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Algebraic generator: [[Algebraic number|positive root]] of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.
Algebraic generator: [[Algebraic number|positive root]] of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.


Vals: {{Val list| 41, 46, 87 }}
Optimal GPV sequence: {{Val list| 41, 46, 87 }}


Badness: 0.023093
Badness: 0.023093
Line 120: Line 120:
Algebraic generator: Gatetone, positive root of 4''x''<sup>6</sup> - 7''x'' - 1. Recurrence converges slowly.
Algebraic generator: Gatetone, positive root of 4''x''<sup>6</sup> - 7''x'' - 1. Recurrence converges slowly.


Vals: {{Val list| 41, 46, 87 }}
Optimal GPV sequence: {{Val list| 41, 46, 87 }}


Badness: 0.018448
Badness: 0.018448
Line 139: Line 139:
: Eigenmonzos (unchanged intervals): 2, 18/17
: Eigenmonzos (unchanged intervals): 2, 18/17


Vals: {{Val list| 41, 46, 87, 220dg, 307dgg }}
Optimal GPV sequence: {{Val list| 41, 46, 87, 220dg, 307dgg }}


Badness: 0.016743
Badness: 0.016743
Line 154: Line 154:
POTE generator: ~8/7 = 234.639
POTE generator: ~8/7 = 234.639


Vals: {{Val list| 5, 41f, 46, 133ff }}
Optimal GPV sequence: {{Val list| 5, 41f, 46, 133ff }}


Badness: 0.033986
Badness: 0.033986
Line 167: Line 167:
POTE generator: ~8/7 = 234.728
POTE generator: ~8/7 = 234.728


Vals: {{Val list| 41e, 46 }}
Optimal GPV sequence: {{Val list| 41e, 46 }}


Badness: 0.054294
Badness: 0.054294
Line 178: Line 178:
POTE generator: ~8/7 = 234.782
POTE generator: ~8/7 = 234.782


Vals: {{Val list| 41ef, 46 }}
Optimal GPV sequence: {{Val list| 41ef, 46 }}


Badness: 0.035836
Badness: 0.035836
Line 189: Line 189:
POTE generator: ~8/7 = 234.145
POTE generator: ~8/7 = 234.145


Vals: {{Val list| 36ce, 41 }}
Optimal GPV sequence: {{Val list| 36ce, 41 }}


Badness: 0.044937
Badness: 0.044937
Line 200: Line 200:
POTE generator: ~8/7 = 234.089
POTE generator: ~8/7 = 234.089


Vals: {{Val list| 36ce, 41 }}
Optimal GPV sequence: {{Val list| 36ce, 41 }}


Badness: 0.032284
Badness: 0.032284
Line 244: Line 244:
: Eigenmonzos (unchanged intervals): 2, 5
: Eigenmonzos (unchanged intervals): 2, 5


Vals: {{Val list| 36e, 41, 77, 118, 159, 277d }}
Optimal GPV sequence: {{Val list| 36e, 41, 77, 118, 159, 277d }}


Badness: 0.026648
Badness: 0.026648
Line 259: Line 259:
POTE generator: ~8/7 = 233.890
POTE generator: ~8/7 = 233.890


Vals: {{Val list| 36e, 41, 77, 118 }}
Optimal GPV sequence: {{Val list| 36e, 41, 77, 118 }}


Badness: 0.028444
Badness: 0.028444
Line 305: Line 305:
POTE generator: ~8/7 = 227.373
POTE generator: ~8/7 = 227.373


Vals: {{Val list| 16, 21, 37b }}
Optimal GPV sequence: {{Val list| 16, 21, 37b }}


Badness: 0.049500
Badness: 0.049500
Line 318: Line 318:
POTE generator: ~8/7 = 227.230
POTE generator: ~8/7 = 227.230


Vals: {{Val list| 16, 21, 37b }}
Optimal GPV sequence: {{Val list| 16, 21, 37b }}


Badness: 0.032664
Badness: 0.032664
Line 331: Line 331:
POTE generator: ~8/7 = 229.535
POTE generator: ~8/7 = 229.535


Vals: {{Val list| 5, 16e, 21, 47c, 68bcce }}
Optimal GPV sequence: {{Val list| 5, 16e, 21, 47c, 68bcce }}


