User:Francium/Miscellaneous rank-2 temperaments

On this page, I explore some unnamed rank-2 temperaments that catched my interest.

7 & 37

Subgroup: 2.3.5.11.13

Comma list: 55/54, 100/99, 512/507

Mapping: [⟨1 5 8 8 2], ⟨0 -6 -10 -8 3]]

POTE generator: ~160/117 = 518.2094

Optimal ET sequence: 7, 23bc, 30, 37, 44

Badness: 1.211

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 & 421

Subgroup: 2.3.7

Comma list: [37 5 -16⟩

Mapping: [⟨1 -17 -3], ⟨0 48 15]]

POTE generator: 464.6264

Optimal ET sequence: 25b, 31, 68, 99, 130, 229, 588, 817, 1405d, 2222dd

Badness: 3.193

11-limit

Subgroup: 2.3.7.11

Comma list: 1362944/1361367, [13 13 -6 -6⟩

Mapping: [⟨1 -17 -3 -31], ⟨0 48 15 89]]

POTE generator: ~847/648 = 464.6259

Badness: 2.532

Dakshdua (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

17-limit

Subgroup: 2.3.5.7.11.13.17

Commas: 1001/1000, 936/935, 1377/1375, 1716/1715, 4096/4095

Mapping: [⟨1 19 2 7 37 -35 -33], ⟨0 -54 1 -13 -104 120 115]]

POTE generator: ~5/4 = 387.0028

Optimal ET sequence: 31, 369, 400, 831

Badness: 1.515

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Commas: 1001/1000, 936/935, 1377/1375, 1716/1715, 2926/2925, 4096/4095

Mapping: [⟨1 19 2 7 37 -35 -33 -38], ⟨0 -54 1 -13 -104 120 115 131]]

POTE generator: ~5/4 = 387.0033

Optimal ET sequence: 31, 369, 400, 831

Badness: 1.393

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

Audreyglende (31 & 677)

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 759375/758912, 589824/588245

Mapping: [⟨1 19 0 9 35], ⟨0 -90 12 -32 -163]]

CTE tuning: ~4320/3773 = 232.1820

Optimal ET sequence: 31, 553bde, 584de, 615, 646, 1323d

Badness: 2.875

31 & 773

Subgroup: 2.3.5.7

Comma list: 2401/2400, [60 -3 -25 1⟩

Mapping: [⟨1 49 -3 12], ⟨0 -98 11 -19]]

POTE generator: ~5859375/4194304 = 580.5918

Optimal ET sequence: 31, 556b, 587b, 618, 649, 680, 711, 1453, 3617c

Badness: 4.036

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 172032/171875, 820125/819896

Mapping: [⟨1 49 -3 12 92], ⟨0 -98 11 -19 -183]]

POTE generator: ~7875/5632 = 580.5924

Optimal ET sequence: 31, 618ee, 649e, 680e, 711, 742, 1453, 2195e, 2937e

Badness: 1.638

31 & 1063

Subgroup: 2.3.5.7

Comma list: 2401/2400, [-97 7 37 0⟩

Mapping: [⟨1 35 -4 8], ⟨0 -148 28 -23]]

POTE generator: ~962072674304/823974609375 = 270.9334

Optimal ET sequence: 31, 970b, 1001, 1032, 1063, 1094, 1125

Badness: 9.148

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

37 & 661

Subgroup: 2.5.7.11.13

Comma list: 75712/75625, 10985/10976, 3200000/3195731

Mapping: [⟨1 23 32 -1 26], ⟨0 -51 -72 11 -55]]

CTE tuning: ~847/640 = 486.5098

Optimal ET sequence: 37, 402df, 439, 476, 513, 550, 587, 624

Badness: 1.129

17-limit

Subgroup: 2.5.7.11.13.17

Comma list: 32768/32725, 140800/140777, 286000/285719, 1328125/1328096

Mapping: [⟨1 23 32 -1 26 -62], ⟨0 -51 -72 11 -55 163]]

CTE tuning: ~847/640 = 486.4954

Optimal ET sequence: 37, 587g, 624, 661, 1285deg

Badness: 1.843

19-limit

Subgroup: 2.5.7.11.13.17.19

Comma list: 3328/3325, 2432/2431, 12103/12100, 10985/10976, 190400/190333

Mapping: [⟨1 23 32 -1 26 -62 -44], ⟨0 -51 -72 11 -55 163 119]]

CTE tuning: ~847/640 = 486.4966

Optimal ET sequence: 37, 587g, 624, 661, 1285deg

Badness: 1.391

23-limit

Subgroup: 2.5.7.11.13.17.19.23

Comma list: 3328/3325, 2432/2431, 12103/12100, 2300/2299, 36179/36176, 10985/10976

