 5 1 12 }}


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


{{Multival|legend=1| 5 1 12 -10 5 25 }}
{{Multival|legend=1| 5 1 12 -10 5 25 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 380.6512
* [[CTE]]: ~2 = 1\1, ~5/4 = 380.651
* [[POTE]]: ~2 = 1\1, ~5/4 = 380.352
* [[POTE]]: ~2 = 1\1, ~5/4 = 380.352


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and [[9-odd-limit]]: ~5/4 = {{monzo| 0 1/5 0 0 }}
* 7- and [[9-odd-limit]]: ~5/4 = {{monzo| 0 1/5 0 0 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 93: Line 93:
Mapping: {{mapping| 1 0 2 -1 6 | 0 5 1 12 -8 }}
Mapping: {{mapping| 1 0 2 -1 6 | 0 5 1 12 -8 }}


{{Multival|legend=1| 5 1 12 -8 -10 5 -30 25 -22 -64 }}
Wedgie: {{Multival| 5 1 12 -8 -10 5 -30 25 -22 -64 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.7200
* CTE: ~2 = 1\1, ~5/4 = 380.720
* POTE: ~2 = 1\1, ~5/4 = 380.696
* POTE: ~2 = 1\1, ~5/4 = 380.696


Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~5/4 = {{monzo| 1/3 1/9 0 0 -1/18 }}
* 11-odd-limit: ~5/4 = {{monzo| 1/3 1/9 0 0 -1/18 }}
: Eigenmonzo (unchanged-interval) basis: 2.11/9
: eigenmonzo (unchanged-interval) basis: 2.11/9


Tuning ranges:  
Tuning ranges:  
Line 107: Line 107:
* 11-odd-limit diamond tradeoff: ~5/4 = [378.910, 386.314] (1/4-comma to untempered)
* 11-odd-limit diamond tradeoff: ~5/4 = [378.910, 386.314] (1/4-comma to untempered)


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


Badness: 0.020352
Badness: 0.020352
Line 121: Line 121:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.4354
* CTE: ~2 = 1\1, ~5/4 = 380.435
* POTE: ~2 = 1\1, ~5/4 = 380.427
* POTE: ~2 = 1\1, ~5/4 = 380.427


Line 128: Line 128:
* 13- and 15-odd-limit diamond tradeoff: ~5/4 = [378.617, 386.314]
* 13- and 15-odd-limit diamond tradeoff: ~5/4 = [378.617, 386.314]


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


Badness: 0.021509
Badness: 0.021509
Line 140: Line 140:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.5103
* CTE: ~2 = 1\1, ~5/4 = 380.510
* POTE: ~2 = 1\1, ~5/4 = 380.604
* POTE: ~2 = 1\1, ~5/4 = 380.604


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


Badness: 0.020633
Badness: 0.020633
Line 155: Line 155:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.4507
* CTE: ~2 = 1\1, ~5/4 = 380.451


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


Badness: 0.020881
Badness: 0.020881
Line 169: Line 169:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.5733
* CTE: ~2 = 1\1, ~5/4 = 380.573


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


Badness: 0.019945
Badness: 0.019945
Line 183: Line 183:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.2706
* CTE: ~2 = 1\1, ~5/4 = 380.271


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


Badness: 0.026232
Badness: 0.026232
Line 197: Line 197:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.3604
* CTE: ~2 = 1\1, ~5/4 = 380.360


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


Badness: 0.023709
Badness: 0.023709
Line 215: Line 215:
* POTE: ~2 = 1\1, ~5/4 = 380.416
* POTE: ~2 = 1\1, ~5/4 = 380.416


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


==== Sorcery ====
==== Sorcery ====
Line 225: Line 225:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.6741
* CTE: ~2 = 1\1, ~5/4 = 380.674
* POTE: ~2 = 1\1, ~5/4 = 380.477
* POTE: ~2 = 1\1, ~5/4 = 380.477