Badness: 0.062683
Badness: 0.062683
Line 344: Line 344:
POTE generator: ~8/7 = 229.059
POTE generator: ~8/7 = 229.059


{{Val list|legend=1| 5, 16e, 21, 68bccef }}
Optimal GPV sequence: {{Val list| 5, 16e, 21, 68bccef }}


Badness: 0.047071
Badness: 0.047071
Line 438: Line 438:
POTE generator: ~8/7 = 226.428
POTE generator: ~8/7 = 226.428


Vals: {{Val list| 5c, 11, 16 }}
Optimal GPV sequence: {{Val list| 5c, 11, 16 }}


Badness: 0.069703
Badness: 0.069703
Line 501: Line 501:
Algebraic generator: Secor59
Algebraic generator: Secor59


Vals: {{Val list| 10, 21e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}
Optimal GPV sequence: {{Val list| 10, 21e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}


Badness: 0.010684
Badness: 0.010684
Line 516: Line 516:
POTE generator: ~15/14 = 116.747
POTE generator: ~15/14 = 116.747


Vals: {{Val list| 10, 21e, 31, 41, 72f, 113f, 185cff }}
Optimal GPV sequence: {{Val list| 10, 21e, 31, 41, 72f, 113f, 185cff }}


Badness: 0.018669
Badness: 0.018669
Line 531: Line 531:
POTE generator: ~15/14 = 116.574
POTE generator: ~15/14 = 116.574


Vals: {{Val list| 31, 72, 103, 175f }}
Optimal GPV sequence: {{Val list| 31, 72, 103, 175f }}


Badness: 0.015715
Badness: 0.015715
Line 544: Line 544:
POTE generator: ~15/14 = 116.585
POTE generator: ~15/14 = 116.585


Vals: {{Val list| 31, 72, 103, 175f }}
Optimal GPV sequence: {{Val list| 31, 72, 103, 175f }}


Badness: 0.012537
Badness: 0.012537
Line 557: Line 557:
POTE generator: ~15/14 = 116.739
POTE generator: ~15/14 = 116.739


Vals: {{Val list| 31f, 41, 72, 185cf, 257cff }}
Optimal GPV sequence: {{Val list| 31f, 41, 72, 185cf, 257cff }}


Badness: 0.017012
Badness: 0.017012
Line 570: Line 570:
POTE generator: ~15/14 = 116.624
POTE generator: ~15/14 = 116.624


Vals: {{Val list| 10, 62, 72 }}
Optimal GPV sequence: {{Val list| 10, 62, 72 }}


Badness: 0.024622
Badness: 0.024622
Line 583: Line 583:
POTE generator: ~15/14 = 116.628
POTE generator: ~15/14 = 116.628


Vals: {{Val list| 10, 62, 72 }}
Optimal GPV sequence: {{Val list| 10, 62, 72 }}


Badness: 0.016130
Badness: 0.016130
Line 596: Line 596:
POTE generator: ~27/26 = 58.288
POTE generator: ~27/26 = 58.288


Vals: {{Val list| 41, 62, 103, 247c, 350bcde }}
Optimal GPV sequence: {{Val list| 41, 62, 103, 247c, 350bcde }}


Badness: 0.025589
Badness: 0.025589
Line 609: Line 609:
POTE generator: ~27/26 = 58.261
POTE generator: ~27/26 = 58.261


Vals: {{Val list| 41, 62, 103 }}
Optimal GPV sequence: {{Val list| 41, 62, 103 }}


Badness: 0.022535
Badness: 0.022535
Line 622: Line 622:
POTE generator: ~16/13 = 361.121
POTE generator: ~16/13 = 361.121


Vals: {{Val list| 103, 113, 216c }}
Optimal GPV sequence: {{Val list| 103, 113, 216c }}


Badness: 0.033198
Badness: 0.033198
Line 635: Line 635:
POTE generator: ~16/13 = 361.123
POTE generator: ~16/13 = 361.123


Vals: {{Val list| 103, 113, 216c }}
Optimal GPV sequence: {{Val list| 103, 113, 216c }}


Badness: 0.024705
Badness: 0.024705
Line 648: Line 648:
POTE generator: ~15/14 = 116.277
POTE generator: ~15/14 = 116.277


