Amity family
The amity family tempers out the 5-limit amity comma, 1600000/1594323. The generator for the amity temperament is the acute minor third, which means the 6/5 just minor third raised by an 81/80 comma to 243/200, and from this it derives its name. If you are looking for a different kind of neutral third this could be the temperament for you.
Amity
In the 5-limit amity is a genuine microtemperament, with 58\205 being a possible tuning. Another good choice is (64/5)1/13, which gives a pure classical major third. Mos scales of 11, 18, 25, 32, 39, 46 or 53 notes are available.
Subgroup: 2.3.5
Comma list: 1600000/1594323
Mapping: [⟨1 3 6], ⟨0 -5 -13]]
Mapping generators: ~2, ~243/200
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.519
Badness: 0.021960
Overview to extensions
The second comma to extend the 5-limit amity include 4375/4374 for amity, 225/224 for houborizic, 65625/65536 for paramity, 126/125 for accord, 245/243 for bamity, 2430/2401 for hamity, 1029/1024 for gamity, 2401/2400 for amicable, and 16875/16807 for familia.
Temperaments discussed elsewhere include:
- Chromat, {10976/10935, 235298/234375} → Hemimage temperaments #Chromat
- Witch, {420175/419904, 1600000/1594323} → Wizmic microtemperaments #Witch
Septimal amity
Septimal amity can be described as the 46 & 53 temperament, which tempers out 4375/4374 and 5120/5103 in the 7-limit. 99edo is a good tuning, with generator 28\99.
Subgroup: 2.3.5.7
Comma list: 4375/4374, 5120/5103
Mapping: [⟨1 3 6 -2], ⟨0 -5 -13 17]]
Wedgie: ⟨⟨ 5 13 -17 9 -41 -76 ]]
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.432
Badness: 0.023649
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4375/4374, 5120/5103
Mapping: [⟨1 3 6 -2 21], ⟨0 -5 -13 17 -62]]
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.464
Optimal GPV sequence: Template:Val list
Badness: 0.031506
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 625/624, 847/845
Mapping: [⟨1 3 6 -2 21 17], ⟨0 -5 -13 17 -62 -47]]
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.481
Optimal GPV sequence: Template:Val list *
* optimal patent val: 205
Badness: 0.028008
Hitchcock
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 2200/2187
Mapping: [⟨1 3 6 -2 6], ⟨0 -5 -13 17 -9]]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.390
Optimal GPV sequence: Template:Val list
Badness: 0.035187
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 176/175, 325/324
Mapping: [⟨1 3 6 -2 6 2], ⟨0 -5 -13 17 -9 6]]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.419
Optimal GPV sequence: Template:Val list
Badness: 0.022448
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 169/168, 176/175, 273/272
Mapping: [⟨1 3 6 -2 6 2 -1], ⟨0 -5 -13 17 -9 6 18]]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.366
Optimal GPV sequence: Template:Val list
Badness: 0.019395
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189
Mapping: [⟨1 3 6 -2 6 2 -1 0], ⟨0 -5 -13 17 -9 6 18 15]]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.407
Optimal GPV sequence: Template:Val list
Badness: 0.017513
Catamite
The catamite temperament (46 & 99ef) tempers out 441/440 (werckisma) and 896/891 (pentacircle) in the 11-limit; 196/195, 352/351 and 364/363 in the 13-limit. The word "catamite" itself is a term for male homosexual, but also a play on the words "cata-" (down) and "amity."