Mapping: [⟨1 23 32 -1 26 -62 -44 -94], ⟨0 -51 -72 11 -55 163 119 243]]

CTE tuning: ~847/640 = 486.4987

Optimal ET sequence: 37, 587gi, 624, 1285deg

Badness: 1.474

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

41, 151, 192, 233, 274

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 & 463

Subgroup: 2.3.5.7

Comma list: 4096000/4084101, 359661568/358722675

Mapping: [⟨1 2 -35 -20], ⟨0 -1 90 55]]

POTE generator: ~4/3 = 497.6285

Optimal ET sequence: 41, 217ccd, 258cd, 299cd, 340c, 381, 422, 885, 1307d, 1729bdd

Badness: 4.045

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 19712/19683, 1296000/1294139

Mapping: [⟨1 2 -35 -20 30], ⟨0 -1 90 55 -64]]

POTE generator: ~4/3 = 497.6281

Optimal ET sequence: 41, 340c, 381, 422, 885, 1307de

Badness: 1.883

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

41 & 607

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 3025/3024, 78975/78848, 218700/218491

Mapping: [⟨1 0 15 10 -8 -18], ⟨0 13 -104 -59 94 178]]

POTE generator: ~160/147 = 146.2905

Optimal ET sequence: 41, 525f, 566

Badness: 2.398

41 & 1063

Subgroup: 2.3.5.7

Comma list: 2401/2400, [80 -52 -5 5⟩

Mapping: [⟨1 5 -67 -31], ⟨0 -10 203 99]]

POTE generator: ~524288/413343 = 409.7856

Optimal ET sequence: 41, 776cc, 817c, 858c, 899c, 940, 981, 2984, 3965bc

Badness: 10.520

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

53 & 673

Subgroup: 2.3.5

Comma list: [51 -60 19⟩

Mapping: [⟨1 -2 -9], ⟨0 19 60]]

POTE generator: ~1162261467/1024000000 = 226.4390

Optimal ET sequence: 16cc, 37cc, 53, 514c, 567, 620, 673, 726, 779, 832, 885, 938

Badness: 40.263

53 & 733

Subgroup: 2.3.5

Comma list: [42 -47 14⟩

Mapping: [⟨1 0 -3], ⟨0 14 47]]

POTE generator: ~64000/59049 = 135.8799

Optimal ET sequence: 44c, 53, 415, 468, 521, 574, 627, 680, 733

Badness: 18.063

53 & 1063

Subgroup: 2.3.5

Comma list: [57 -55 13⟩

Mapping: [⟨1 6 21], ⟨0 -13 -55]]

POTE generator: ~163840000/129140163 = 407.5202

Optimal ET sequence: 50cc, 53, 427c, 480, 533, 586, 639, 692, 745, 798, 851, 2500b, 3351b

Badness: 22.373

53 & 1193

Subgroup: 2.3.5

Comma list: [87 -71 11⟩

Mapping: [⟨1 2 5], ⟨0 -11 -71]]

POTE generator: ~1638400/1594323 = 45.2622

Optimal ET sequence: 26cc, 27cc, 53, 557c, 610c, 663c, 716, 769, 822, 875, 928, 981, 1034, 1087

Badness: 29.067

53 & 1759

Subgroup: 2.3.5

Comma list: [132 -95 8⟩

Mapping: ⟨1 4 31], ⟨0 -8 -95]]

POTE generator: ~655360/531441 = 362.2490

Optimal ET sequence: 53, 752c, 805c, 858c, 911c, 964c, 1017c, 1070c, 1123, 1176, 1229, 1282, 1335, 1388, 1441, 1494

Badness: 25.296

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 & 457

Subgroup: 2.3.5.7

Comma list: 26873856/26796875, 40500000/40353607

Mapping: [⟨1 -11 -7 -9], ⟨0 81 60 76]]

POTE generator: ~2401/2160 = 186.4436

Optimal ET sequence: 45bcd, 103, 251, 354, 605d, 959d, 1313d

Badness: 5.981

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 166698/166375, 2737152/2734375

Mapping: [⟨1 -11 -7 -9 -20], ⟨0 81 60 76 151]]

POTE generator: ~49/44 = 186.4402

Optimal ET sequence: 45bcdee, 103, 251e, 354

Badness: 2.869

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 1716/1715, 4225/4224, 34398/34375

Mapping: [⟨1 -11 -7 -9 -20 -5], ⟨0 81 60 76 151 56]]

POTE generator: ~39/35 = 186.4399

Optimal ET sequence: 45bcdee, 103, 251e, 354

Badness: 1.642

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 540/539, 936/935, 1377/1375, 1716/1715, 4225/4224

Mapping: [⟨1 -11 -7 -9 -20 -5 3], ⟨0 81 60 76 151 56 7]]

