Xenharmonic Wiki

Meantone family: Difference between revisions

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→Septimal meantone: someone moved migration away without moving its 13-limit extension
Revert to -CTWE/KE. It was a readability hell
Line 20: Line 20:
{{Multival|legend=1| 1 4 4 }}
{{Multival|legend=1| 1 4 4 }}


[[Optimal tuning]]:
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 697.2143
* [[CTE]]: ~2 = 1\1, ~3/2 = 697.2143
* [[CTWE]]: ~2 = 1\1, ~3/2 = 696.6512


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 31: Line 29:
* 5-odd-limit [[diamond monotone]]: ~3/2 = [685.714, 720.000] (4\7 to 3\5)
* 5-odd-limit [[diamond monotone]]: ~3/2 = [685.714, 720.000] (4\7 to 3\5)
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955] (1/3-comma to Pyth.)
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955] (1/3-comma to Pyth.)
* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955]


{{Optimal ET sequence|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b }}
{{Optimal ET sequence|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b }}
Line 67: Line 64:
Sval mapping: {{mapping| 1 0 -4 5 | 0 1 4 -1 }}
Sval mapping: {{mapping| 1 0 -4 5 | 0 1 4 -1 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0387
* CTE: ~2 = 1\1, ~3/2 = 696.0387
* CTWE: ~2 = 1\1, ~3/2 = 693.1206


Optimal ET sequence: {{Optimal ET sequence| 5, 7, 19e, 26e }}
Optimal ET sequence: {{Optimal ET sequence| 5, 7, 19e, 26e }}
Line 90: Line 85:
{{Multival|legend=1| 1 4 10 4 13 12 }}
{{Multival|legend=1| 1 4 10 4 13 12 }}


[[Optimal tuning]]:
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 696.9521
* [[CTE]]: ~2 = 1\1, ~3/2 = 696.9521
* [[CTWE]]: ~2 = 1\1, ~3/2 = 696.6562


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 121: Line 114:
Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}
Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.1676
* CTE: ~2 = 1\1, ~3/2 = 697.1676
* CTWE: ~2 = 1\1, ~3/2 = 697.0315


Minimax tuning:  
Minimax tuning:  
Line 150: Line 141:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 | 0 1 4 10 18 15 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 | 0 1 4 10 18 15 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8552
* CTE: ~2 = 1\1, ~3/2 = 696.8552
* CTWE: ~2 = 1\1, ~3/2 = 696.7085


Minimax tuning:  
Minimax tuning:  
Line 171: Line 160:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 | 0 1 4 10 18 15 26 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 | 0 1 4 10 18 15 26 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6486
* CTE: ~2 = 1\1, ~3/2 = 696.6486
* CTWE: ~2 = 1\1, ~3/2 = 696.4563


{{Optimal ET sequence|legend=1| 12fg, 19eg, 31, 50e }}
{{Optimal ET sequence|legend=1| 12fg, 19eg, 31, 50e }}
Line 186: Line 173:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 -40 | 0 1 4 10 18 15 26 28 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 -40 | 0 1 4 10 18 15 26 28 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5551
* CTE: ~2 = 1\1, ~3/2 = 696.5551
* CTWE: ~2 = 1\1, ~3/2 = 696.3526


{{Optimal ET sequence|legend=1| 12fghh, 19egh, 31, 50e }}
{{Optimal ET sequence|legend=1| 12fghh, 19egh, 31, 50e }}
Line 203: Line 188:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 | 0 1 4 10 18 15 7 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 | 0 1 4 10 18 15 7 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0360
* CTE: ~2 = 1\1, ~3/2 = 697.0360
* CTWE: ~2 = 1\1, ~3/2 = 696.6155


{{Optimal ET sequence|legend=1| 12f, 19eg, 31g }}
{{Optimal ET sequence|legend=1| 12f, 19eg, 31g }}
Line 218: Line 201:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 -10 | 0 1 4 10 18 15 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 -10 | 0 1 4 10 18 15 7 9 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2161
* CTE: ~2 = 1\1, ~3/2 = 697.2161
* CTWE: ~2 = 1\1, ~3/2 = 696.6169


