User:Francium/Miscellaneous rank-2 temperaments
On this page, I explore some unnamed rank-2 temperaments that catched my interest.
Berkenthin (19 & 239)
Subgroup: 2.3.5
Comma list: [-26 -29 31⟩
Mapping: [⟨1 13 13], ⟨0 -31 -29]]
POTE generator: ~39182082048/30517578125 = 441.8700
Optimal ET sequence: 19, 144bc, 163bc, 182b, 201, 220, 239, 258, 277, 535, 1882c
Badness: 19.828
7-limit
Subgroup: 2.3.5.7
Comma list: 10976/10935, 48828125/48771072
Mapping: [⟨1 13 13 33], ⟨0 -31 -29 -82]]
POTE generator: ~4032/3125 = 441.8483
Optimal ET sequence: 19, 144bcddd, 163bcdd, 182bdd, 201d, 220, 239, 497, 736
Badness: 3.566
Totziens (19 & 251)
Subgroup: 2.3.5
Comma list: [22 33 -32⟩
Mapping: [⟨1 10 11], ⟨0 -32 -33]]
POTE generator: ~6/5 = 315.5643
Optimal ET sequence: 19, 156bc, 175bc, 194bc, 213, 232, 251, 270, 289, 559, 1407, 1966, 2525, 10659c
Badness: 2.830
7-limit
Subgroup: 2.3.5.7
Comma list: 4375/4374, 7710244864/7688671875
Mapping: [⟨1 10 11 27], ⟨0 -32 -33 -92]]
POTE generator: ~6/5 = 315.5565
Optimal ET sequence: 19, 175bcddd, 194bcdd, 213dd, 232d, 251, 270, 2449c, 2719c, 2989bc
Badness: 1.422
Denjoy (19 & 349)
Subgroup: 2.3.5
Comma list: [-32 -34 37⟩
Mapping: [⟨1 -14 -12], ⟨0 37 34]]
POTE generator: ~244140625/181398528 = 505.4605
Optimal ET sequence: 19, 178bc, 197bc, 216b, 235b, 254, 273, 292, 311, 641
Badness: 40.121
11-limit
Subgroup: 2.3.5.11
Comma list: 1953125/1948617, 4322682045/4294967296
Mapping: [⟨1 -14 -12 46], ⟨0 37 34 -101]]
POTE generator: ~1375/1024 = 505.4459
Optimal ET sequence: 19, 292ee, 311e, 330e, 349, 1028cee, 1377cceee, 1726bccceee
Badness: 12.504
Brzezinska (19 & 563)
Subgroup: 2.3.5
Comma list: [38 61 -58⟩
Mapping: [⟨1 26 28], ⟨0 -58 -61]]
POTE generator: ~19073486328125/14281868906496 = 505.1394
Optimal ET sequence: 19, 297bbcc, 316bbcc, 335bbcc, 354bcc, 373bc, 392bc, 411bc, 430c, 449, 468, 487, 506, 1537, 2043, 4592c
Badness: 49.390
Greensleeves (19 & 631)
Subgroup: 2.3.5
Comma list: [-50 -71 70⟩
Mapping: [⟨1 20 21], ⟨0 -70 -71]]
POTE generator: ~6/5 = 315.6862
Optimal ET sequence: 19, 403bbcc, 422bbcc, 441bbcc, 460bc, 479bc, 498bc, 517bc, 536, 555, 574, 593, 612
Badness: 17.150
7-limit
Subgroup: 2.3.5.7
Comma list: 4375/4374, [37 -20 -18 13⟩
Mapping: [⟨1 20 21 57], ⟨0 -70 -71 -206]]
POTE generator: ~6/5 = 315.6854
Optimal ET sequence: 19, 517bcddd, 536dd, 555d, 574d, 593, 612, 1205, 1817, 2429, 4246, 6675
Badness: 1.798
Wegener (29 & 227)
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 2080/2079, 1001/1000, 268912/268125
Mapping: [⟨1 2 -13 -15 -10 -11], ⟨0 -2 74 86 65 71]]
POTE generator: ~15/13 = 248.4809
Optimal ET sequence: 29, 111ccddeeff, 140cdef, 169cdf, 198
Badness: 1.796
31 & 197
Subgroup: 2.3.5.7
Comma list: 225/224, 201768035/201326592
Mapping: [⟨1 -7 10 1], ⟨0 19 -17 4]
POTE generator: ~16384/12005 = 542.1310
Optimal ET sequence: 31, 104, 135, 166, 197
Badness: 3.161
31 & 227
Subgroup: 2.3.5.7
Comma list: 235298/234375, 65625/65536
Mapping: [⟨1 -2 3 3], ⟨0 37 -7 -2]]
POTE generator: ~2560/2401 = 116.2790
