Hemifamity temperaments: Difference between revisions
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== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 35: | Line 34: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 49: | Line 47: | ||
=== 17-limit === | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 63: | Line 60: | ||
=== 19-limit === | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 77: | Line 73: | ||
== Buteo == | == Buteo == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 91: | Line 86: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 105: | Line 99: | ||
= Undecental = | = Undecental = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 121: | Line 114: | ||
= Leapday = | = Leapday = | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 135: | Line 127: | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 151: | Line 142: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 165: | Line 155: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 179: | Line 168: | ||
== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 193: | Line 181: | ||
=== 19-limit === | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 207: | Line 194: | ||
=== Leapling === | === Leapling === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 223: | Line 209: | ||
{{main| Mystery }} | {{main| Mystery }} | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 251: | Line 236: | ||
{{Val list|legend=1| 29, 58, 87, 145 }} | {{Val list|legend=1| 29, 58, 87, 145 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.103734 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 265: | Line 249: | ||
Vals: {{Val list| 29, 58, 87, 145 }} | Vals: {{Val list| 29, 58, 87, 145 }} | ||
Badness: 0. | Badness: 0.034291 | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 279: | Line 262: | ||
Vals: {{Val list| 29, 58, 87, 145, 232, 377cef }} | Vals: {{Val list| 29, 58, 87, 145, 232, 377cef }} | ||
Badness: 0. | Badness: 0.018591 | ||
= Quanic = | = Quanic = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 293: | Line 275: | ||
{{Val list|legend=1| 94, 111, 205 }} | {{Val list|legend=1| 94, 111, 205 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.179475 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 307: | Line 288: | ||
Vals: {{Val list| 94, 111, 205 }} | Vals: {{Val list| 94, 111, 205 }} | ||
Badness: 0. | Badness: 0.058678 | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 321: | Line 301: | ||
Vals: {{Val list| 94, 111, 205 }} | Vals: {{Val list| 94, 111, 205 }} | ||
Badness: 0. | Badness: 0.032481 | ||
== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 335: | Line 314: | ||
Vals: {{Val list| 94, 111, 205 }} | Vals: {{Val list| 94, 111, 205 }} | ||
Badness: 0. | Badness: 0.021112 | ||
== 19-limit == | == 19-limit == | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 349: | Line 327: | ||
Vals: {{Val list| 94, 111, 205 }} | Vals: {{Val list| 94, 111, 205 }} | ||
Badness: 0. | Badness: 0.017273 | ||
= Supers = | = Supers = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 368: | Line 345: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 382: | Line 358: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 396: | Line 371: | ||
== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 410: | Line 384: | ||
= Alphaquarter = | = Alphaquarter = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 423: | Line 396: | ||
{{Val list|legend=1| 87, 152, 239, 391 }} | {{Val list|legend=1| 87, 152, 239, 391 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.116594 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 437: | Line 409: | ||
Vals: {{Val list| 87, 152, 239, 391 }} | Vals: {{Val list| 87, 152, 239, 391 }} | ||
Badness: 0. | Badness: 0.029638 | ||
= Septiquarter = | = Septiquarter = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 453: | Line 424: | ||
{{Val list|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }} | {{Val list|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }} | ||
[[Badness]]: 0. | [[Badness]]: 0.053760 | ||
== Semiseptiquarter == | == Semiseptiquarter == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 467: | Line 437: | ||