Vals: {{Val list| 10e, 21, 31 }}
Optimal GPV sequence: {{Val list| 10e, 21, 31 }}


Badness: 0.032946
Badness: 0.032946
Line 661: Line 661:
POTE generator: ~15/14 = 116.268
POTE generator: ~15/14 = 116.268


Vals: {{Val list| 10e, 21, 31 }}
Optimal GPV sequence: {{Val list| 10e, 21, 31 }}


Badness: 0.029452
Badness: 0.029452
Line 674: Line 674:
POTE generator: ~33/32 = 58.408
POTE generator: ~33/32 = 58.408


Vals: {{Val list| 20, 21, 41, 144e, 185cee, 226cee }}
Optimal GPV sequence: {{Val list| 20, 21, 41, 144e, 185cee, 226cee }}


Badness: 0.059232
Badness: 0.059232
Line 687: Line 687:
POTE generator: ~33/32 = 58.430
POTE generator: ~33/32 = 58.430


Vals: {{Val list| 20, 21, 41, 144eff, 185ceeff }}
Optimal GPV sequence: {{Val list| 20, 21, 41, 144eff, 185ceeff }}


Badness: 0.043151
Badness: 0.043151
Line 700: Line 700:
POTE generator: ~11/8 = 541.668
POTE generator: ~11/8 = 541.668


Vals: {{Val list| 11, 20, 31, 82e, 113e, 144ee }}
Optimal GPV sequence: {{Val list| 11, 20, 31, 82e, 113e, 144ee }}


Badness: 0.042687
Badness: 0.042687
Line 728: Line 728:
POTE generator: ~320/243 = 483.276
POTE generator: ~320/243 = 483.276


Vals: {{Val list| 72, 77, 149, 221e, 293de }}
Optimal GPV sequence: {{Val list| 72, 77, 149, 221e, 293de }}


Badness: 0.028467
Badness: 0.028467
Line 741: Line 741:
POTE generator: ~120/91 = 483.256
POTE generator: ~120/91 = 483.256


Vals: {{Val list| 72, 77, 149, 221ef }}
Optimal GPV sequence: {{Val list| 72, 77, 149, 221ef }}


Badness: 0.021900
Badness: 0.021900
Line 754: Line 754:
POTE generator: ~45/34 = 483.261
POTE generator: ~45/34 = 483.261


Vals: {{Val list| 72, 77, 149, 221ef }}
Optimal GPV sequence: {{Val list| 72, 77, 149, 221ef }}


Badness: 0.015701
Badness: 0.015701
Line 818: Line 818:
: Eigenmonzos (unchanged intervals): 2, 9/7
: Eigenmonzos (unchanged intervals): 2, 9/7


Vals: {{Val list| 26, 46, 72, 118, 190 }}
Optimal GPV sequence: {{Val list| 26, 46, 72, 118, 190 }}


Badness: 0.015479
Badness: 0.015479
Line 824: Line 824:
Scales: [[Unidec26]]
Scales: [[Unidec26]]


=== Ekadash ===
==== Ekadash ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 835: Line 835:
POTE generator: ~10/9 = 183.187
POTE generator: ~10/9 = 183.187


Vals: {{Val list| 26f, 46f, 72, 118, 190, 262df, 452cdef }}
Optimal GPV sequence: {{Val list| 26f, 46f, 72, 118, 190, 262df, 452cdef }}


Badness: 0.020381
Badness: 0.020381
Line 841: Line 841:
Scales: [[Unidec26]]
Scales: [[Unidec26]]


=== Hendec ===
==== Hendec ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 852: Line 852:
POTE generator: ~10/9 = 183.198
POTE generator: ~10/9 = 183.198


Vals: {{Val list| 26, 46, 72, 190ff }}
Optimal GPV sequence: {{Val list| 26, 46, 72, 190ff }}


Badness: 0.017707
Badness: 0.017707
Line 858: Line 858:
Scales: [[Unidec26]]
Scales: [[Unidec26]]


==== 17-limit ====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 869: Line 869:
POTE generator: ~10/9 = 183.196
POTE generator: ~10/9 = 183.196


Vals: {{Val list| 26, 46, 72, 190ffg }}
Optimal GPV sequence: {{Val list| 26, 46, 72, 190ffg }}