Optimal ET sequence: 31, 165, 196, 227, 258, 289
Badness: 2.917
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 3388/3375, 151263/151250
Mapping: [⟨1 -2 3 3 -1], ⟨0 37 -7 -2 46]]
POTE generator: ~294/275 = 116.2717
Optimal ET sequence: 9, 22, 31, 53, 84e, 87, 118, 258e, 376de, 547dee
Badness: 2.101
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 352/351, 385/384, 16807/16731
Mapping: [⟨1 -2 3 3 -1 10], ⟨0 37 -7 -2 46 -65]]
POTE generator: ~294/275 = 116.2869
Badness: 2.393
31 & 317
Subgroup: 2.5.7
Comma list: 281484423828125/281474976710656
Mapping: [⟨1 0 6], ⟨0 8 -11]]
POTE generator: ~262144/214375 = 348.2889
Optimal ET sequence: 7, 24, 31, 224, 255, 286, 317, 348, 379, 410, 789, 6691, 7480, 8269, 9058, 9847, 10636
Badness: 0.015
11-limit
Subgroup: 2.5.7.11
Comma list: 5767168/5764801, 537109375/536870912
Mapping: [⟨1 0 6 29], ⟨0 8 -11 -88]]
POTE generator: ~16807/13750 = 348.2809
Optimal ET sequence: 31, 255e, 286e, 317, 348, 379, 727, 3287, 4014, 4741, 5468
Badness: 0.811
31 & 367
Subgroup: 2.3.5
Comma list: [-156 12 59⟩
Mapping: [⟨1 13 0], ⟨0 -59 12]]
POTE generator: ~2500/2187 = 232.1720
Optimal ET sequence: 31, 305b, 336, 367, 398, 429, 460, 889, 1349
Badness: 90.743
31 & 397
Subgroup: 2.3.5
Comma list: [55 -1 -23⟩
Mapping: [⟨1 9 2], ⟨0 -46 2]]
POTE generator: ~4096/3645 = 193.4315
Optimal ET sequence: 28b, 31, 90, 121, 152, 335, 822, 1157c, 1492c, 2649cc
Badness: 9.862
31 & 431
Subgroup: 2.3.5.7
Comma list: 2401/2400, 8589934592/8544921875
Mapping: [⟨1 19 2 7], ⟨0 -54 1 -13]]
POTE generator: ~ 5/4 = 386.9969
31, 214b, 245b, 276b, 307, 338, 369, 400), 769, 1169c, 1938cc
Badness: 3.038
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 2401/2400, 46656/46585
Mapping: [⟨1 19 2 7 37], ⟨0 -54 1 -13 -104]]
POTE generator: ~5/4 = 386.9992
Optimal ET sequence: 31, 276bee, 307e, 338e, 369, 400, 1969ccee
Badness: 1.372
13-limit
Subgroup: 2.3.5.7.11.13
Commas: 1001/1000, 1716/1715, 4096/4095, 75816/75625
Mapping: [⟨1 19 2 7 37 -35], ⟨0 -54 1 -13 -104 120]]
POTE generator: ~5/4 = 387.0031
Optimal ET sequence: 31, 369, 400, 831
Badness: 1.798
31 & 449
Subgroup: 2.3.5.7
Comma list: 6144/6125, [7 -4 -16 13⟩
Mapping: [⟨1 -3 2 1], ⟨0 71 5 28]]
POTE generator: ~256/245 = 77.498
Optimal ET sequence: 31, 294bbd, 325bd, 356bd, 387bd, 418d, 449, 480, 991cd
Badness: 8.502
Adriansonka (31 & 569)
Subgroup: 2.3.5.7
Comma list: 65625/65536, 678223072849/675000000000
Mapping: [⟨1 -35 10 1], ⟨0 81 -17 4]]
CTE tuning: ~1875/1372 = 542.0577
Optimal ET sequence: 31, 476b, 507, 538, 569, 600, 631
Badness: 7.921
11-limit
Subgroup: 2.3.5.7.11
Comma list: 42592/42525, 65625/65536, 422576/421875
Mapping: [⟨1 -35 10 1 -53], ⟨0 81 -17 4 125]]
CTE tuning: ~308/225 = 542.0730
Optimal ET sequence: 31, 476b, 507, 538, 569, 600e
Badness: 3.942
31 & 577
Subgroup: 2.5.7
Comma list: [60 -21 -4⟩
Mapping: [⟨1 4 -6], ⟨0 -4 21]]
CTE tuning: ~21875/16384 = 503.2464
Optimal ET sequence: 12d, 19d, 31, 298, 329, 360, 391, 422, 453, 484, 515, 546, 3307ccdd, 3853cccdd