Vals: {{Val list| 94, 198, 292, 490 }} | Vals: {{Val list| 94, 198, 292, 490 }} | ||
Badness: 0. | Badness: 0.064160 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 481: | Line 450: | ||
Vals: {{Val list| 94, 198, 490f }} | Vals: {{Val list| 94, 198, 490f }} | ||
Badness: 0. | Badness: 0.034834 | ||
= Tricot | = Tricot = | ||
{{see also|Tricot family}} | {{see also|Tricot family}} | ||
The generator for tricot is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot can be described as 53&70 temperament (also known as ''trimot''), tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit. | The generator for tricot is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot can be described as 53&70 temperament (also known as ''trimot''), tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit. | ||
Subgroup: 2.3.5 | |||
[[Comma]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883 | |||
[[Mapping]]: [<1 0 -13|, <0 3 29|] | |||
[[POTE tuning|POTE generator]]: ~59049/40960 = 634.012 | |||
{{Val list|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }} | |||
[[Badness]]: 0.046093 | |||
== 7-limit (aka Trimot) == | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 503: | Line 485: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 517: | Line 498: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 531: | Line 511: | ||
= Ketchup = | = Ketchup = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 547: | Line 526: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 561: | Line 539: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 575: | Line 552: | ||
== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 589: | Line 565: | ||
== 19-limit == | == 19-limit == | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 603: | Line 578: | ||
== 23-limit == | == 23-limit == | ||
Subgroup: 2.3.5.7.11.13.17.19.23 | Subgroup: 2.3.5.7.11.13.17.19.23 | ||
| Line 615: | Line 589: | ||
Badness: 0.014033 | Badness: 0.014033 | ||
= Undim = | |||
Subgroup: 2.3.5 | |||
[[Comma list]]: {{monzo| 41 -20 -4 }} = 2199023255552/2179240250625 | |||
[[Mapping]]: [{{val| 4 0 41 }}, {{val| 0 1 -5 }}] | |||
Mapping generators: ~1215/1024, ~3 | |||
[[POTE generator]]: ~3/2 = 702.736 | |||
{{Val list|legend=1| 12, 104, 116, 128, 140, 152, 620, 772, 924c, 1076bc, 1228bc }} | |||
[[Badness]]: 0.241703 | |||
== 7-limit == | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 5120/5103, 390625/388962 | |||
[[Mapping]]: [{{val| 4 0 41 81 }}, {{val| 0 1 -5 -11 }}] | |||
{{Multival|legend=1| 4 -20 -44 -41 -81 -46 }} | |||
[[POTE generator]]: ~3/2 = 702.736 | |||
{{Val list|legend=1| 12, 128, 140, 152, 292 }} | |||
[[Badness]]: 0.062754 | |||
== 11-limit == | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 1375/1372, 5120/5103, 5632/5625 | |||
Mapping: [{{val| 4 0 41 81 128 }}, {{val| 0 1 -5 -11 -18 }}] | |||
POTE generator: ~3/2 = 702.689 | |||
Vals: {{Val list| 12, 128e, 140, 152, 292, 444d, 596d }} | |||
Badness: 0.034837 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 13:07, 28 April 2021
The hemifamity temperaments temper out the hemifamity comma, [10 -6 1 -1⟩ = 5120/5103, dividing an exact or approximate septimal diesis, [2 2 -1 -1⟩ = 36/35 into two equal steps.
Belonging to it and considered below are buzzard, undecental, leapday, mystery, quanic and ketchup. Other hemifamity temperaments are dominant, garibaldi, hemififths, amity, misty, rodan, countercata and kwai.
Buzzard
Subgroup: 2.3.5.7
Comma list: 1728/1715, 5120/5103
Mapping: [⟨1 0 -6 4], ⟨0 4 21 -3]]
Wedgie: ⟨⟨ 4 21 -3 24 -16 -66 ]]
POTE generator: ~21/16 = 475.636
Badness: 0.047963
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 5120/5103
Mapping: [⟨1 0 -6 4 -12], ⟨0 4 21 -3 39]]
POTE generator: ~21/16 = 475.700
Vals: Template:Val list
Badness: 0.034484
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 540/539, 676/675
Mapping: [⟨1 0 -6 4 -12 -7], ⟨0 4 21 -3 39 27]]
POTE generator: ~21/16 = 475.697
Vals: Template:Val list
Badness: 0.018842
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 256/255, 351/350, 442/441, 540/539
Mapping: [⟨1 0 -6 4 -12 -7 14], ⟨0 4 21 -3 39 27 -25]]
POTE generator: ~21/16 = 475.692
Vals: Template:Val list