{{Optimal ET sequence|legend=1| 12f, 19egh, 31gh }}
{{Optimal ET sequence|legend=1| 12f, 19egh, 31gh }}
Line 235: Line 216:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9080
* CTE: ~2 = 1\1, ~3/2 = 696.9080
* CTWE: ~2 = 1\1, ~3/2 = 696.9823


{{Optimal ET sequence|legend=1| 12f, 31 }}
{{Optimal ET sequence|legend=1| 12f, 31 }}
Line 250: Line 229:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 9 | 0 1 4 10 18 15 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 9 | 0 1 4 10 18 15 -5 -3 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9308
* CTE: ~2 = 1\1, ~3/2 = 696.9308
* CTWE: ~2 = 1\1, ~3/2 = 697.1061


{{Optimal ET sequence|legend=1| 12f, 31 }}
{{Optimal ET sequence|legend=1| 12f, 31 }}
Line 267: Line 244:
Mapping: {{mapping| 1 0 -4 -13 -25 29 | 0 1 4 10 18 -16 }}
Mapping: {{mapping| 1 0 -4 -13 -25 29 | 0 1 4 10 18 -16 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2582
* CTE: ~2 = 1\1, ~3/2 = 697.2582
* CTWE: ~2 = 1\1, ~3/2 = 697.2627


Minimax tuning:  
Minimax tuning:  
Line 290: Line 265:
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 | 0 1 4 10 18 -16 -5 }}
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 | 0 1 4 10 18 -16 -5 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2996
* CTE: ~2 = 1\1, ~3/2 = 697.2996
* CTWE: ~2 = 1\1, ~3/2 = 697.3303


{{Optimal ET sequence|legend=1| 12, 31, 43, 74g }}
{{Optimal ET sequence|legend=1| 12, 31, 43, 74g }}
Line 305: Line 278:
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 9 | 0 1 4 10 18 -16 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 9 | 0 1 4 10 18 -16 -5 -3 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.3271
* CTE: ~2 = 1\1, ~3/2 = 697.3271
* CTWE: ~2 = 1\1, ~3/2 = 697.3736


{{Optimal ET sequence|legend=1| 12, 31, 43, 74gh }}
{{Optimal ET sequence|legend=1| 12, 31, 43, 74gh }}
Line 322: Line 293:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 | 0 1 4 10 18 27 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 | 0 1 4 10 18 27 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5155
* CTE: ~2 = 1\1, ~3/2 = 697.5155
* CTWE: ~2 = 1\1, ~3/2 = 697.5241


Minimax tuning:  
Minimax tuning:  
Line 341: Line 310:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -56 | 0 1 4 10 18 27 38 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -56 | 0 1 4 10 18 27 38 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5076
* CTE: ~2 = 1\1, ~3/2 = 697.5076
* CTWE: ~2 = 1\1, ~3/2 = 697.5113


{{Optimal ET sequence|legend=1| 12fg, 31fg, 43 }}
{{Optimal ET sequence|legend=1| 12fg, 31fg, 43 }}
Line 356: Line 323:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -56 -59 | 0 1 4 10 18 27 38 40 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -56 -59 | 0 1 4 10 18 27 38 40 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.4848
* CTE: ~2 = 1\1, ~3/2 = 697.4848
* CTWE: ~2 = 1\1, ~3/2 = 697.4815


{{Optimal ET sequence|legend=1| 12fghh, 31fgh, 43 }}
{{Optimal ET sequence|legend=1| 12fghh, 31fgh, 43 }}
Line 371: Line 336:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 | 0 1 4 10 18 27 7 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 | 0 1 4 10 18 27 7 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.6098
* CTE: ~2 = 1\1, ~3/2 = 697.6098
* CTWE: ~2 = 1\1, ~3/2 = 697.4333