Badness: 5.455
11-limit
Comma list: 4302592/4296875, [44 -5 -14 2⟩
Mapping: [⟨1 4 -6 -54], ⟨0 -4 21 137]]
CTE tuning: ~21875/16384 = 503.2468
Optimal ET sequence: 31, 391ee, 422ee, 453e, 484e, 515, 546, 2153cde, 2699ccde, 3245ccddee, 3791cccddee
Badness: 6.490
37 & 307
Subgroup: 2.5.7
Comma list: [20 -34 21⟩
Mapping: [⟨1 8 12], ⟨0 -21 -34]]
CTE tuning: ~1475789056/1220703125 = 324.444
Optimal ET sequence: 11cd, 26cdd, 37, 159, 196, 233, 270, 503, 773, 1816, 2589c
Badness: 7.966
11-limit
Subgroup: 2.5.7.11
Comma list: 102487/102400, 4302592/4296875
Mapping: [⟨1 8 12 4], ⟨0 -21 -34 -2]]
CTE tuning: ~15125/12544 = 324.4587
Optimal ET sequence: 11cd, 37, 159, 196, 233, 270, 503
Badness: 0.511
13-limit
Subgroup: 2.5.7.11.13
Comma list: 1001/1000, 6656/6655, 105644/105625
Mapping: [⟨1 8 12 4 11], ⟨0 -21 -34 -2 -27]]
CTE tuning: ~650/539 = 324.4626
Optimal ET sequence: 11cdf, 37, 159, 196, 233, 270, 503, 773, 1276f
Badness: 0.290
17-limit
Subgroup: 2.5.7.11.13.17
Comma list: 1001/1000, 7744/7735, 32768/32725, 105644/105625
Mapping: [⟨1 8 12 4 11 -17], ⟨0 -21 -34 -2 -27 78]]
CTE tuning: ~650/539 = 324.4083
Optimal ET sequence: 37, 233g, 270, 307
Badness: 0.929
19-limit
Subgroup: 2.5.7.11.13.17.19
Comma list: 1001/1000, 3328/3325, 2128/2125, 7744/7735, 105644/105625
Mapping: [⟨1 8 12 4 11 -17 -9], ⟨0 -21 -34 -2 -27 78 49]]
CTE tuning: ~650/539 = 324.4173
Optimal ET sequence: 37, 233g, 270, 307, 577g, 884g
Badness: 0.809
37 & 577
Subgroup: 2.5.7
Comma list: [20 -34 21⟩
Mapping: [⟨1 8 12], ⟨0 -42 -68]]
CTE tuning: ~1475789056/1220703125 = 324.444
Optimal ET sequence: 11cd, 26cdd, 37, 159, 196, 233, 270, 503, 773, 1816, 2589c
Badness: 7.966
11-limit
Subgroup: 2.5.7.11
Comma list: 102487/102400, 4302592/4296875
Mapping: [⟨1 8 12 4], ⟨0 -42 -68 -4]]
CTE tuning: ~3773/3125 = 324.451
Optimal ET sequence: 11cd, 37, 159, 196, 233, 270, 503
Badness: 0.511
13-limit
Subgroup: 2.5.7.11.13
Comma list: 1001/1000, 10985/10976, 75712/75625
Mapping: [⟨1 8 12 4 11], ⟨0 -42 -68 -4 -54]]
CTE tuning: ~169/140 = 324.446
Optimal ET sequence: 11cdf, 37, 159, 196, 233, 270, 503, 773, 1276f
Badness: 0.290
41 & 167
Subgroup: 2.3.5.7
Comma list: 2401/2400, 179200/177147
Mapping: [⟨1 5 17 11], ⟨0 -10 -43 -24]]
CTE tuning: ~80/63 = 409.639
Optimal ET sequence: 38ccd, 41, 126, 167, 208, 375b
Badness: 2.943
11-limit
Subgroup: 2.3.5.7
Comma list: 896/891, 2200/2187, 2401/2400
Mapping: [⟨1 5 17 11 -2], ⟨0 -10 -43 -24 16]]
CTE tuning: ~80/63 = 409.630
Optimal ET sequence: 41, 126, 167, 208, 375be
Badness: 1.816
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 896/891, 2401/2400
Mapping: [⟨1 5 17 11 -2 -12], ⟨0 -10 -43 -24 16 46]]
CTE tuning: ~195/154 = 409.617
Optimal ET sequence: 41, 126, 167, 208, 375be
Badness: 1.782
41 & 197
Subgroup: 2.3.5.7
Comma list: 225/224, 4202539929/4194304000
Mapping: [⟨1 0 5 5], ⟨0 13 -22 -18]]
POTE generator: ~160/147 = 146.1953
Optimal ET sequence: 33, 41, 115, 156, 197
Badness: 3.049
41 & 227
Subgroup: 2.3.5.7
Comma list: 5120/5103, 117649/116640