Badness: 0.018403
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539
Mapping: [⟨1 0 -6 4 -12 -7 14 -12], ⟨0 4 21 -3 39 27 -25 41]]
POTE generator: ~21/16 = 475.679
Vals: Template:Val list
Badness: 0.015649
Buteo
Subgroup: 2.3.5.7.11
Comma list: 99/98, 385/384, 2200/2187
Mapping: [⟨1 0 -6 4 9], ⟨0 4 21 -3 -14]]
POTE generator: ~21/16 = 475.436
Vals: Template:Val list
Badness: 0.060238
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 275/273, 385/384, 572/567
Mapping: [⟨1 0 -6 4 9 -7], ⟨0 4 21 -3 -14 27]]
POTE generator: ~21/16 = 475.464
Vals: Template:Val list
Badness: 0.039854
Undecental
Subgroup: 2.3.5.7
Comma list: 5120/5103, 235298/234375
Mapping: [⟨1 0 61 71], ⟨0 1 -37 -43]]
Wedgie: ⟨⟨ 1 -37 -43 -61 -71 4 ]]
POTE generator: ~3/2 = 703.039
Badness: 0.094603
Leapday
Subgroup: 2.3.5
Comma list: 10737418240/10460353203
Mapping: [⟨1 0 -31], ⟨0 1 21]]
POTE generator: ~3/2 = 704.179
Badness: 0.523182
7-limit
Subgroup: 2.3.5.7
Comma list: 686/675, 5120/5103
Mapping: [⟨1 0 -31 -21], ⟨0 1 21 15]]
Wedgie: ⟨⟨ 1 21 15 31 21 -24 ]]
POTE generator: ~3/2 = 704.263
Badness: 0.096123
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 441/440, 686/675
Mapping: [⟨1 0 -31 -21 -14], ⟨0 1 21 15 11]]
POTE generator: ~3/2 = 704.250
Vals: Template:Val list
Badness: 0.038624
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 169/168, 352/351
Mapping: [⟨1 0 -31 -21 -14 -9], ⟨0 1 21 15 11 8]]
POTE generator: ~3/2 = 704.214
Vals: Template:Val list
Badness: 0.024732
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 121/120, 136/135, 154/153, 169/168
Mapping: [⟨1 0 -31 -21 -14 -9 -34], ⟨0 1 21 15 11 8 24]]
POTE generator: ~3/2 = 704.229
Vals: Template:Val list
Badness: 0.017863
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168
Mapping: [⟨1 0 -31 -21 -14 -9 -34 9], ⟨0 1 21 15 11 8 24 -3]]
POTE generator: ~3/2 = 704.135
Vals: Template:Val list
Badness: 0.017356
Leapling
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168
Mapping: [⟨1 0 -31 -21 -14 -9 -34 -37], ⟨0 1 21 15 11 8 24 26]]
POTE generator: ~3/2 = 704.123
Vals: Template:Val list
Badness: 0.019065
Mystery
Subgroup: 2.3.5
Comma list: [46 -29⟩
Mapping: [⟨29 46 0], ⟨0 0 1]]
Mapping generators: ~531441/524288, ~5
POTE generator: ~5/4 = 387.408
Badness: 1.020556
7-limit
Subgroup: 2.3.5.7
Comma list: 5120/5103, 50421/50000
Mapping: [⟨29 46 0 14], ⟨0 0 1 1]]
Wedgie: ⟨⟨ 0 29 29 46 46 -14 ]]
POTE generator: ~5/4 = 388.646
Badness: 0.103734
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891, 3388/3375
Mapping: [⟨29 46 0 14 33], ⟨0 0 1 1 1]]
POTE generator: ~5/4 = 388.460
Vals: Template:Val list
Badness: 0.034291
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 676/675
Mapping: [⟨29 46 0 14 33 40], ⟨0 0 1 1 1 1]]
POTE generator: ~5/4 = 388.354
Vals: Template:Val list
Badness: 0.018591
Quanic
Subgroup: 2.3.5.7
Comma list: 5120/5103, 5832000/5764801
Mapping: [⟨1 1 -4 0], ⟨0 5 54 24]]
POTE generator: ~160/147 = 140.493
Badness: 0.179475
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1331/1323, 5120/5103
Mapping: [⟨1 1 -4 0 1], ⟨0 5 54 24 21]]
POTE generator: ~88/81 = 140.489
Vals: Template:Val list
Badness: 0.058678
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 729/728, 1331/1323
Mapping: [⟨1 1 -4 0 1 3], ⟨0 5 54 24 21 6]]
POTE generator: ~13/12 = 140.496
Vals: Template:Val list
Badness: 0.032481
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 442/441, 540/539, 715/714, 847/845
Mapping: [⟨1 1 -4 0 1 3 -2], ⟨0 5 54 24 21 6 52]]
POTE generator: ~13/12 = 140.497
Vals: Template:Val list
Badness: 0.021112
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714
Mapping: [⟨1 1 -4 0 1 3 -2 -5], ⟨0 5 54 24 21 6 52 79]]
POTE generator: ~13/12 = 140.496
Vals: Template:Val list
Badness: 0.017273
Supers
Subgroup: 2.3.5.7
Comma list: 5120/5103, 118098/117649
Mapping: [⟨2 1 -12 2], ⟨0 3 23 5]]
Wedgie: ⟨⟨ 6 46 10 59 -1 -106 ]]
POTE generator: ~9/7 = 434.218
Badness: 0.092748
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993, 5120/5103
Mapping: [⟨2 1 -12 2 -9], ⟨0 3 23 5 22]]
POTE generator: ~9/7 = 434.217
Vals: Template:Val list
Badness: 0.028240
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 729/728, 1575/1573
