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Meantone family: Difference between revisions

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* strict range: [694.786, 701.955]
* strict range: [694.786, 701.955]


{{Vals|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }}
{{Val list|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }}


[[Badness]]: 0.00736
[[Badness]]: 0.00736
Line 200: Line 200:
Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly.
Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly.


{{Vals|legend=1| 12, 19, 31, 81, 112b, 143b }}
{{Val list|legend=1| 12, 19, 31, 81, 112b, 143b }}


[[Badness]]: 0.0137
[[Badness]]: 0.0137
Line 229: Line 229:
Mapping generators: ~63/44, ~3
Mapping generators: ~63/44, ~3


{{Vals|legend=1| 12, 26de, 38d, 50 }}
{{Val list|legend=1| 12, 26de, 38d, 50 }}


Badness: 0.0381
Badness: 0.0381
Line 257: Line 257:
Mapping generators: ~55/39, ~3
Mapping generators: ~55/39, ~3


{{Vals|legend=1| 12f, 26deff, 38df, 50 }}
{{Val list|legend=1| 12f, 26deff, 38df, 50 }}


Badness: 0.0288
Badness: 0.0288
Line 298: Line 298:
[[Algebraic generator]]: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.
[[Algebraic generator]]: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.


{{Vals|legend=1| 12, 19e, 31, 105, 136b, 167be, 198be }}
{{Val list|legend=1| 12, 19e, 31, 105, 136b, 167be, 198be }}


Badness: 0.0170
Badness: 0.0170
Line 328: Line 328:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 12f, 19e, 31 }}
{{Val list|legend=1| 12f, 19e, 31 }}


Badness: 0.0180
Badness: 0.0180
Line 361: Line 361:
* strict range: [696.774, 700.000]
* strict range: [696.774, 700.000]


{{Vals|legend=1| 12, 19ef, 31, 43, 74 }}
{{Val list|legend=1| 12, 19ef, 31, 43, 74 }}


Badness: 0.0259
Badness: 0.0259
Line 389: Line 389:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 12f, 31f, 43 }}
{{Val list|legend=1| 12f, 31f, 43 }}


Badness: 0.0264
Badness: 0.0264
Line 417: Line 417:
Mapping generators: ~2, ~26/15
Mapping generators: ~2, ~26/15


{{Vals|legend=1| 19e, 43, 62, 167bef }}
{{Val list|legend=1| 19e, 43, 62, 167bef }}


Badness: 0.0314
Badness: 0.0314
Line 458: Line 458:
Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.
Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.


{{Vals|legend=1| 12e, 19, 31, 81 }}
{{Val list|legend=1| 12e, 19, 31, 81 }}


[[Badness]]: 0.0215
[[Badness]]: 0.0215
Line 494: Line 494:
* strict range: [694.737, 696.774]
* strict range: [694.737, 696.774]


{{Vals|legend=1| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }}
{{Val list|legend=1| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }}


Badness: 0.0209
Badness: 0.0209
Line 522: Line 522:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 12e, 19, 31f, 50ff, 81fff }}
{{Val list|legend=1| 12e, 19, 31f, 50ff, 81fff }}


Badness: 0.0277
Badness: 0.0277
Line 550: Line 550:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19, 31e, 50ee }}
{{Val list|legend=1| 7d, 12, 19, 31e, 50ee }}


Badness: 0.0214
Badness: 0.0214
Line 578: Line 578:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 12f, 19, 31e, 50ee }}
{{Val list|legend=1| 12f, 19, 31e, 50ee }}


Badness: 0.0212
Badness: 0.0212
Line 606: Line 606:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0248
Badness: 0.0248
Line 634: Line 634:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0255
Badness: 0.0255
Line 662: Line 662:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0223
Badness: 0.0223
Line 690: Line 690:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0201
Badness: 0.0201
Line 718: Line 718:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0182
Badness: 0.0182
Line 746: Line 746:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0171
Badness: 0.0171
Line 774: Line 774:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0161
Badness: 0.0161
Line 802: Line 802:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0154
Badness: 0.0154
Line 830: Line 830:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0139
Badness: 0.0139
Line 858: Line 858:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12, 19 }}
{{Val list|legend=1| 7d, 12, 19 }}