Mapping: [⟨1 0 -11 -1], ⟨0 5 42 12]]
POTE generator: ~56/45 = 380.6339
Optimal ET sequence: 19cc, 22c, 41, 104c, 145, 186, 413
Badness: 2.852
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 2200/2187, 67228/66825
Mapping: [⟨1 0 -11 -1 19], ⟨0 5 42 12 -49]]
POTE generator: ~96/77 = 380.6090
Optimal ET sequence: 41, 145e, 186, 227
Badness: 2.774
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 325/324, 352/351, 67228/66825
Mapping: [⟨1 0 -11 -1 19 24], ⟨0 5 42 12 -49 -64]]
POTE generator: ~96/77 = 380.6135
Optimal ET sequence: 41, 145ef, 186, 227
Badness: 2.307
41 & 233
Subgroup: 2.3.5.7
Comma list: 2401/2400, 124556484375/123363917824
Mapping: [⟨1 9 -19 -6], ⟨0 -16 46 19]]
POTE generator: ~30375/21952 = 556.1960
Optimal ET sequence: 41, 151, 192, 233, 274, 315, 589bcd
Badness: 4.209
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 540/539, 5053640625/5035261952
Mapping: [⟨1 9 -19 -6 22], ⟨0 -16 46 19 -40]]
POTE generator: ~2475/1792 = 556.2083
Badness: 2.494
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 540/539, 21168/21125, 81675/81536
Mapping: [⟨1 9 -19 -6 22 38], ⟨0 -16 46 19 -40 -74]]
POTE generator: ~91/66 = 556.2131
Optimal ET sequence: 41, 192, 233, 274, 507b
Badness: 2.034
41 & 337
(better described as 41 & 255)
Subgroup: 2.3.5.7
Comma list: 16875/16807, 7381125/7340032
Mapping: [⟨1 4 -8 -4], ⟨0 -11 47 31]]
POTE generator: ~784/675 = 263.5183
Optimal ET sequence: 41, 173, 214, 255, 296, 551, 847c
Badness: 3.414
41 & 359
Subgroup: 2.3.5
Comma list: [155 -89 -6⟩
Mapping: [⟨1 1 11], ⟨0 6 -89]]
POTE generator: ~2187/2048 = 117.0069
Optimal ET sequence: 41, 236cc, 277c, 318c, 359, 400, 441
Badness: 46.849
7-limit
Subgroup: 2.3.5.7
Comma list: 2401/2400, 11785390260224/11767897353375
Mapping: [⟨1 1 11 7], ⟨0 6 -89 -43]]
POTE generator: ~15/14 = 117.0067
Optimal ET sequence: 41, 236cc, 277c, 318c, 359, 400, 441
Badness: 1.383
11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 200704/200475, 46656/46585
Mapping: [⟨1 1 11 7 -2], ⟨0 6 -89 -43 56]]
POTE generator: ~77/72 = 117.0029
Optimal ET sequence: 41, 318c, 359, 400, 841e, 1241e
Badness: 1.716
41 & 373
Subgroup: 2.3.5.7
Comma list: 2401/2400, [-35 18 4 -1⟩
Mapping: [⟨1 5 -15 -5], ⟨0 -14 71 32]]
POTE generator: ~1215/1024 = 292.7572
Optimal ET sequence: 41, 209c, 250c, 291, 332, 373, 414, 787
Badness: 3.790
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 2401/2400, 4428675/4415488
Mapping: [⟨1 5 -15 -5 22], ⟨0 -14 71 32 -76]]
POTE generator: ~4096/3465 = 292.7564
Optimal ET sequence: 41, 291e, 332e, 373, 414, 787e, 1201bcde, 1988bcddee
Badness: 1.849
41 & 421
Subgroup: 2.3.7
Comma list: [-125 47 18⟩
Mapping: [⟨1 -5 20], ⟨0 18 -47]]
POTE generator: ~9/7 = 438.9747
Optimal ET sequence: 41, 298, 339, 380, 421, 462, 503, 544, 585, 2966bddd
Badness: 78.897
11-limit
Subgroup: 2.3.7.11
Comma list: 2893401/2883584, 208971104256/208422380089
Mapping: [⟨1 -5 20 -28], ⟨0 18 -47 86]]
POTE generator: ~9/7 = 438.9681
Optimal ET sequence: 41, 380e, 421, 462, 503, 1047, 1550b