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


Badness: 0.025829
Badness: 0.025829
Line 240: Line 240:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.7839
* CTE: ~2 = 1\1, ~5/4 = 380.784
* POTE: ~2 = 1\1, ~5/4 = 380.729
* POTE: ~2 = 1\1, ~5/4 = 380.729


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


Badness: 0.023768
Badness: 0.023768
Line 255: Line 255:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.6248
* CTE: ~2 = 1\1, ~5/4 = 380.625


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


Badness: 0.023232
Badness: 0.023232
Line 269: Line 269:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.7876
* CTE: ~2 = 1\1, ~5/4 = 380.788
* POTE: ~2 = 1\1, ~5/4 = 380.787
* POTE: ~2 = 1\1, ~5/4 = 380.787


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


Badness: 0.025275
Badness: 0.025275
Line 284: Line 284:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.8373
* CTE: ~2 = 1\1, ~5/4 = 380.837
* POTE: ~2 = 1\1, ~5/4 = 380.827
* POTE: ~2 = 1\1, ~5/4 = 380.827


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


Badness: 0.022032
Badness: 0.022032
Line 299: Line 299:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.7411
* CTE: ~2 = 1\1, ~5/4 = 380.741


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


Badness: 0.021101
Badness: 0.021101
Line 313: Line 313:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 1\2, ~5/4 = 380.5385
* CTE: ~55/39 = 1\2, ~5/4 = 380.539
* POTE: ~55/39 = 1\2, ~5/4 = 380.508
* POTE: ~55/39 = 1\2, ~5/4 = 380.508


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


Badness: 0.055443
Badness: 0.055443
Line 328: Line 328:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 1\2, ~5/4 = 380.5533
* CTE: ~17/12 = 1\2, ~5/4 = 380.553
* POTE: ~17/12 = 1\2, ~5/4 = 380.508
* POTE: ~17/12 = 1\2, ~5/4 = 380.508


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


Badness: 0.035654
Badness: 0.035654
Line 343: Line 343:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 1\2, ~5/4 = 380.4704
* CTE: ~17/12 = 1\2, ~5/4 = 380.470


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


Badness: 0.031291
Badness: 0.031291
Line 359: Line 359:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 381.2311
* CTE: ~2 = 1\1, ~5/4 = 381.231
* POTE: ~2 = 1\1, ~5/4 = 381.019
* POTE: ~2 = 1\1, ~5/4 = 381.019


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


Badness: 0.027109
Badness: 0.027109
Line 374: Line 374:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 381.1957
* CTE: ~2 = 1\1, ~5/4 = 381.196
* POTE: ~2 = 1\1, ~5/4 = 380.520
* POTE: ~2 = 1\1, ~5/4 = 380.520


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


Badness: 0.025522
Badness: 0.025522
Line 389: Line 389:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 381.2884
* CTE: ~2 = 1\1, ~5/4 = 381.288
* POTE: ~2 = 1\1, ~5/4 = 380.619
* POTE: ~2 = 1\1, ~5/4 = 380.619


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


Badness: 0.020201
Badness: 0.020201
Line 404: Line 404:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 381.4641
* CTE: ~2 = 1\1, ~5/4 = 381.464


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


Badness: 0.019004
Badness: 0.019004
Line 418: Line 418:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.8157
* CTE: ~2 = 1\1, ~5/4 = 380.816
* POTE: ~2 = 1\1, ~5/4 = 380.483
* POTE: ~2 = 1\1, ~5/4 = 380.483


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


Badness: 0.026089
Badness: 0.026089
Line 433: Line 433:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.9518
* CTE: ~2 = 1\1, ~5/4 = 380.952
* POTE: ~2 = 1\1, ~5/4 = 380.604
* POTE: ~2 = 1\1, ~5/4 = 380.604


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


Badness: 0.020274
Badness: 0.020274
Line 448: Line 448:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.8658
* CTE: ~2 = 1\1, ~5/4 = 380.866