{{Optimal ET sequence|legend=1| 12f, 31fg, 43g }}
{{Optimal ET sequence|legend=1| 12f, 31fg, 43g }}
Line 386: Line 349:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 -10 | 0 1 4 10 18 27 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 -10 | 0 1 4 10 18 27 7 9 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.7012
* CTE: ~2 = 1\1, ~3/2 = 697.7012
* CTWE: ~2 = 1\1, ~3/2 = 697.4045


{{Optimal ET sequence|legend=1| 12f, 19effgh, 31fgh, 43gh }}
{{Optimal ET sequence|legend=1| 12f, 19effgh, 31fgh, 43gh }}
Line 401: Line 362:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 | 0 1 4 10 18 27 -5 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 | 0 1 4 10 18 27 -5 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5384
* CTE: ~2 = 1\1, ~3/2 = 697.5384
* CTWE: ~2 = 1\1, ~3/2 = 697.6222


{{Optimal ET sequence|legend=1| 12f, 43 }}
{{Optimal ET sequence|legend=1| 12f, 43 }}
Line 416: Line 375:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 9 | 0 1 4 10 18 27 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 9 | 0 1 4 10 18 27 -5 -3 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5550
* CTE: ~2 = 1\1, ~3/2 = 697.5550
* CTWE: ~2 = 1\1, ~3/2 = 697.6887


{{Optimal ET sequence|legend=1| 12f, 43 }}
{{Optimal ET sequence|legend=1| 12f, 43 }}
Line 433: Line 390:
: mapping generators: ~2, ~26/15
: mapping generators: ~2, ~26/15


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6109
* CTE: ~2 = 1\1, ~26/15 = 948.6109
* CTWE: ~2 = 1\1, ~26/15 = 948.5065


{{Optimal ET sequence|legend=1| 19e, 43, 62 }}
{{Optimal ET sequence|legend=1| 19e, 43, 62 }}
Line 448: Line 403:
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 | 0 2 8 20 36 11 33 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 | 0 2 8 20 36 11 33 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6173
* CTE: ~2 = 1\1, ~26/15 = 948.6173
* CTWE: ~2 = 1\1, ~26/15 = 948.5169


{{Optimal ET sequence|legend=1| 19eg, 43, 62 }}
{{Optimal ET sequence|legend=1| 19eg, 43, 62 }}
Line 463: Line 416:
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 -25 | 0 2 8 20 36 11 33 37 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 -25 | 0 2 8 20 36 11 33 37 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~19/11 = 948.6088
* CTE: ~2 = 1\1, ~19/11 = 948.6088
* CTWE: ~2 = 1\1, ~19/11 = 948.5111


{{Optimal ET sequence|legend=1| 19egh, 43, 62 }}
{{Optimal ET sequence|legend=1| 19egh, 43, 62 }}
Line 480: Line 431:
: mapping generators: ~55/39, ~3
: mapping generators: ~55/39, ~3


Optimal tuning:
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 697.1678
* CTE: ~55/39 = 1\2, ~3/2 = 697.1678
* CTWE: ~55/39 = 1\2, ~3/2 = 697.0545


{{Optimal ET sequence|legend=1| 12f, 38deefff, 50eff, 62, 136b }}
{{Optimal ET sequence|legend=1| 12f, 38deefff, 50eff, 62, 136b }}
Line 495: Line 444:
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 | 0 1 4 10 18 21 1 }}
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 | 0 1 4 10 18 21 1 }}


Optimal tuning:
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1740
* CTE: ~17/12 = 1\2, ~3/2 = 697.1740
* CTWE: ~17/12 = 1\2, ~3/2 = 696.9858


{{Optimal ET sequence|legend=1| 12f, 50eff, 62, 136bg }}
{{Optimal ET sequence|legend=1| 12f, 50eff, 62, 136bg }}
Line 510: Line 457:
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 -1 | 0 1 4 10 18 21 1 3 }}
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 -1 | 0 1 4 10 18 21 1 3 }}


Optimal tuning:
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1871
* CTE: ~17/12 = 1\2, ~3/2 = 697.1871
* CTWE: ~17/12 = 1\2, ~3/2 = 696.9638