Badness: 6.355
13-limit
Subgroup: 2.3.7.11.13
Comma list: 85293/85184, 53361/53248, 216513/215306
Mapping: [⟨1 -5 20 -28 -38], ⟨0 18 -47 86 114]]
POTE generator: ~156/121 = 438.9595
Optimal ET sequence: 41, 380e, 421, 462
Badness: 4.703
41 & 509
Subgroup: 2.3.5.7
Comma list: 2401/2400, [40 -27 0 1⟩
Mapping: [⟨1 1 -29 -13], ⟨0 2 107 54]]
POTE generator: ~49/40 = 351.278
Optimal ET sequence: 41, 263ccd, 304ccd, 345c, 386c, 427c, 468, 509, 1486bc
Badness: 6.884
41 & 523
(better known as 41 & 441)
Subgroup: 2.3.5.7
Comma list: 2401/2400, [35 -23 -3 3⟩
Mapping: [⟨1 1 11 7], ⟨0 6 -89 -43]]
POTE generator: ~15/14 = 117.006
Optimal ET sequence: 41, 236cc, 277c, 318c, 359, 400, 441
Badness: 1.383
11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 19712/19683, 166375/165888
Mapping: [⟨1 1 11 7 -6], ⟨0 6 -89 -43 97]]
POTE generator: ~77/72 = 117.025
Optimal ET sequence: 41, 400e, 441e, 482, 1487cdee
Badness: 3.127
41 & 571
Subgroup: 2.3.5.7
Comma list: 2401/2400, [50 -31 -4 3⟩
Mapping: [⟨1 5 -39 -17], ⟨0 -10 121 58]]
POTE generator: ~2657205/2097152 = 409.8044
Optimal ET sequence: 41, 407c, 448, 489c, 530, 571, 612, 2407, 3019, 3631d, 4243d
Badness: 1.987
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 2401/2400, 645922816/645700815
Mapping: [⟨1 5 -39 -17 40], ⟨0 -10 121 58 -107]]
POTE generator: ~308/243 = 409.8034
Badness: 1.291
43 & 233
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 1001/1000, 21168/21125, 81675/81536
Mapping: [⟨1 8 -8 -17 -13 9], ⟨0 -23 37 71 59 -19]]
POTE generator: ~40/33 = 334.7481
Optimal ET sequence: 43, 147de, 190, 423d, 613bde
Badness: 1.813
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 441/440, 561/560, 1275/1274, 1156/1155, 21168/21125
Mapping: [⟨1 8 -8 -17 -13 9 -16], ⟨0 -23 37 71 59 -19 72]]
POTE generator: ~17/14 = 334.7511
Optimal ET sequence: 43, 147deg, 190g, 233, 423dg
Badness: 1.592
Mehlem (53 & 179)
Subgroup: 2.3.5
Comma list: [12 -31 16⟩
Mapping: [⟨1 4 7], ⟨0 -16 -31]]
POTE generator: ~10/9 = 181.0964
Optimal ET sequence: 20c, 33c, 53, 338, 391, 444, 497, 550, 603, 656, 1259b
Badness: 10.511
7-limit
Subgroup: 2.3.5.7
Comma list: 4375/4374, 65536/64827
Mapping: [⟨1 4 7 1], ⟨0 -16 -31 12]]
POTE generator: ~10/9 = 181.0314
Optimal ET sequence: 20c, 53, 126, 179, 232d
Badness: 3.333
53 & 239
Subgroup: 2.3.5
Comma list: 390625000/387420489
Mapping: [⟨1 2 3], ⟨0 -11 -18]]
POTE generator: ~250/243 = 45.2329
Optimal ET sequence: 25bcc, 26, 27, 53, 239, 292, 345, 398, 451
Badness: 2.750
7-limit
Subgroup: 2.3.5.7
Comma list: 5120/5103, 95703125/95551488
Mapping: [⟨1 2 3 1], ⟨0 -11 -18 48]]
POTE generator: ~250/243 = 45.1995
Optimal ET sequence: 53, 186, 239, 292, 531, 823bd
Badness: 2.937
53 & 307
Subgroup: 2.9.5
Comma list: 32805/32768
Mapping: [⟨1 0 15], ⟨0 7 -28]]
POTE generator: ~512/375 = 543.3531
Optimal ET sequence: 6, 29, 35, 41, 47, 53, 59, 171, 230, 519, 749
Badness: 0.100
53 & 467
Subgroup: 2.3.5
Comma list: [-36 11 8⟩
Mapping: [⟨1 4 -1], ⟨0 -8 11]]
POTE generator: ~10125/8192 = 362.3210