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


Badness: 0.019518
Badness: 0.019518
Line 462: Line 462:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 379.7959
* CTE: ~2 = 1\1, ~5/4 = 379.796
* POTE: ~2 = 1\1, ~5/4 = 379.642
* POTE: ~2 = 1\1, ~5/4 = 379.642


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


Badness: 0.039282
Badness: 0.039282
Line 477: Line 477:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 379.8847
* CTE: ~2 = 1\1, ~5/4 = 379.885
* POTE: ~2 = 1\1, ~5/4 = 379.791
* POTE: ~2 = 1\1, ~5/4 = 379.791


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


Badness: 0.031938
Badness: 0.031938
Line 492: Line 492:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.2159
* CTE: ~2 = 1\1, ~5/4 = 380.216


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


Badness: 0.028074
Badness: 0.028074
Line 506: Line 506:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 379.5237
* CTE: ~2 = 1\1, ~5/4 = 379.524


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


Badness: 0.029556
Badness: 0.029556
Line 520: Line 520:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 379.7574
* CTE: ~2 = 1\1, ~5/4 = 379.757
* POTE: ~2 = 1\1, ~5/4 = 379.116
* POTE: ~2 = 1\1, ~5/4 = 379.116


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


Badness: 0.033317
Badness: 0.033317
Line 535: Line 535:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.4163
* CTE: ~2 = 1\1, ~5/4 = 380.416
* POTE: ~2 = 1\1, ~5/4 = 380.232
* POTE: ~2 = 1\1, ~5/4 = 380.232


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


Badness: 0.030706
Badness: 0.030706
Line 550: Line 550:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.3523
* CTE: ~2 = 1\1, ~5/4 = 380.352
* POTE: ~2 = 1\1, ~5/4 = 380.189
* POTE: ~2 = 1\1, ~5/4 = 380.189


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


Badness: 0.023547
Badness: 0.023547
Line 565: Line 565:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.2809
* CTE: ~2 = 1\1, ~5/4 = 380.281
* POTE: ~2 = 1\1, ~5/4 = 380.114
* POTE: ~2 = 1\1, ~5/4 = 380.114


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


Badness: 0.020756
Badness: 0.020756
Line 580: Line 580:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 380.3389
* CTE: ~2 = 1\1, ~5/4 = 380.339


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


Badness: 0.018625
Badness: 0.018625
Line 594: Line 594:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~5/4 = 380.7317
* CTE: ~99/70 = 1\2, ~5/4 = 380.732
* POTE: ~99/70 = 1\2, ~5/4 = 380.223
* POTE: ~99/70 = 1\2, ~5/4 = 380.223


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


Badness: 0.035864
Badness: 0.035864
Line 609: Line 609:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~5/4 = 380.4171
* CTE: ~99/70 = 1\2, ~5/4 = 380.417
* POTE: ~99/70 = 1\2, ~5/4 = 379.920
* POTE: ~99/70 = 1\2, ~5/4 = 379.920


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


Badness: 0.034551
Badness: 0.034551
Line 624: Line 624:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 1\2, ~5/4 = 380.4329
* CTE: ~17/12 = 1\2, ~5/4 = 380.433


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


Badness: 0.023775
Badness: 0.023775
Line 638: Line 638:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/11 = 409.7603
* CTE: ~2 = 1\1, ~14/11 = 409.760
* POTE: ~2 = 1\1, ~14/11 = 409.910
* POTE: ~2 = 1\1, ~14/11 = 409.910


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


Badness: 0.038519
Badness: 0.038519
Line 653: Line 653:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/11 = 409.8421
* CTE: ~2 = 1\1, ~14/11 = 409.842
* POTE: ~2 = 1\1, ~14/11 = 410.004
* POTE: ~2 = 1\1, ~14/11 = 410.004


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


Badness: 0.030280
Badness: 0.030280
Line 668: Line 668:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/11 = 409.8958
* CTE: ~2 = 1\1, ~14/11 = 409.896