{{Optimal ET sequence|legend=1| 12f, 50eff, 62 }}
{{Optimal ET sequence|legend=1| 12f, 50eff, 62 }}
Line 531: Line 476:
: mapping generator: ~2, ~3
: mapping generator: ~2, ~3


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5311
* CTE: ~2 = 1\1, ~3/2 = 696.5311
* CTWE: ~2 = 1\1, ~3/2 = 696.4509


Minimax tuning:  
Minimax tuning:  
Line 561: Line 504:
Mapping: {{mapping| 1 0 -4 -13 24 -20 | 0 1 4 10 -13 15 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 | 0 1 4 10 -13 15 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3563
* CTE: ~2 = 1\1, ~3/2 = 696.3563
* CTWE: ~2 = 1\1, ~3/2 = 696.2347


Minimax tuning:  
Minimax tuning:  
Line 584: Line 525:
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 | 0 1 4 10 -13 15 26 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 | 0 1 4 10 -13 15 26 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3508
* CTE: ~2 = 1\1, ~3/2 = 696.3508
* CTWE: ~2 = 1\1, ~3/2 = 696.2195


{{Optimal ET sequence|legend=1| 19g, 31, 50, 81, 131bd }}
{{Optimal ET sequence|legend=1| 19g, 31, 50, 81, 131bd }}
Line 599: Line 538:
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 -40 | 0 1 4 10 -13 15 26 28 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 -40 | 0 1 4 10 -13 15 26 28 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3471
* CTE: ~2 = 1\1, ~3/2 = 696.3471
* CTWE: ~2 = 1\1, ~3/2 = 696.2137


{{Optimal ET sequence|legend=1| 19gh, 31, 50, 81 }}
{{Optimal ET sequence|legend=1| 19gh, 31, 50, 81 }}
Line 614: Line 551:
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 | 0 1 4 10 -13 15 -5 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 | 0 1 4 10 -13 15 -5 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4388
* CTE: ~2 = 1\1, ~3/2 = 696.4388
* CTWE: ~2 = 1\1, ~3/2 = 696.4114


{{Optimal ET sequence|legend=1| 19, 31 }}
{{Optimal ET sequence|legend=1| 19, 31 }}
Line 629: Line 564:
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 9 | 0 1 4 10 -13 15 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 9 | 0 1 4 10 -13 15 -5 -3 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4838
* CTE: ~2 = 1\1, ~3/2 = 696.4838
* CTWE: ~2 = 1\1, ~3/2 = 696.4973


{{Optimal ET sequence|legend=1| 12ef, 19, 31 }}
{{Optimal ET sequence|legend=1| 12ef, 19, 31 }}
Line 644: Line 577:
Mapping: {{mapping| 1 0 -4 -13 24 10 | 0 1 4 10 -13 -4 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 | 0 1 4 10 -13 -4 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2827
* CTE: ~2 = 1\1, ~3/2 = 696.2827
* CTWE: ~2 = 1\1, ~3/2 = 696.4246


Minimax tuning:  
Minimax tuning:  
Line 663: Line 594:
Mapping: {{mapping| 1 0 -4 -13 24 10 12 | 0 1 4 10 -13 -4 -5 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 12 | 0 1 4 10 -13 -4 -5 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4069
* CTE: ~2 = 1\1, ~3/2 = 696.4069
* CTWE: ~2 = 1\1, ~3/2 = 696.4129


{{Optimal ET sequence|legend=1| 12e, 19 }}
{{Optimal ET sequence|legend=1| 12e, 19 }}
Line 678: Line 607:
Mapping: {{mapping| 1 0 -4 -13 24 10 12 9 | 0 1 4 10 -13 -4 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 12 9 | 0 1 4 10 -13 -4 -5 -3 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4731
* CTE: ~2 = 1\1, ~3/2 = 696.4731
* CTWE: ~2 = 1\1, ~3/2 = 696.4949