Badness: 0.0138
Badness: 0.0138
Line 886: Line 886:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12f, 19f, 31eff }}
{{Val list|legend=1| 7d, 12f, 19f, 31eff }}


Badness: 0.0242
Badness: 0.0242
Line 916: Line 916:
Mapping generator: ~3
Mapping generator: ~3


{{Vals|legend=1| 7d, 12e, 19e }}
{{Val list|legend=1| 7d, 12e, 19e }}


Badness: 0.0315
Badness: 0.0315
Line 944: Line 944:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 7d, 12e, 19e }}
{{Val list|legend=1| 7d, 12e, 19e }}


Badness: 0.0263
Badness: 0.0263
Line 1,051: Line 1,051:
Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.
Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.


{{Vals|legend=1| 7, 19, 26, 45 }}
{{Val list|legend=1| 7, 19, 26, 45 }}


[[Badness]]: 0.0386
[[Badness]]: 0.0386
Line 1,084: Line 1,084:
* strict range: [692.308, 694.737]
* strict range: [692.308, 694.737]


{{Vals|legend=1| 7, 19, 26, 45, 71bc, 116bcde }}
{{Val list|legend=1| 7, 19, 26, 45, 71bc, 116bcde }}


Badness: 0.0338
Badness: 0.0338
Line 1,117: Line 1,117:
* strict range: [692.308, 694.737]
* strict range: [692.308, 694.737]


{{Vals|legend=1| 7, 19, 26, 45f, 71bcf, 116bcdef }}
{{Val list|legend=1| 7, 19, 26, 45f, 71bcf, 116bcdef }}


Badness: 0.0223
Badness: 0.0223
Line 1,206: Line 1,206:
* strict range: [240.000, 257.143]
* strict range: [240.000, 257.143]


{{Vals|legend=1| 5, 14c, 19 }}
{{Val list|legend=1| 5, 14c, 19 }}


[[Badness]]: 0.0267
[[Badness]]: 0.0267
Line 1,239: Line 1,239:
* strict range: [252.632, 257.143]
* strict range: [252.632, 257.143]


{{Vals|legend=1| 14c, 19, 33cd, 52cd }}
{{Val list|legend=1| 14c, 19, 33cd, 52cd }}


Badness: 0.0290
Badness: 0.0290
Line 1,272: Line 1,272:
* strict range: 694.737
* strict range: 694.737


{{Vals|legend=1| 14cf, 19, 33cdff, 52cdf }}
{{Val list|legend=1| 14cf, 19, 33cdff, 52cdf }}


Badness: 0.0225
Badness: 0.0225
Line 1,300: Line 1,300:
Mapping generators: ~2, ~7/4
Mapping generators: ~2, ~7/4


{{Vals|legend=1| 14c, 19e, 33cdee }}
{{Val list|legend=1| 14c, 19e, 33cdee }}


Badness: 0.0285
Badness: 0.0285
Line 1,328: Line 1,328:
Mapping generators: ~2, ~7/4
Mapping generators: ~2, ~7/4


{{Vals|legend=1| 19e, 24, 43de }}
{{Val list|legend=1| 19e, 24, 43de }}


Badness: 0.0396
Badness: 0.0396
Line 1,356: Line 1,356:
Mapping generators: ~2, ~7/4
Mapping generators: ~2, ~7/4


{{Vals|legend=1| 19e, 24, 43de }}
{{Val list|legend=1| 19e, 24, 43de }}


Badness: 0.0257
Badness: 0.0257
Line 1,384: Line 1,384:
Mapping generators: ~2, ~7/4
Mapping generators: ~2, ~7/4


{{Vals|legend=1| 19, 24, 43d }}
{{Val list|legend=1| 19, 24, 43d }}


Badness: 0.0357
Badness: 0.0357
Line 1,425: Line 1,425:
* strict range: [700.000, 715.587]
* strict range: [700.000, 715.587]