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


Badness: 0.025491
Badness: 0.025491
Line 682: Line 682:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/11 = 409.8836
* CTE: ~2 = 1\1, ~14/11 = 409.884


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


Badness: 0.020277
Badness: 0.020277
Line 729: Line 729:
* 11-odd-limit diamond tradeoff: ~5/4 = [347.408, 386.314]
* 11-odd-limit diamond tradeoff: ~5/4 = [347.408, 386.314]


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


Badness: 0.048038
Badness: 0.048038
Line 741: Line 741:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 378.1761
* CTE: ~2 = 1\1, ~5/4 = 378.176
* POTE: ~2 = 1\1, ~5/4 = 377.653
* POTE: ~2 = 1\1, ~5/4 = 377.653


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


Badness: 0.030386
Badness: 0.030386
Line 759: Line 759:
* POTE: ~2 = 1\1, ~5/4 = 377.832
* POTE: ~2 = 1\1, ~5/4 = 377.832


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


Badness: 0.046970
Badness: 0.046970
Line 774: Line 774:
* POTE: ~2 = 1\1, ~5/4 = 377.838
* POTE: ~2 = 1\1, ~5/4 = 377.838


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


Badness: 0.028732
Badness: 0.028732
Line 806: Line 806:
* CTE: ~2 = 1\1, ~5/4 = 377.388
* CTE: ~2 = 1\1, ~5/4 = 377.388


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


Badness: 0.046775
Badness: 0.046775
Line 820: Line 820:
* CTE: ~2 = 1\1, ~5/4 = 376.914
* CTE: ~2 = 1\1, ~5/4 = 376.914


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


Badness: 0.038328
Badness: 0.038328


== Brightstone ==
== Brightstone ==
{{See also| Archytas clan }}
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 852: Line 850:
* CTE: ~2 = 1\1, ~5/4 = 381.790
* CTE: ~2 = 1\1, ~5/4 = 381.790


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


Badness: 0.047379
Badness: 0.047379
Line 866: Line 864:
* CTE: ~2 = 1\1, ~5/4 = 381.732
* CTE: ~2 = 1\1, ~5/4 = 381.732


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


Badness: 0.039703
Badness: 0.039703
Line 921: Line 919:
* POTE: ~2 = 1\1, ~22/15 = 673.340
* POTE: ~2 = 1\1, ~22/15 = 673.340


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


Badness: 0.045623
Badness: 0.045623
Line 936: Line 934:
* POTE: ~2 = 1\1, ~22/15 = 673.359
* POTE: ~2 = 1\1, ~22/15 = 673.359


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


Badness: 0.033081
Badness: 0.033081
Line 970: Line 968:
* POTE: ~2 = 1\1, ~28/25 = 204.956
* POTE: ~2 = 1\1, ~28/25 = 204.956


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


Badness: 0.061572
Badness: 0.061572
Line 985: Line 983:
* POTE: ~2 = 1\1, ~28/25 = 205.028
* POTE: ~2 = 1\1, ~28/25 = 205.028


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


Badness: 0.044047
Badness: 0.044047
Line 1,015: Line 1,013:
* CTE: ~2 = 1\1, ~11/8 = 556.122
* CTE: ~2 = 1\1, ~11/8 = 556.122


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


Badness: 0.101724
Badness: 0.101724
Line 1,029: Line 1,027:
* CTE: ~2 = 1\1, ~11/8 = 556.106
* CTE: ~2 = 1\1, ~11/8 = 556.106


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


Badness: 0.067742
Badness: 0.067742
Line 1,044: Line 1,042:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~8/7 = 1\5, ~5/4 = 380.499 (~256/245 = 99.501)
* [[CTE]]: ~8/7 = 1\5, ~5/4 = 380.499 (~256/245 = 99.501)
* [[POTE]]: ~8/7 = 1\5, ~5/4 = 379.7131 (~256/245 = 100.2869)
* [[POTE]]: ~8/7 = 1\5, ~5/4 = 379.713 (~256/245 = 100.287)


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