{{Optimal ET sequence|legend=1| 12e, 19 }}
{{Optimal ET sequence|legend=1| 12e, 19 }}
Line 693: Line 620:
Mapping: {{mapping| 1 0 -4 -13 24 10 -7 | 0 1 4 10 -13 -4 7 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 -7 | 0 1 4 10 -13 -4 7 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6614
* CTE: ~2 = 1\1, ~3/2 = 696.6614
* CTWE: ~2 = 1\1, ~3/2 = 696.4462


{{Optimal ET sequence|legend=1| 12e, 19g, 31fg }}
{{Optimal ET sequence|legend=1| 12e, 19g, 31fg }}
Line 708: Line 633:
Mapping: {{mapping| 1 0 -4 -13 24 10 -7 -10 | 0 1 4 10 -13 -4 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 -7 -10 | 0 1 4 10 -13 -4 7 9 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0160
* CTE: ~2 = 1\1, ~3/2 = 697.0160
* CTWE: ~2 = 1\1, ~3/2 = 696.6337


{{Optimal ET sequence|legend=1| 12e, 19gh, 31fgh }}
{{Optimal ET sequence|legend=1| 12e, 19gh, 31fgh }}
Line 725: Line 648:
Mapping: {{mapping| 1 0 -4 -13 -6 | 0 1 4 10 6 }}
Mapping: {{mapping| 1 0 -4 -13 -6 | 0 1 4 10 6 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1527
* CTE: ~2 = 1\1, ~3/2 = 696.1527
* CTWE: ~2 = 1\1, ~3/2 = 696.2083


Tuning ranges:  
Tuning ranges:  
Line 744: Line 665:
Mapping: {{mapping| 1 0 -4 -13 -6 -20 | 0 1 4 10 6 15 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 | 0 1 4 10 6 15 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0983
* CTE: ~2 = 1\1, ~3/2 = 696.0983
* CTWE: ~2 = 1\1, ~3/2 = 696.1241


{{Optimal ET sequence|legend=1| 7df, 12f, 19, 31e }}
{{Optimal ET sequence|legend=1| 7df, 12f, 19, 31e }}
Line 759: Line 678:
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 | 0 1 4 10 6 15 -5 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 | 0 1 4 10 6 15 -5 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2161
* CTE: ~2 = 1\1, ~3/2 = 696.2161
* CTWE: ~2 = 1\1, ~3/2 = 696.4999


{{Optimal ET sequence|legend=1| 12f, 19, 31e }}
{{Optimal ET sequence|legend=1| 12f, 19, 31e }}
Line 774: Line 691:
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 9 | 0 1 4 10 6 15 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 9 | 0 1 4 10 6 15 -5 -3 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2774
* CTE: ~2 = 1\1, ~3/2 = 696.2774
* CTWE: ~2 = 1\1, ~3/2 = 696.6370


{{Optimal ET sequence|legend=1| 12f, 19, 31e }}
{{Optimal ET sequence|legend=1| 12f, 19, 31e }}
Line 789: Line 704:
Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 | 0 1 4 10 6 15 7 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 | 0 1 4 10 6 15 7 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4501
* CTE: ~2 = 1\1, ~3/2 = 696.4501
* CTWE: ~2 = 1\1, ~3/2 = 696.1417


{{Optimal ET sequence|legend=1| 7dfg, 12f, 19g }}
{{Optimal ET sequence|legend=1| 7dfg, 12f, 19g }}
Line 804: Line 717:
Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 -10 | 0 1 4 10 6 15 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 -10 | 0 1 4 10 6 15 7 9 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.7925
* CTE: ~2 = 1\1, ~3/2 = 696.7925
* CTWE: ~2 = 1\1, ~3/2 = 696.3052


{{Optimal ET sequence|legend=1| 7dfgh, 12f, 19gh }}
{{Optimal ET sequence|legend=1| 7dfgh, 12f, 19gh }}
Line 819: Line 730:
Mapping: {{mapping| 1 0 -4 -13 -6 10 | 0 1 4 10 6 -4 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 | 0 1 4 10 6 -4 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7897
* CTE: ~2 = 1\1, ~3/2 = 695.7897
* CTWE: ~2 = 1\1, ~3/2 = 695.2045