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891, 4375/4374
Mapping: [⟨1 3 6 -2 -7], ⟨0 -5 -13 17 37]]
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.340
Optimal GPV sequence: Template:Val list
Badness: 0.040976
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 4375/4374
Mapping: [⟨1 3 6 -2 -7 -11], ⟨0 -5 -13 17 37 52]]
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.313
Optimal GPV sequence: Template:Val list
Badness: 0.034215
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155
Mapping: [⟨1 3 6 -2 -7 -11 -1], ⟨0 -5 -13 17 37 52 18]]
Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.313
Optimal GPV sequence: Template:Val list
Badness: 0.021193
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475
Mapping: [⟨1 3 6 -2 -7 -11 -1 -13], ⟨0 -5 -13 17 37 52 18 61]]
Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.325
Optimal GPV sequence: Template:Val list
Badness: 0.018864
Hemiamity
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 5120/5103
Mapping: [⟨2 1 -1 13 13], ⟨0 5 13 -17 -14]]
Mapping generators: ~99/70, ~64/55
Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.561
Optimal GPV sequence: Template:Val list
Badness: 0.031307
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 1716/1715, 3025/3024
Mapping: [⟨2 1 -1 13 13 20], ⟨0 5 13 -17 -14 -29]]
Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.583
Optimal GPV sequence: Template:Val list
Badness: 0.025784
Accord
Subgroup: 2.3.5.7
Comma list: 126/125, 100352/98415
Mapping: [⟨1 3 6 11], ⟨0 -5 -13 -29]]
Wedgie: ⟨⟨ 5 13 29 9 32 31 ]]
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 338.993
Badness: 0.095612
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 896/891
Mapping: [⟨1 3 6 11 6], ⟨0 -5 -13 -29 -9]]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.047
Optimal GPV sequence: Template:Val list
Badness: 0.042468
Houborizic
The houborizic temperament (53&113) tempers out the marvel comma, 225/224. It is so named because it is closely related to the houboriz tuning (generator: 339.774971 cents).
Subgroup: 2.3.5.7
Comma list: 225/224, 1250000/1240029
Mapping: [⟨1 3 6 13], ⟨0 -5 -13 -36]]
Wedgie: ⟨⟨ 5 13 36 9 43 47 ]]
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.763
Badness: 0.066638
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 1250000/1240029
Mapping: [⟨1 3 6 13 -9], ⟨0 -5 -13 -36 44]]
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.763
Optimal GPV sequence: Template:Val list
Badness: 0.067891
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 2200/2197
Mapping: [⟨1 3 6 13 -9 2], ⟨0 -5 -13 -36 44 6]]
Optimal tuning (POTE): ~2 = 1\1, ~39/32 = 339.764
Optimal GPV sequence: Template:Val list
Badness: 0.032996
Houbor
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 2200/2187
Mapping: [⟨1 3 6 13 6], ⟨0 -5 -13 -36 -9]]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.814
Optimal GPV sequence: Template:Val list
Badness: 0.045232
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273, 325/324
Mapping: [⟨1 3 6 13 6 2], ⟨0 -5 -13 -36 -9 6]]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.784
Optimal GPV sequence: Template:Val list
Badness: 0.031331
Paramity
The paramity temperament (53 & 311) tempers out the horwell comma (65625/65536) and garischisma (33554432/33480783).
Subgroup: 2.3.5.7
Comma list: 65625/65536, 1600000/1594323
Mapping: [⟨1 3 6 -17], ⟨0 -5 -13 70]]
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.553
Badness: 0.113655
11-limit
Subgroup: 2.3.5.7.11
Comma list: 6250/6237, 19712/19683, 41503/41472
Mapping: [⟨1 3 6 -17 36], ⟨0 -5 -13 70 -115]]
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554
Optimal GPV sequence: Template:Val list
Badness: 0.064853
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683
Mapping: [⟨1 3 6 -17 36 17], ⟨0 -5 -13 70 -115 -47]]
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554
Optimal GPV sequence: Template:Val list
Badness: 0.030347
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430
Mapping: [⟨1 3 6 -17 36 17 -31], ⟨0 -5 -13 70 -115 -47 124]]
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.555
Optimal GPV sequence: Template:Val list
Badness: 0.024118
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197
Mapping: [⟨1 3 6 -17 36 17 -31 15], ⟨0 -5 -13 70 -115 -47 124 -38]]
Optimal tuning (POTE): ~2 = 1\1, ~208/171 = 339.555
Optimal GPV sequence: Template:Val list
Badness: 0.017420
Bamity
Bamity has a period of half octave and tempers out the sensamagic comma, 245/243. The name bamity is a play on the words bi- and amity.
Subgroup: 2.3.5.7
Comma list: 245/243, 64827/64000
Mapping: [⟨2 1 -1 3], ⟨0 5 13 6]]
Mapping generators: ~343/240, ~7/6
Wedgie: ⟨⟨ 10 26 12 18 -9 -45 ]]
Optimal tuning (POTE): ~343/240 = 1\2, ~7/6 = 260.402
Badness: 0.083601
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 245/243, 441/440
Mapping: [⟨2 1 -1 3 3], ⟨0 5 13 6 9]]
Optimal tuning (POTE): ~99/70 = 1\2, ~7/6 = 260.393
Optimal GPV sequence: Template:Val list
Badness: 0.035504
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 245/243, 441/440
Mapping: [⟨2 1 -1 3 3 0], ⟨0 5 13 6 9 17]]
Optimal tuning (POTE): ~55/39 = 1\2, ~7/6 = 260.618
Optimal GPV sequence: Template:Val list
Badness: 0.030885
Hamity
Hamity has a generator of about 430 cents which represents 9/7. It is also generated by half of acute minor "tenth" (acute minor third of 243/200 plus an octave), and its name is a play on the words half and amity.