{{Vals|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }}
{{Val list|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }}


[[Badness]]: 0.0207
[[Badness]]: 0.0207
Line 1,458: Line 1,458:
* strict range: [700.000, 705.882]
* strict range: [700.000, 705.882]


{{Vals|legend=1| 5, 12, 17c, 29cde }}
{{Val list|legend=1| 5, 12, 17c, 29cde }}


Badness: 0.0242
Badness: 0.0242
Line 1,491: Line 1,491:
* strict range: 705.882
* strict range: 705.882


{{Vals|legend=1| 12f, 17c, 29cdef }}
{{Val list|legend=1| 12f, 17c, 29cdef }}


Badness: 0.0241
Badness: 0.0241
Line 1,517: Line 1,517:
Mapping: [{{val| 1 0 -4 6 13 -9 }}, {{val| 0 1 4 -2 -6 8 }}]
Mapping: [{{val| 1 0 -4 6 13 -9 }}, {{val| 0 1 4 -2 -6 8 }}]


{{Vals|legend=1| 5, 12, 17c, 46cde }}
{{Val list|legend=1| 5, 12, 17c, 46cde }}


Badness: 0.0273
Badness: 0.0273
Line 1,545: Line 1,545:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5e, 7, 12, 19d, 43de }}
{{Val list|legend=1| 5e, 7, 12, 19d, 43de }}


Badness: 0.0220
Badness: 0.0220
Line 1,573: Line 1,573:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5ef, 7, 12, 19d, 31def }}
{{Val list|legend=1| 5ef, 7, 12, 19d, 31def }}


Badness: 0.0270
Badness: 0.0270
Line 1,601: Line 1,601:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5ef, 7, 12, 19d, 31def }}
{{Val list|legend=1| 5ef, 7, 12, 19d, 31def }}


Badness: 0.0245
Badness: 0.0245
Line 1,629: Line 1,629:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5ef, 7, 12, 19d, 31def }}
{{Val list|legend=1| 5ef, 7, 12, 19d, 31def }}


Badness: 0.0204
Badness: 0.0204
Line 1,657: Line 1,657:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5e, 7, 12f, 19df }}
{{Val list|legend=1| 5e, 7, 12f, 19df }}


</div></div>
</div></div>
Line 1,683: Line 1,683:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5e, 12e, 17c, 46cd }}
{{Val list|legend=1| 5e, 12e, 17c, 46cd }}


Badness: 0.0366
Badness: 0.0366
Line 1,711: Line 1,711:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5e, 12e, 17c }}
{{Val list|legend=1| 5e, 12e, 17c }}


Badness: 0.0274
Badness: 0.0274
Line 1,739: Line 1,739:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5, 7, 12e }}
{{Val list|legend=1| 5, 7, 12e }}


Badness: 0.0261
Badness: 0.0261
Line 1,767: Line 1,767:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5, 7, 12ef, 19def }}
{{Val list|legend=1| 5, 7, 12ef, 19def }}


Badness: 0.0233
Badness: 0.0233
Line 1,795: Line 1,795:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5, 7, 12ef, 19def }}
{{Val list|legend=1| 5, 7, 12ef, 19def }}


Badness: 0.0245
Badness: 0.0245
Line 1,823: Line 1,823:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5, 7, 12ef, 19def }}
{{Val list|legend=1| 5, 7, 12ef, 19def }}


Badness: 0.0211
Badness: 0.0211
Line 1,855: Line 1,855:
[[Wedgie]]: {{wedgie| 1 4 3 4 2 -4 }}
[[Wedgie]]: {{wedgie| 1 4 3 4 2 -4 }}


{{Vals|legend=1| 5, 7d, 12d }}
{{Val list|legend=1| 5, 7d, 12d }}


[[Badness]]: 0.0248
[[Badness]]: 0.0248
Line 1,881: Line 1,881:
Mapping: [{{val| 1 0 -4 -2 5 }}, {{val| 0 1 4 3 -1 }}]
Mapping: [{{val| 1 0 -4 -2 5 }}, {{val| 0 1 4 3 -1 }}]