Optimal ET sequence: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc
Badness: 3.055
7-limit
Subgroup: 2.3.5.7
Comma list: 4375/4374, 69198046875/68719476736
Mapping: [⟨1 4 -1 33], ⟨0 -8 11 -100]]
POTE generator: ~10125/8192 = 362.3181
Optimal ET sequence: 53, 255d, 308d, 361, 414, 2123bccdd
Badness: 4.674
53 & 499
Subgroup: 2.3.5
Comma list: [63 -50 7⟩
Mapping: [⟨1 0 -9], ⟨0 7 50]
POTE generator: ~2560/2187 = 271.7276
Optimal ET sequence: 22c, 31c, 53, 393, 446, 499, 552, 605, 658, 711, 764, 6165b, 6929b, 7693b, 8457b, 9221bbc, 9985bbc, 10749bbc
Badness: 8.860
7-limit
Subgroup: 2.3.5.7
Comma list: 26873856/26796875, 33554432/33480783
Mapping: [⟨1 0 -9 25], ⟨0 7 50 -98]]
POTE generator: ~1024/875 = 271.7017
Optimal ET sequence: 53, 393, 446, 499, 552, 2155ccdd, 2707bcccdd
Badness: 6.432
103 & 167
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 3025/3024, 1716/1715, 4225/4224
Mapping: [⟨1 -25 -16 -13 -26 -6], ⟨0 74 51 44 82 27]]
POTE generator: ~440/343 = 431.1062
Badness: 0.662
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 1001/1000, 1225/1224, 715/714, 936/935, 4225/4224
Mapping: [⟨1 -25 -16 -13 -26 -6 -11], ⟨0 74 51 44 82 27 42]]
POTE generator: ~440/343 = 431.1087
Optimal ET sequence: 39bce, 64be, 103, 167, 270
Badness: 1.068
103 & 227
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 1001/1000, 4225/4224, 50421/50336
Mapping: [⟨1 -36 -11 -1 -17 -12], ⟨0 79 28 8 43 33]]
POTE generator: ~490/352 = 570.9053
Optimal ET sequence: 21b, 103, 227, 330e
Badness: 2.198
103 & 503
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 46656/46585, 766656/765625
Mapping: [⟨1 -41 -34 -26 -60], ⟨0 102 87 69 152]]
POTE generator: ~4/3 = 500.9986
Optimal ET sequence: 91bcdee, 103, 297e, 400, 1303c, 1703ce
Badness: 2.344
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 4225/4224, 75816/75625
Mapping: [⟨1 -41 -34 -26 -60 -13], ⟨0 102 87 69 152 40]]
POTE generator: ~4/3 = 500.9970
Optimal ET sequence: 91bcdee, 103, 297e, 400, 503, 903
Badness: 1.735
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 1001/1000, 936/935, 1377/1375, 1716/1715, 4225/4224
Mapping: [⟨1 -41 -34 -26 -60 -13 2], ⟨0 102 87 69 152 40 5]]
POTE generator: ~4/3 = 500.9972
Badness: 1.402
103 & 647
Subgroup: 2.5.7.11.13
Comma list: 105644/105625, 5462275/5451776, 200000/199927
Mapping: [⟨1 25 23 60 27], ⟨0 -73 -65 -182 -75]]
POTE generator: ~3872/3125 = 372.7948
Optimal ET sequence: 103, 338e, 441, 544, 1735cd
Badness: 1.978
113 & 409
Subgroup: 2.3.7.11
Comma list: 5038848/5021863, 235782657/234881024
Mapping: [⟨1 4 16 -1], ⟨0 -13 -71 24]]
POTE generator: ~8192/7203 = 222.9728
Optimal ET sequence: 70, 113, 183, 296
Badness: 5.092
13-limit
Subgroup: 2.3.7.11.13
Comma list: 729/728, 19773/19712, 718848/717409
Mapping: [⟨1 4 16 -1 5], ⟨0 -13 -71 24 -7]]
POTE generator: ~91/80 = 222.9746
Optimal ET sequence: 70, 113, 183, 296
Badness: 1.829
193 & 547
Subgroup: 2.3.5.7
Comma list: 589824/588245, 23066015625/23018340352
Mapping: [⟨1 0 4 2], ⟨0 51 -54 26]]