Badness: 0.011676
Badness: 0.011676
Line 902: Line 902:
POTE generator: ~6/5 = 321.847
POTE generator: ~6/5 = 321.847


Vals: {{Val list| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
Optimal GPV sequence: {{Val list| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}


Badness: 0.025659
Badness: 0.025659
Line 915: Line 915:
POTE generator: ~6/5 = 321.994
POTE generator: ~6/5 = 321.994


Vals: {{Val list| 11cf, 15, 26, 41 }}
Optimal GPV sequence: {{Val list| 11cf, 15, 26, 41 }}


Badness: 0.021478
Badness: 0.021478
Line 958: Line 958:
POTE generator: ~15/11 = 541.729
POTE generator: ~15/11 = 541.729


Vals: {{Val list| 20ce, 31, 113c, 144c, 175c, 381bccdee }}
Optimal GPV sequence: {{Val list| 20ce, 31, 113c, 144c, 175c, 381bccdee }}


Badness: 0.053459
Badness: 0.053459
Line 971: Line 971:
POTE generator: ~15/11 = 541.606
POTE generator: ~15/11 = 541.606


Vals: {{Val list| 20ce, 31, 51ce, 82cf, 113cf, 144cf }}
Optimal GPV sequence: {{Val list| 20ce, 31, 51ce, 82cf, 113cf, 144cf }}


Badness: 0.047015
Badness: 0.047015
Line 999: Line 999:
POTE generator: ~27/22 = 358.5713
POTE generator: ~27/22 = 358.5713


Vals: {{Val list| 10, 77, 87, 164 }}
Optimal GPV sequence: {{Val list| 10, 77, 87, 164 }}


Badness: 0.054655
Badness: 0.054655
Line 1,012: Line 1,012:
POTE generator: ~16/13 = 358.5739
POTE generator: ~16/13 = 358.5739


Vals: {{Val list| 10, 77, 87, 164 }}
Optimal GPV sequence: {{Val list| 10, 77, 87, 164 }}


Badness: 0.028187
Badness: 0.028187
Line 1,042: Line 1,042:
POTE generator: ~27/25 = 137.990
POTE generator: ~27/25 = 137.990


Vals: {{Val list| 26, 61, 87, 200, 287d, 487cdd }}
Optimal GPV sequence: {{Val list| 26, 61, 87, 200, 287d, 487cdd }}


Badness: 0.057307
Badness: 0.057307
Line 1,055: Line 1,055:
POTE generator: ~13/12 = 137.990
POTE generator: ~13/12 = 137.990


Vals: {{Val list| 26, 61, 87, 200, 487cdd }}
Optimal GPV sequence: {{Val list| 26, 61, 87, 200, 487cdd }}


Badness: 0.028393
Badness: 0.028393


== Tritriple ==
== Tritriple ==
Subgroup: 2.3.5
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tritriple]].''
 
[[Comma list]]: {{monzo| 31 20 -27 }}
 
[[Mapping]]: [{{val| 1 -11 -7 }}, {{val| 0 27 20 }}]
 
[[POTE generator]]: ~864/625 = 559.332
 
{{Val list|legend=1| 15, 88, 103, 118, 959, 1077 }}
 
[[Badness]]: 0.283570


=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 1,096: Line 1,085:
POTE generator: ~242/175 = 559.293
POTE generator: ~242/175 = 559.293


Vals: {{Val list| 15, 88, 103, 118, 339de }}
Optimal GPV sequence: {{Val list| 15, 88, 103, 118, 339de }}


Badness: 0.035350
Badness: 0.035350
Line 1,124: Line 1,113:
POTE generator: ~847/625 = 524.210
POTE generator: ~847/625 = 524.210


Vals: {{Val list| 16, 55be, 71, 87, 103, 190 }}
Optimal GPV sequence: {{Val list| 16, 55be, 71, 87, 103, 190 }}


Badness: 0.040785
Badness: 0.040785
Line 1,137: Line 1,126:
POTE generator: ~65/48 = 524.209
POTE generator: ~65/48 = 524.209


Vals: {{Val list| 16, 55be, 71, 87, 103, 190 }}
Optimal GPV sequence: {{Val list| 16, 55be, 71, 87, 103, 190 }}


Badness: 0.021636
Badness: 0.021636
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