{{Vals|legend=1| 5, 7d, 12de }}
{{Val list|legend=1| 5, 7d, 12de }}


Badness: 0.0252
Badness: 0.0252
Line 1,911: Line 1,911:
Wedgie: {{wedgie| 1 4 5 4 5 0 }}
Wedgie: {{wedgie| 1 4 5 4 5 0 }}


{{Vals|legend=1| 5d, 7, 12dd }}
{{Val list|legend=1| 5d, 7, 12dd }}


Badness: 0.0453
Badness: 0.0453
Line 1,939: Line 1,939:
Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Vals|legend=1| 5de, 7, 12dd }}
{{Val list|legend=1| 5de, 7, 12dd }}


Badness: 0.0325
Badness: 0.0325
Line 1,965: Line 1,965:
Mapping: [{{val| 1 0 -4 -21 }}, {{val| 0 1 4 15 }}]
Mapping: [{{val| 1 0 -4 -21 }}, {{val| 0 1 4 15 }}]


{{Vals|legend=1| 5d, 12d, 17c, 29c }}
{{Val list|legend=1| 5d, 12d, 17c, 29c }}


Badness: 0.1342
Badness: 0.1342
Line 1,991: Line 1,991:
Mapping: [{{val| 1 0 -4 -21 -14 }}, {{val| 0 1 4 15 11 }}]
Mapping: [{{val| 1 0 -4 -21 -14 }}, {{val| 0 1 4 15 11 }}]


{{Vals|legend=1| 5de, 12de, 17c, 29c }}
{{Val list|legend=1| 5de, 12de, 17c, 29c }}


Badness: 0.0633
Badness: 0.0633
Line 2,017: Line 2,017:
Mapping: [{{val| 1 0 -4 -21 -14 -9 }}, {{val| 0 1 4 15 11 8 }}]
Mapping: [{{val| 1 0 -4 -21 -14 -9 }}, {{val| 0 1 4 15 11 8 }}]


{{Vals|legend=1| 5de, 12de, 17c, 29c }}
{{Val list|legend=1| 5de, 12de, 17c, 29c }}


</div></div>
</div></div>
Line 2,054: Line 2,054:
[[Wedgie]]: {{wedgie| 2 8 8 8 7 -4 }}
[[Wedgie]]: {{wedgie| 2 8 8 8 7 -4 }}


{{Vals|legend=1| 12, 26, 38, 102bcd, 140bccd, 178bbccdd }}
{{Val list|legend=1| 12, 26, 38, 102bcd, 140bccd, 178bbccdd }}


[[Badness]]: 0.0311
[[Badness]]: 0.0311
Line 2,090: Line 2,090:
* strict range: [685.714, 700.000]
* strict range: [685.714, 700.000]


{{Vals|legend=1| 12, 14c, 26, 90bce, 116bcce }}
{{Val list|legend=1| 12, 14c, 26, 90bce, 116bcce }}


Badness: 0.0231
Badness: 0.0231
Line 2,123: Line 2,123:
* strict range: 692.308 (26)
* strict range: 692.308 (26)


{{Vals|legend=1| 12f, 14cf, 26, 38e }}
{{Val list|legend=1| 12f, 14cf, 26, 38e }}


Badness: 0.0216
Badness: 0.0216
Line 2,151: Line 2,151:
Mapping generators: ~7/5, ~3
Mapping generators: ~7/5, ~3


{{Vals|legend=1| 12f, 14c, 26f, 38eff }}
{{Val list|legend=1| 12f, 14c, 26f, 38eff }}


Badness: 0.0265
Badness: 0.0265
Line 2,179: Line 2,179:
Mapping generators: ~7/5, ~3
Mapping generators: ~7/5, ~3


{{Vals|legend=1| 12e, 14c, 26e, 40cee }}
{{Val list|legend=1| 12e, 14c, 26e, 40cee }}