Subgroup: 2.3.5.7
Comma list: 2430/2401, 4000/3969
Mapping: [⟨1 -2 -7 -4], ⟨0 10 26 19]]
Wedgie: ⟨⟨ 10 26 19 18 2 -29 ]]
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.219
Badness: 0.073956
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 2200/2187
Mapping: [⟨1 -2 -7 -4 -3], ⟨0 10 26 19 18]]
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.192
Optimal GPV sequence: Template:Val list
Badness: 0.042947
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 275/273, 572/567
Mapping: [⟨1 -2 -7 -4 -3 -11], ⟨0 10 26 19 18 41]]
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.216
Optimal GPV sequence: Template:Val list
Badness: 0.029753
Gamity
The gamity temperament (46 & 113) tempers out the gamelisma, 1029/1024. It splits the interval of grave major sixth (~400/243, an octave minus acute minor third) in three.
Subgroup: 2.3.5.7
Comma list: 1029/1024, 1071875/1062882
Mapping: [⟨1 -2 -7 4], ⟨0 15 39 -5]]
Wedgie: ⟨⟨ 15 39 -5 27 -50 -121 ]]
Optimal tuning (POTE): ~2 = 1\1, ~189/160 = 286.787
Badness: 0.125733
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 1071875/1062882
Mapping: [⟨1 -2 -7 4 8], ⟨0 15 39 -5 -19]]
Optimal tuning (POTE): ~2 = 1\1, ~33/28 = 286.797
Optimal GPV sequence: Template:Val list
Badness: 0.051111
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384, 10985/10976
Mapping: [⟨1 -2 -7 4 8 8], ⟨0 15 39 -5 -19 -18]]
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.789
Optimal GPV sequence: Template:Val list
Badness: 0.030297
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757
Mapping: [⟨1 -2 -7 4 8 8 6], ⟨0 15 39 -5 -19 -18 -8]]
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.795
Optimal GPV sequence: Template:Val list
Badness: 0.022036
Trinity
The trinity temperament (152 & 159) tempers out the meter, 703125/702464. It splits the interval of acute minor tenth (~243/100, an octave plus acute minor third) in three. It was so named for the following reason – 133\311 (133 steps of 311edo) is a possible generator, which is placed around 3\7 (1.1¢ flat), three of which makes acute minor third of ~243/200 with octave reduction.
Subgroup: 2.3.5.7
Comma list: 703125/702464, 1600000/1594323
Mapping: [⟨1 8 19 46], ⟨0 -15 -39 -101]]
Wedgie: ⟨⟨ 15 39 101 27 118 125 ]]
Optimal tuning (POTE): ~2 = 1\1, ~168/125 = 513.178
Badness: 0.119453
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 19712/19683
Mapping: [⟨1 8 19 46 18], ⟨0 -15 -39 -101 -34]]
POTE generator: ~121/90 = 513.177
Optimal GPV sequence: Template:Val list
Badness: 0.031296
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689
Mapping: [⟨1 8 19 46 18 64], ⟨0 -15 -39 -101 -34 -141]]
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.182
Optimal GPV sequence: Template:Val list
Badness: 0.026418
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619
Mapping: [⟨1 8 19 46 18 64 -22], ⟨0 -15 -39 -101 -34 -141 61]]
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186
Optimal GPV sequence: Template:Val list
Badness: 0.025588
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573
Mapping: [⟨1 8 19 46 18 64 -22 53], ⟨0 -15 -39 -101 -34 -141 61 -114]]
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185
Optimal GPV sequence: Template:Val list
Badness: 0.018412
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104
Mapping: [⟨1 8 19 46 18 64 -22 53 49], ⟨0 -15 -39 -101 -34 -141 61 -114 -104]]
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185
Optimal GPV sequence: Template:Val list
Badness: 0.014343
29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044
Mapping: [⟨1 8 19 46 18 64 -22 53 49 72], ⟨0 -15 -39 -101 -34 -141 61 -114 -104 -157]]
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186
Optimal GPV sequence: Template:Val list
Badness: 0.012038
Amicable
The amicable temperament tempers out the amity comma and the canousma in addition to the breedsma, and is closely associated with the canou temperament.