POTE generator: ~49/48 = 37.2913
Optimal ET sequence: 32, 129, 161, 193, 354, 547, 901d, 1255d
Badness: 7.020
193 & 607
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 3025/3024, 78975/78848, 218700/218491
Mapping: [⟨1 26 2 42 60 -22], ⟨0 -76 1 -122 -176 80]
POTE generator: ~5/4 = 385.5044
Optimal ET sequence: 193, 414, 607, 1021c
Badness: 2.529
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831
Mapping: [⟨1 26 2 42 60 -22 33], ⟨0 -76 1 -122 -176 80 -90]
POTE generator: ~5/4 = 385.5044
Optimal ET sequence: 193, 414, 607, 1021c
Badness: 1.693
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 625/624, 1225/1224, 3025/3024, 1729/1728, 6669/6664, 26775/26752
Mapping: [⟨1 26 2 42 60 -22 33 64], ⟨0 -76 1 -122 -176 80 -90 -186]]
POTE generator: ~5/4 = 385.5037
Optimal ET sequence: 193, 414h, 607, 1021chh
Badness: 1.618
233 & 317
Subgroup: 2.5.7.11
Comma list: 537109375/536870912, 40353607/40262750
Mapping: [⟨1 -1 22 40], ⟨0 9 -52 -99]]
POTE generator: ~15488/12005 = 442.9148
Optimal ET sequence: 65e, 84, 149, 233, 783, 1016, 1249, 1482
Badness: 3.492
13-limit
Subgroup: 2.5.7.11.13
Comma list: 75712/75625, 10985/10976, 5462275/5451776
Mapping: [⟨1 -1 22 40 24], ⟨0 9 -52 -99 -55]]
POTE generator: ~455/352 = 442.9140
Optimal ET sequence: 65ef, 84, 149, 233, 783, 1016f, 1249f
Badness: 1.410
239 & 569
Subgroup: 2.3.5.7
Comma list: 823543/820125, 68359375/68024448
Mapping: [⟨1 8 9 13], ⟨0 -73 -76 -116]]
POTE generator: ~729/686 = 105.4479
Optimal ET sequence: 34bcdd, 57bcd, 91, 148d, 239, 330, 569
Badness: 8.274
11-limit
Subgroup: 2.3.5.7.11
Comma list: 42875/42768, 42592/42525, 151263/151250
Mapping: [⟨1 8 9 13 22], ⟨0 -73 -76 -116 -211]]
POTE generator: ~729/686 = 105.4456
Optimal ET sequence: 57bcdeee, 91e, 148dee, 239, 569, 808
Badness: 3.518
277 & 641
Subgroup: 2.3.5
Comma list: [-56 -13 33⟩
Mapping: [⟨1 16 8], ⟨0 -33 -13]]
POTE generator: ~3125/2304 = 524.1873
Optimal ET sequence: 16, 55b, 71, 87, 190, 277
Badness: 28.283
311 & 379
Subgroup: 2.3.5.7
Comma list: 2401/2400, [-23 -11 15 2⟩
Mapping: [⟨1 -5 -2 -1], ⟨0 64 42 37]]
POTE generator: ~78125/72576 = 123.4671
Optimal ET sequence: 29bbcd, 39bc, 68, 175, 243, 311, 554, 865, 1419cd
Badness: 3.518
11-limit
Subgroup: 2.3.5.7.11
Comma list: 6250/6237, 2401/2400, 2097152/2096325
Mapping: [⟨1 -5 -2 -1 12], ⟨0 64 42 37 -83]]
POTE generator: ~275/256 = 123.4730
Optimal ET sequence: 68, 175e, 243, 311
Badness: 3.125
311 & 503
Subgroup: 2.3.5.7
Comma list: 2401/2400, [-95 21 29 -2⟩
Mapping: [⟨1 43 -28 -2], ⟨0 -112 82 13]]
POTE generator: ~18984375/14680064 = 443.7335
Optimal ET sequence: 119, 192, 311, 814, 1125, 3064d, 4189cdd, 5314cdd
Badness: 7.820
11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 496125/495616, 100663296/100656875
Mapping: [⟨1 43 -28 -2 36], ⟨0 -112 82 13 -88]]
POTE generator: ~21175/16384 = 443.7337
Optimal ET sequence: 119, 192, 311, 503, 814, 1125, 1939
Badness: 2.599
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2401/2400, 4225/4224, 59535/59488, 6656/6655