Mapping: [⟨2 1 -12 2 -9 -2], ⟨0 3 23 5 22 13]]
POTE generator: ~9/7 = 434.221
Vals: Template:Val list
Badness: 0.021645
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 170/169, 289/288, 352/351, 442/441, 561/560
Mapping: [⟨2 1 -12 2 -9 -2 6], ⟨0 3 23 5 22 13 3]]
POTE generator: ~9/7 = 434.181
Vals: Template:Val list
Badness: 0.021316
Alphaquarter
Subgroup: 2.3.5.7
Comma list: 5120/5103, 29360128/29296875
Mapping: [⟨1 2 2 0], ⟨0 -9 7 61]]
Wedgie: ⟨⟨ 9 -7 -61 -32 -122 -122 ]]
POTE generator: ~16128/15625 = 55.243
Badness: 0.116594
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 5120/5103
Mapping: [⟨1 2 2 0 3], ⟨0 -9 7 61 10]]
POTE generator: ~33/32 = 55.243
Vals: Template:Val list
Badness: 0.029638
Septiquarter
Subgroup: 2.3.5.7
Comma list: 5120/5103, 420175/419904
Mapping: [⟨1 3 10 2], ⟨0 -7 -38 4]]
Wedgie: ⟨⟨ 7 38 -4 44 -26 -116 ]]
POTE generator: ~147/128 = 242.453
Badness: 0.053760
Semiseptiquarter
Subgroup: 2.3.5.7.11
Comma list: 5120/5103, 9801/9800, 14641/14580
Mapping: [⟨2 6 20 4 15], ⟨0 -7 -38 4 -20]]
POTE generators: ~121/105 = 242.4511
Vals: Template:Val list
Badness: 0.064160
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 1716/1715, 14641/14580
Mapping: [⟨2 6 20 4 15 7], ⟨0 -7 -38 4 -20 1]]
POTE generators: ~121/105 = 242.4448
Vals: Template:Val list
Badness: 0.034834
Tricot
The generator for tricot is the real cube root of third harmonic, 31/3, tuned between 63/44 and 13/9. Tricot can be described as 53&70 temperament (also known as trimot), tempering out the tricot comma, [39 -29 3⟩ in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit.
Subgroup: 2.3.5
Comma: [39 -29 3⟩ = 68719476736000/68630377364883
Mapping: [<1 0 -13|, <0 3 29|]
POTE generator: ~59049/40960 = 634.012
Badness: 0.046093
7-limit (aka Trimot)
Subgroup: 2.3.5.7
Comma list: 2430/2401, 5120/5103
Mapping: [⟨1 0 -13 -3], ⟨0 3 29 11]]
Wedgie: ⟨⟨ 3 29 11 39 9 -56 ]]
POTE generator: ~81/56 = 634.026
Badness: 0.100127
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 5120/5103
Mapping: [⟨1 0 -13 -3 -5], ⟨0 3 29 11 16]]
POTE generator: ~63/44 = 634.027
Vals: Template:Val list
Badness: 0.056134
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 169/168, 352/351
Mapping: [⟨1 0 -13 -3 -5 0], ⟨0 3 29 11 16 7]]
POTE generator: ~13/9 = 634.012
Vals: Template:Val list
Badness: 0.032102
Ketchup
Subgroup: 2.3.5.7
Comma list: 5120/5103, 1071875/1062882
Mapping: [⟨2 3 4 6], ⟨0 4 15 -9]]
Wedgie: ⟨⟨ 8 30 -18 29 -51 -126 ]]
POTE generator: ~64/63 = ~81/80 = 25.719
Badness: 0.084538
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1331/1323, 2200/2187
Mapping: [⟨2 3 4 6 7], ⟨0 4 15 -9 -2]]
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.693
Vals: Template:Val list
Badness: 0.039555
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 847/845, 1331/1323
Mapping: [⟨2 3 4 6 7 8], ⟨0 4 15 -9 -2 -14]]
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.697
Vals: Template:Val list
Badness: 0.024824
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 325/324, 352/351, 385/384, 561/560
Mapping: [⟨2 3 4 6 7 8 8], ⟨0 4 15 -9 -2 -14 4]]
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.701
Vals: Template:Val list
Badness: 0.016591
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560
Mapping: [⟨2 3 4 6 7 8 8 9], ⟨0 4 15 -9 -2 -14 4 -12]]
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.660
Vals: Template:Val list
Badness: 0.018170
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384
Mapping: [⟨2 3 4 6 7 8 8 9 9], ⟨0 4 15 -9 -2 -14 4 -12 1]]
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.661
Vals: Template:Val list
Badness: 0.014033
Undim
Subgroup: 2.3.5
Comma list: [41 -20 -4⟩ = 2199023255552/2179240250625
Mapping: [⟨4 0 41], ⟨0 1 -5]]
Mapping generators: ~1215/1024, ~3
POTE generator: ~3/2 = 702.736
Badness: 0.241703
7-limit
Subgroup: 2.3.5.7
Comma list: 5120/5103, 390625/388962
Mapping: [⟨4 0 41 81], ⟨0 1 -5 -11]]
Wedgie: ⟨⟨ 4 -20 -44 -41 -81 -46 ]]
POTE generator: ~3/2 = 702.736
Badness: 0.062754
11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 5120/5103, 5632/5625
Mapping: [⟨4 0 41 81 128], ⟨0 1 -5 -11 -18]]
POTE generator: ~3/2 = 702.689
Vals: Template:Val list
Badness: 0.034837