While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 & 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 & 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 & 113) and pseudoamorous (14cf & 99ef) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semioctave period and the ~21/20 generator with harry, but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.
Subgroup: 2.3.5.7
Comma list: 2401/2400, 1600000/1594323
Mapping: [⟨1 3 6 5], ⟨0 -20 -52 -31]]
Wedgie: ⟨⟨ 20 52 31 36 -7 -74 ]]
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.880
Badness: 0.045473
Amical
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 131072/130977, 1600000/1594323
Mapping: [⟨1 3 6 5 -8], ⟨0 -20 -52 -31 162]]
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8843
Optimal GPV sequence: Template:Val list
Badness: 0.100668
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206
Mapping: [⟨1 3 6 5 -8 -5], ⟨0 -20 -52 -31 162 123]]
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8838
Optimal GPV sequence: Template:Val list
Badness: 0.049893
Amorous
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 6250/6237, 19712/19683
Mapping: [⟨1 3 6 5 14], ⟨0 -20 -52 -31 -149]]
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8896
Optimal GPV sequence: Template:Val list
Badness: 0.048924
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647
Mapping: [⟨1 3 6 5 14 17], ⟨0 -20 -52 -31 -149 -188]]
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8910
Optimal GPV sequence: Template:Val list
Badness: 0.034681
Pseudoamical
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1375/1372, 1600000/1594323
Mapping: [⟨1 3 6 5 -1], ⟨0 -20 -52 -31 63]]
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9091
Optimal GPV sequence: Template:Val list
Badness: 0.085837
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 1375/1372, 19773/19712
Mapping: [⟨1 3 6 5 -1 2], ⟨0 -20 -52 -31 63 24]]
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9127
Optimal GPV sequence: Template:Val list
Badness: 0.047025
Pseudoamorous
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 980000/970299
Mapping: [⟨1 3 6 5 7], ⟨0 -20 -52 -31 -50]]
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8917
Optimal GPV sequence: Template:Val list
Badness: 0.056583
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 364/363, 441/440, 1875/1859
Mapping: [⟨1 3 6 5 7 10], ⟨0 -20 -52 -31 -50 -89]]
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9164
Optimal GPV sequence: Template:Val list
Badness: 0.042826
Floral
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800, 14641/14580
Mapping: [⟨2 6 12 10 13], ⟨0 -20 -52 -31 -43]]
Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8788
Optimal GPV sequence: Template:Val list
Badness: 0.065110
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580
Mapping: [⟨2 6 12 10 13 19], ⟨0 -20 -52 -31 -43 -82]]
Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8750
Optimal GPV sequence: Template:Val list
Badness: 0.037013
Humorous
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024, 1600000/1594323
Mapping: [⟨1 3 6 5 3], ⟨0 -40 -104 -62 13]]
Optimal tuning (POTE): ~2 = 1\1, ~4096/3993 = 42.4391
Optimal GPV sequence: Template:Val list
Badness: 0.058249
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024
Mapping: [⟨1 3 6 5 3 6], ⟨0 -40 -104 -62 13 -65]]
Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 42.4391
Optimal GPV sequence: Template:Val list
Badness: 0.028267
Familia
The familia temperament (113 & 152) tempers out the mirkwai comma, 16875/16807. It splits the interval of acute minor tenth (~243/100) in five.
Subgroup: 2.3.5.7
Comma list: 16875/16807, 1600000/1594323
Mapping: [⟨1 8 19 20], ⟨0 -25 -65 -67]]
Wedgie: ⟨⟨ 25 65 67 45 36 -27 ]]
Optimal tuning (POTE): ~2 = 1\1, ~11907/10000 = 307.941
Badness: 0.144551
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 1600000/1594323
Mapping: [⟨1 8 19 20 5], ⟨0 -25 -65 -67 -6]]
Optimal tuning (POTE): ~2 = 1\1, ~3200/2673 = 307.906
Optimal GPV sequence: Template:Val list
Badness: 0.051740
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1375/1372, 2205/2197
Mapping: [⟨1 8 19 20 5 25], ⟨0 -25 -65 -67 -6 -83]]
Optimal tuning (POTE): ~2 = 1\1, ~143/120 = 307.913
Optimal GPV sequence: Template:Val list
Badness: 0.038473