Badness: 0.0386
Badness: 0.0386
Line 2,207: Line 2,207:
Mapping generators: ~7/5, ~3
Mapping generators: ~7/5, ~3


{{Vals|legend=1| 12, 14ce }}
{{Val list|legend=1| 12, 14ce }}


Badness: 0.0431
Badness: 0.0431
Line 2,291: Line 2,291:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7, 17c, 24, 31, 100e, 131bee }}
{{Val list|legend=1| 7, 17c, 24, 31, 100e, 131bee }}


Badness: 0.0261
Badness: 0.0261
Line 2,318: Line 2,318:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7, 17c, 24, 31, 55, 86ef, 141ceff }}
{{Val list|legend=1| 7, 17c, 24, 31, 55, 86ef, 141ceff }}


Badness: 0.0261
Badness: 0.0261
Line 2,359: Line 2,359:
Algebraic generator: Mohabis, real root of 3''x''<sup>3</sup> - 3''x''<sup>2</sup> - 1, 348.6067 cents. Corresponding recurrence converges quickly.
Algebraic generator: Mohabis, real root of 3''x''<sup>3</sup> - 3''x''<sup>2</sup> - 1, 348.6067 cents. Corresponding recurrence converges quickly.


{{Vals|legend=1| 7, 24, 31 }}
{{Val list|legend=1| 7, 24, 31 }}


[[Badness]]: 0.0557
[[Badness]]: 0.0557
Line 2,391: Line 2,391:
: Eigenmonzos: 2, 5
: Eigenmonzos: 2, 5


{{Vals|legend=1| 7, 24, 31 }}
{{Val list|legend=1| 7, 24, 31 }}


Badness: 0.0261
Badness: 0.0261
Line 2,418: Line 2,418:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7, 24, 31 }}
{{Val list|legend=1| 7, 24, 31 }}


Badness: 0.0234
Badness: 0.0234
Line 2,445: Line 2,445:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7, 24, 31, 86ef }}
{{Val list|legend=1| 7, 24, 31, 86ef }}


Badness: 0.0206
Badness: 0.0206
Line 2,472: Line 2,472:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7, 24, 31, 55, 86efh }}
{{Val list|legend=1| 7, 24, 31, 55, 86efh }}


Badness: 0.0173
Badness: 0.0173
Line 2,500: Line 2,500:
Mapping generators: ~2, ~25/21
Mapping generators: ~2, ~25/21


{{Vals|legend=1| 17c, 24, 65c, 89cd }}
{{Val list|legend=1| 17c, 24, 65c, 89cd }}


Badness: 0.0777
Badness: 0.0777
Line 2,528: Line 2,528:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 17c, 24, 65c, 89cd }}
{{Val list|legend=1| 17c, 24, 65c, 89cd }}


Badness: 0.0362
Badness: 0.0362
Line 2,556: Line 2,556:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 17c, 24, 41c, 65c }}
{{Val list|legend=1| 17c, 24, 41c, 65c }}


Badness: 0.0287
Badness: 0.0287
Line 2,585: Line 2,585:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7d, 24d, 31, 100de, 131bdee, 162bdee }}
{{Val list|legend=1| 7d, 24d, 31, 100de, 131bdee, 162bdee }}


Badness: 0.0255
Badness: 0.0255
Line 2,613: Line 2,613:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7d, 24d, 31, 55d }}
{{Val list|legend=1| 7d, 24d, 31, 55d }}


Badness: 0.0281
Badness: 0.0281
Line 2,640: Line 2,640:
Mapping: [{{val| 1 1 0 8 2 }}, {{val| 0 2 8 -18 5 }}]
Mapping: [{{val| 1 1 0 8 2 }}, {{val| 0 2 8 -18 5 }}]


{{Vals|legend=1| 7, 31dd, 38d, 45e, 83bcddee }}
{{Val list|legend=1| 7, 31dd, 38d, 45e, 83bcddee }}