{{Optimal ET sequence|legend=1| 7d, 12, 19 }}
{{Optimal ET sequence|legend=1| 7d, 12, 19 }}
Line 834: Line 743:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 | 0 1 4 10 6 -4 -5 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 | 0 1 4 10 6 -4 -5 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0114
* CTE: ~2 = 1\1, ~3/2 = 696.0114
* CTWE: ~2 = 1\1, ~3/2 = 695.8771


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 849: Line 756:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 | 0 1 4 10 6 -4 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 | 0 1 4 10 6 -4 -5 -3 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1196
* CTE: ~2 = 1\1, ~3/2 = 696.1196
* CTWE: ~2 = 1\1, ~3/2 = 696.1262


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 955: Line 860:
Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 | 0 1 4 10 6 -4 7 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 | 0 1 4 10 6 -4 7 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4125
* CTE: ~2 = 1\1, ~3/2 = 696.4125
* CTWE: ~2 = 1\1, ~3/2 = 695.5584


{{Optimal ET sequence|legend=1| 7dg, 12, 19g }}
{{Optimal ET sequence|legend=1| 7dg, 12, 19g }}
Line 970: Line 873:
Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 -10 | 0 1 4 10 6 -4 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 -10 | 0 1 4 10 6 -4 7 9 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9500
* CTE: ~2 = 1\1, ~3/2 = 696.9500
* CTWE: ~2 = 1\1, ~3/2 = 695.9548


{{Optimal ET sequence|legend=1| 7dgh, 12, 19gh }}
{{Optimal ET sequence|legend=1| 7dgh, 12, 19gh }}
Line 985: Line 886:
Mapping: {{mapping| 1 0 -4 -13 -6 -1 | 0 1 4 10 6 3 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -1 | 0 1 4 10 6 3 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6202
* CTE: ~2 = 1\1, ~3/2 = 695.6202
* CTWE: ~2 = 1\1, ~3/2 = 696.7474


{{Optimal ET sequence|legend=1| 7d, 12f, 19f }}
{{Optimal ET sequence|legend=1| 7d, 12f, 19f }}
Line 1,000: Line 899:
Mapping: {{mapping| 1 0 -4 -13 -6 -1 -7 | 0 1 4 10 6 3 7 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -1 -7 | 0 1 4 10 6 3 7 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2789
* CTE: ~2 = 1\1, ~3/2 = 696.2789
* CTWE: ~2 = 1\1, ~3/2 = 697.1744


{{Optimal ET sequence|legend=1| 7dg, 12f }}
{{Optimal ET sequence|legend=1| 7dg, 12f }}
Line 1,015: Line 912:
Mapping: {{mapping| 1 0 -4 -13 -6 -1 -7 -10 | 0 1 4 10 6 3 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -1 -7 -10 | 0 1 4 10 6 3 7 9 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8486
* CTE: ~2 = 1\1, ~3/2 = 696.8486
* CTWE: ~2 = 1\1, ~3/2 = 697.7122


{{Optimal ET sequence|legend=1| 7dgh, 12f }}
{{Optimal ET sequence|legend=1| 7dgh, 12f }}
Line 1,032: Line 927:
Mapping: {{mapping| 1 0 -4 -13 5 | 0 1 4 10 -1 }}
Mapping: {{mapping| 1 0 -4 -13 5 | 0 1 4 10 -1 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.7022
* CTE: ~2 = 1\1, ~3/2 = 696.7022
* CTWE: ~2 = 1\1, ~3/2 = 695.1805


{{Optimal ET sequence|legend=1| 7d, 12e, 19e }}
{{Optimal ET sequence|legend=1| 7d, 12e, 19e }}
Line 1,047: Line 940:
Mapping: {{mapping| 1 0 -4 -13 5 10 | 0 1 4 10 -1 -4 }}
Mapping: {{mapping| 1 0 -4 -13 5 10 | 0 1 4 10 -1 -4 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2408
* CTE: ~2 = 1\1, ~3/2 = 696.2408
* CTWE: ~2 = 1\1, ~3/2 = 695.0144