Mapping: [⟨1 43 -28 -2 36 71], ⟨0 -112 82 13 -88 -182]]
POTE generator: ~84/65 = 443.7338
Optimal ET sequence: 119f, 192, 311, 503, 814, 1125, 1939
Badness: 1.410
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 12376/12375, 2401/2400, 14400/14399, 4225/4224, 11016/11011
Mapping: [⟨1 43 -28 -2 36 71 -34], ⟨0 -112 82 13 -88 -182 103]]
POTE generator: ~84/65 = 443.7340
Optimal ET sequence: 192, 311, 503, 814, 1939g, 2753dg
Badness: 1.111
311 & 571
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 2401/2400, 294885080956928/294197433834375
Mapping: [⟨1 11 -22 -7 37], ⟨0 -48 124 50 -171]]
POTE generator: ~63/55 = 235.3736
Optimal ET sequence: 10, 18bcd, 21e, 23bc, 31, 41, 72, 167, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee
Badness: 2.441
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 3025/3024, 2401/2400, 47432/47385, 114345/114244
Mapping: [⟨1 11 -22 -7 37 19], ⟨0 -48 124 50 -171 -78]]
POTE generator: ~63/55 = 235.3738
Badness: 1.528
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 2431/2430, 12376/12375, 2601/2600, 8624/8619, 2401/2400
Mapping: [⟨1 11 -22 -7 37 19 -22], ⟨0 -48 124 50 -171 -78 133]]
POTE generator: ~63/55 = 235.3741
Optimal ET sequence: 260, 311, 571, 882
Badness: 1.212
Sweepaway (311 & 607)
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 625/624, 3025/3024, 405769/405504
Mapping: [⟨1 20 17 -6 12 44], ⟨0 -69 -55 33 -32 -151]]
POTE generator: ~65/54 = 320.2613
Optimal ET sequence: 15, 281f, 296, 311, 607, 918c
Badness: 1.583
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 2080/2079, 625/624, 1225/1224, 3025/3024, 270725/270336
Mapping: [⟨1 20 17 -6 12 44 -21], ⟨0 -69 -55 33 -32 -151 94]]
POTE generator: ~65/54 = 320.2617
Optimal ET sequence: 15, 296, 311, 607, 918c
Badness: 1.503
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Commas: 2080/2079, 625/624, 1225/1224, 3025/3024, 1729/1728, 26775/26752
Mapping: [⟨1 20 17 -6 12 44 -21 28], ⟨0 -69 -55 33 -32 -151 94 -89]]
POTE generator: ~65/54 = 320.2615
Optimal ET sequence: 15, 296, 311, 607, 918ch
Badness: 1.274
311 & 1063
Subgroup: 2.3.5.7
Comma list: 2401/2400, 3367254360064/3363025078125
Mapping: [⟨1 11 -22 -7], ⟨0 -24 62 25]]
POTE generator: ~21/16 = 470.7489
Optimal ET sequence: 51, 79c, 130, 311, 441, 2776, 3217, 3658, 4099, 4540, 4981
Badness: 1.127
11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 19712/19683, 9453125/9437184
Mapping: [⟨1 11 -22 -7 98], ⟨0 -24 62 25 -241]]
POTE generator: ~21/16 = 470.7429
Optimal ET sequence: 130e, 181e, 311, 752, 1063
Badness: 4.158
379 & 577
Subgroup: 2.5.7
Comma list: [40 -13 25⟩
Mapping: [⟨1 20 12], ⟨0 -100 -52]]
POTE generator: ~80/49 = 848.548
Optimal ET sequence: 17c, 24c, 41, 99, 140, 239, 379, 1376, 1755, 2134, 6023, 8157, 10291d
Badness: 0.785
11-limit
Subgroup: 2.5.7.11
Comma list: 102487/102400, [28 11 -24 4⟩
Mapping: [⟨1 20 12 10], ⟨0 -100 -52 -37]]
POTE generator: ~133100/117649 = 212.1377
Optimal ET sequence: 17c, 164c, 181, 198, 379
Badness: 3.762