Badness: 0.0588
Badness: 0.0588
Line 2,666: Line 2,666:
Mapping: [{{val| 1 1 0 8 2 6 }}, {{val| 0 2 8 -18 5 -8 }}]
Mapping: [{{val| 1 1 0 8 2 6 }}, {{val| 0 2 8 -18 5 -8 }}]


{{Vals|legend=1| 7, 31ddf, 38df, 45ef, 83bcddeeff }}
{{Val list|legend=1| 7, 31ddf, 38df, 45ef, 83bcddeeff }}


Badness: 0.0343
Badness: 0.0343
Line 2,699: Line 2,699:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7, 17c, 24d, 41cd }}
{{Val list|legend=1| 7, 17c, 24d, 41cd }}


</div></div>
</div></div>
Line 2,725: Line 2,725:
Mapping generators: ~2, ~11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7, 17c, 24d, 41cd }}
{{Val list|legend=1| 7, 17c, 24d, 41cd }}


</div></div>
</div></div>
Line 2,753: Line 2,753:
[[Wedgie]]: {{wedgie| 8 32 6 32 -13 -76 }}
[[Wedgie]]: {{wedgie| 8 32 6 32 -13 -76 }}


{{Vals|legend=1| 26, 48c, 74, 174bd, 248bd }}
{{Val list|legend=1| 26, 48c, 74, 174bd, 248bd }}


[[Badness]]: 0.2588
[[Badness]]: 0.2588
Line 2,781: Line 2,781:
Mapping generators: ~363/256, ~77/64
Mapping generators: ~363/256, ~77/64


{{Vals|legend=1| 26, 48c, 74, 248bd, 322bd }}
{{Val list|legend=1| 26, 48c, 74, 248bd, 322bd }}


Badness: 0.1015
Badness: 0.1015
Line 2,809: Line 2,809:
Mapping generators: ~55/39, ~63/52
Mapping generators: ~55/39, ~63/52


{{Vals|legend=1| 26, 48c, 74, 174bd, 248bd, 322bd }}
{{Val list|legend=1| 26, 48c, 74, 174bd, 248bd, 322bd }}


Badness: 0.0535
Badness: 0.0535
Line 2,850: Line 2,850:
: [[Eigenmonzo]]s: 2, 5
: [[Eigenmonzo]]s: 2, 5


{{Vals|legend=1| 5, 26, 31 }}
{{Val list|legend=1| 5, 26, 31 }}


[[Badness]]: 0.0371
[[Badness]]: 0.0371
Line 2,878: Line 2,878:
Mapping generators: ~2, ~8/7
Mapping generators: ~2, ~8/7


{{Vals|legend=1| 5, 26, 31, 88, 150be, 181bee }}
{{Val list|legend=1| 5, 26, 31, 88, 150be, 181bee }}


Badness: 0.0256
Badness: 0.0256
Line 2,906: Line 2,906:
Mapping generators: ~2, ~8/7
Mapping generators: ~2, ~8/7


{{Vals|legend=1| 5, 26, 31, 57, 88 }}
{{Val list|legend=1| 5, 26, 31, 57, 88 }}


Badness: 0.0240
Badness: 0.0240
Line 2,934: Line 2,934:
Mapping generators: ~2, ~8/7
Mapping generators: ~2, ~8/7


{{Vals|legend=1| 5e, 26, 57e, 83bce }}
{{Val list|legend=1| 5e, 26, 57e, 83bce }}


Badness: 0.0557
Badness: 0.0557
Line 2,962: Line 2,962:
Mapping generators: ~2, ~8/7
Mapping generators: ~2, ~8/7


{{Vals|legend=1| 5e, 26, 57e, 83bce }}
{{Val list|legend=1| 5e, 26, 57e, 83bce }}


Badness: 0.0341
Badness: 0.0341
Line 2,990: Line 2,990:
Mapping generators: ~2, ~8/7
Mapping generators: ~2, ~8/7