{{Optimal ET sequence|legend=1| 7d, 12e, 19e }}
{{Optimal ET sequence|legend=1| 7d, 12e, 19e }}
Line 1,066: Line 957:
: mapping generators: ~63/44, ~3
: mapping generators: ~63/44, ~3


Optimal tuning:
Optimal tuning (CTE): ~63/44 = 1\2, ~3/2 = 696.5199
* CTE: ~63/44 = 1\2, ~3/2 = 696.5199
* CTWE: ~63/44 = 1\2, ~3/2 = 696.1908


{{Optimal ET sequence|legend=1| 12, 26de, 38d, 50 }}
{{Optimal ET sequence|legend=1| 12, 26de, 38d, 50 }}
Line 1,081: Line 970:
Mapping: {{mapping| 2 0 -8 -26 -31 -40 | 0 1 4 10 12 15 }}
Mapping: {{mapping| 2 0 -8 -26 -31 -40 | 0 1 4 10 12 15 }}


Optimal tuning:
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 696.3410
* CTE: ~55/39 = 1\2, ~3/2 = 696.3410
* CTWE: ~55/39 = 1\2, ~3/2 = 696.0066


{{Optimal ET sequence|legend=1| 12f, 26deff, 38df, 50 }}
{{Optimal ET sequence|legend=1| 12f, 26deff, 38df, 50 }}
Line 1,096: Line 983:
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 | 0 1 4 10 12 15 1 }}
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 | 0 1 4 10 12 15 1 }}


Optimal tuning:
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 696.3526
* CTE: ~17/12 = 1\2, ~3/2 = 696.3526
* CTWE: ~17/12 = 1\2, ~3/2 = 695.9317


{{Optimal ET sequence|legend=1| 12f, 38df, 50 }}
{{Optimal ET sequence|legend=1| 12f, 38df, 50 }}
Line 1,111: Line 996:
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 -1 | 0 1 4 10 12 15 1 3 }}
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 -1 | 0 1 4 10 12 15 1 3 }}


Optimal tuning:
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 696.3837
* CTE: ~17/12 = 1\2, ~3/2 = 696.3837
* CTWE: ~17/12 = 1\2, ~3/2 = 695.8947


{{Optimal ET sequence|legend=1| 12f, 26deff, 38df, 50 }}
{{Optimal ET sequence|legend=1| 12f, 26deff, 38df, 50 }}
Line 1,128: Line 1,011:
: mapping generators: ~2, ~11/10
: mapping generators: ~2, ~11/10


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7074
* CTE: ~2 = 1\1, ~11/10 = 167.7074
* CTWE: ~2 = 1\1, ~11/10 = 167.7749


{{Optimal ET sequence|legend=1| 7d, 36d, 43, 50, 93 }}
{{Optimal ET sequence|legend=1| 7d, 36d, 43, 50, 93 }}
Line 1,143: Line 1,024:
Mapping: {{mapping| 1 2 4 7 5 3 | 0 -3 -12 -30 -11 5 }}
Mapping: {{mapping| 1 2 4 7 5 3 | 0 -3 -12 -30 -11 5 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7121
* CTE: ~2 = 1\1, ~11/10 = 167.7121
* CTWE: ~2 = 1\1, ~11/10 = 167.7728


{{Optimal ET sequence|legend=1| 7d, 43, 50, 93 }}
{{Optimal ET sequence|legend=1| 7d, 43, 50, 93 }}
Line 1,158: Line 1,037:
Mapping: {{mapping| 1 2 4 7 5 3 8 | 0 -3 -12 -30 -11 5 -28 }}
Mapping: {{mapping| 1 2 4 7 5 3 8 | 0 -3 -12 -30 -11 5 -28 }}


Optimal tuning:
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7047
* CTE: ~2 = 1\1, ~11/10 = 167.7047
* CTWE: ~2 = 1\1, ~11/10 = 167.7682


{{Optimal ET sequence|legend=1| 7dg, 43, 50, 93 }}
{{Optimal ET sequence|legend=1| 7dg, 43, 50, 93 }}
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