{{Vals|legend=1| 31, 129, 160be, 191bce, 222bce, 253bcee }}
{{Val list|legend=1| 31, 129, 160be, 191bce, 222bce, 253bcee }}


Badness: 0.0313
Badness: 0.0313
Line 3,018: Line 3,018:
Mapping generators: ~2, ~8/7
Mapping generators: ~2, ~8/7


{{Vals|legend=1| 31, 36, 67, 98 }}
{{Val list|legend=1| 31, 36, 67, 98 }}


Badness: 0.0369
Badness: 0.0369
Line 3,055: Line 3,055:
Algebraic generator: Sceptre2, the positive root of 9''x''<sup>2</sup> + ''x'' - 16, or (sqrt (577) - 1)/18, which is 425.9311 cents.
Algebraic generator: Sceptre2, the positive root of 9''x''<sup>2</sup> + ''x'' - 16, or (sqrt (577) - 1)/18, which is 425.9311 cents.


{{Vals|legend=1| 14c, 17c, 31 }}
{{Val list|legend=1| 14c, 17c, 31 }}


[[Badness]]: 0.0460
[[Badness]]: 0.0460
Line 3,089: Line 3,089:
Mapping generators: ~2, ~9/7
Mapping generators: ~2, ~9/7


{{Vals|legend=1| 14c, 17c, 31 }}
{{Val list|legend=1| 14c, 17c, 31 }}


Badness: 0.0216
Badness: 0.0216
Line 3,117: Line 3,117:
Mapping generators: ~2, ~9/7
Mapping generators: ~2, ~9/7


{{Vals|legend=1| 14c, 17c, 31, 79cf }}
{{Val list|legend=1| 14c, 17c, 31, 79cf }}


Badness: 0.0255
Badness: 0.0255
Line 3,145: Line 3,145:
Mapping generators: ~2, ~9/7
Mapping generators: ~2, ~9/7


{{Vals|legend=1| 14cf, 31, 45ef, 76e }}
{{Val list|legend=1| 14cf, 31, 45ef, 76e }}


Badness: 0.0245
Badness: 0.0245
Line 3,173: Line 3,173:
Mapping generators: ~2, ~9/7
Mapping generators: ~2, ~9/7


{{Vals|legend=1| 14cf, 31, 76e }}
{{Val list|legend=1| 14cf, 31, 76e }}


</div></div>
</div></div>
Line 3,199: Line 3,199:
Mapping generators: ~2, ~9/7
Mapping generators: ~2, ~9/7


{{Vals|legend=1| 14cf, 31, 76e }}
{{Val list|legend=1| 14cf, 31, 76e }}


</div></div>
</div></div>
Line 3,225: Line 3,225:
Mapping generators: ~2, ~9/7
Mapping generators: ~2, ~9/7


{{Vals|legend=1| 14ce, 17ce, 31, 107b }}
{{Val list|legend=1| 14ce, 17ce, 31, 107b }}


[[Badness]]: 0.0568
[[Badness]]: 0.0568
Line 3,263: Line 3,263:
Algebraic generator: Radix, the real root of ''x''<sup>5</sup> - 2''x''<sup>4</sup> + 2''x''<sup>3</sup> - 2''x''<sup>2</sup> + 2''x'' - 2, also a root of ''x''<sup>6</sup> - ''x''<sup>5</sup> - 2. The recurrence converges.
Algebraic generator: Radix, the real root of ''x''<sup>5</sup> - 2''x''<sup>4</sup> + 2''x''<sup>3</sup> - 2''x''<sup>2</sup> + 2''x'' - 2, also a root of ''x''<sup>6</sup> - ''x''<sup>5</sup> - 2. The recurrence converges.


{{Vals|legend=1| 17c, 19, 55, 74d }}
{{Val list|legend=1| 17c, 19, 55, 74d }}


[[Badness]]: 0.0467
[[Badness]]: 0.0467
Line 3,291: Line 3,291:
Mapping generators: ~2, ~10/7
Mapping generators: ~2, ~10/7


{{Vals|legend=1| 17c, 19, 36, 91cee }}
{{Val list|legend=1| 17c, 19, 36, 91cee }}


Badness: 0.0407
Badness: 0.0407
Line 3,320: Line 3,320:
Mapping generators: ~2, ~10/7
Mapping generators: ~2, ~10/7


{{Vals|legend=1| 17c, 19, 36, 91ceef }}
{{Val list|legend=1| 17c, 19, 36, 91ceef }}


Badness: 0.0273
Badness: 0.0273
Line 3,348: Line 3,348:
Mapping generators: ~2, ~10/7
Mapping generators: ~2, ~10/7


{{Vals|legend=1| 17c, 19e, 36e }}
{{Val list|legend=1| 17c, 19e, 36e }}


Badness: 0.0416
Badness: 0.0416
Line 3,376: Line 3,376:
Mapping generators: ~2, ~10/7
Mapping generators: ~2, ~10/7


{{Vals|legend=1| 17cee, 19 }}
{{Val list|legend=1| 17cee, 19 }}


Badness: 0.0548
Badness: 0.0548
Line 3,404: Line 3,404:
Mapping generators: ~2, ~10/7
Mapping generators: ~2, ~10/7


{{Vals|legend=1| 17cee, 19 }}
{{Val list|legend=1| 17cee, 19 }}


Badness: 0.0361
Badness: 0.0361
Line 3,435: Line 3,435:
Wedgie: {{wedgie| 5 30 7 20 -3 -40 }}
Wedgie: {{wedgie| 5 30 7 20 -3 -40 }}


{{Vals|legend=1| 17c, 26, 43, 69, 112bd }}
{{Val list|legend=1| 17c, 26, 43, 69, 112bd }}


Badness: 0.1087
Badness: 0.1087
Line 3,463: Line 3,463:
Mapping generators: ~2, ~12/11
Mapping generators: ~2, ~12/11


{{Vals|legend=1| 17c, 26, 43, 69 }}
{{Val list|legend=1| 17c, 26, 43, 69 }}


Badness: 0.0479
Badness: 0.0479
Line 3,491: Line 3,491:
Mapping generators: ~2, ~12/11
Mapping generators: ~2, ~12/11


{{Vals|legend=1| 17c, 26, 43, 69 }}
{{Val list|legend=1| 17c, 26, 43, 69 }}


Badness: 0.0293
Badness: 0.0293
Line 3,519: Line 3,519:
Mapping generators: ~2, ~12/11
Mapping generators: ~2, ~12/11


{{Vals|legend=1| 17cg, 26, 43, 69 }}
{{Val list|legend=1| 17cg, 26, 43, 69 }}


Badness: 0.0209
Badness: 0.0209
Line 3,547: Line 3,547:
Mapping generators: ~2, ~12/11
Mapping generators: ~2, ~12/11


{{Vals|legend=1| 17cgh, 26, 43, 69 }}
{{Val list|legend=1| 17cgh, 26, 43, 69 }}


Badness: 0.0182
Badness: 0.0182
Line 3,577: Line 3,577:
Wedgie: {{wedgie| 0 0 19 0 30 44 }}
Wedgie: {{wedgie| 0 0 19 0 30 44 }}


{{Vals|legend=1| 19, 38, 57, 76, 95bc }}
{{Val list|legend=1| 19, 38, 57, 76, 95bc }}


Badness: 0.0770
Badness: 0.0770
Line 3,605: Line 3,605:
Mapping generators: ~21/20, ~11
Mapping generators: ~21/20, ~11


{{Vals|legend=1| 19, 38d }}
{{Val list|legend=1| 19, 38d }}


Badness: 0.0364
Badness: 0.0364
Line 3,633: Line 3,633:
Mapping generators: ~21/20, ~11
Mapping generators: ~21/20, ~11


{{Vals|legend=1| 19, 38d }}
{{Val list|legend=1| 19, 38d }}


Badness: 0.0229
Badness: 0.0229
Retrieved from "https://en.xen.wiki/w/Meantone_family"