POTE generator: ~39/35 =186.4396

Optimal ET sequence: 103, 251e, 354

Badness: 1.399

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

Wiloliquy (103 & 700)

Subgroup: 2.5.7.13.17

Comma list: 31250/31213, 10985/10976, 177482125/177209344

Mapping: [⟨1 38 48 37 -4], ⟨0 -75 -95 -70 17]]

POTE generator: ~50176/36125 = 570.8538

Optimal ET sequence: 103, 391, 494, 597, 2285cfg

Badness: 1.690

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

113 & 709

Subgroup: 2.3.11.13.17

Comma list: 971074/970299, 2097152/2093663, 60915712/60886809

Mapping: [⟨1 -44 17 -64 42], ⟨0 101 -30 150 -84]]

POTE generator: ~33048/24167 = 541.6049

Optimal ET sequence: 113, 483f, 596f, 709, 822, 935, 1757e

Badness: 3.748

19-limit

Subgroup: 2.3.11.13.17.19

Comma list: 2432/2431, 278528/278179, 793152/793117, 68054272/68049963

Mapping: [⟨1 -44 17 -64 42 -12], ⟨0 101 -30 150 -84 36]]

POTE generator: ~4199/3072 = 541.6049

Optimal ET sequence: 113, 483f, 596f, 709, 822, 935, 1757e

Badness: 1.676

31-limit

Subgroup: 2.3.11.13.17.19.31

Comma list: 2432/2431, 1024/1023, 25296/25289, 793152/793117, 68054272/68049963

Mapping: [⟨1 -44 17 -64 42 -12 37], ⟨0 101 -30 150 -84 36 -71]]

POTE generator: ~4199/3072 = 541.6055

Optimal ET sequence: 113, 483f, 596f, 709, 822k

Badness: 1.718

37-limit

Subgroup: 2.3.11.13.17.19.31.37

Comma list: 2432/2431, 1024/1023, 3553/3552, 25296/25289, 793152/793117, 681472/681207

Mapping: [⟨1 -44 17 -64 42 -12 37 86], ⟨0 101 -30 150 -84 36 -71 -179]]

POTE generator: ~4199/3072 = 541.6062

Optimal ET sequence: 113, 483f, 596f, 709, 822kl

Badness: 1.939

167 & 311

Subgroup: 2.3.5.7.11.13

Comma list: 3025/3024, 6250/6237, 2401/2400, 4225/4224

Mapping: [⟨1 -13 -14 -9 -8 7], ⟨0 84 94 68 66 -19]]

POTE generator: ~44/39 = 208.3614

Optimal ET sequence: 23bc, 144, 167, 311

Badness: 1.904

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 595/594, 1225/1224, 3025/3024, 2500/2499, 4225/4224

Mapping: [⟨1 -13 -14 -9 -8 7 -23], ⟨0 84 94 68 66 -19 156]]

POTE generator: ~44/39 = 208.3624

Optimal ET sequence: 144g, 167, 311, 1100bef

Badness: 1.547

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

193 & 653

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520

Mapping: [⟨1 -18 16 -46 -64 18 -27 -20 21], ⟨0 63 -44 157 217 -46 100 78 -53]]

POTE generator: ~243/196 = 373.0467

Badness: 1.271

29-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520, 2205/2204

Mapping: [⟨1 -18 16 -46 -64 18 -27 -20 21 -94], ⟨0 63 -44 157 217 -46 100 78 -53 318]]

POTE generator: ~243/196 = 373.0471

Badness: 1.364

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

233 & 659

Subgroup: 2.5.7.11.13.17

Comma list: 6656/6655, 105644/105625, 557375/557056, 22578125/22550528

Mapping: [⟨1 -10 30 40 101 146], ⟨0 29 -64 -86 -229 -334]]

POTE generator: ~325/242 = 509.8664

Optimal ET sequence: 193fgg, 233, 659, 892, 1125

Badness: 2.422

23-limit

Subgroup: 2.5.7.11.13.17.23

Comma list: 5635/5632, 25025/25024, 6656/6655, 105644/105625, 50575/50531

Mapping: [⟨1 -10 30 40 101 146 -1], ⟨0 29 -64 -86 -229 -334 13]]

POTE generator: ~1375/1024 = 509.8663

Optimal ET sequence: 233, 659, 892, 1125, 2017

Badness: 1.679

31-limit

Subgroup: 2.5.7.11.13.17.23.31

Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 105644/105625, 180625/180544

Mapping: [⟨1 -10 30 40 101 146 -1 115], ⟨0 29 -64 -86 -229 -334 13 -259]]

POTE generator: ~1375/1024 = 509.8661

Optimal ET sequence: 233, 659, 892, 1125, 2017k

Badness: 1.405

37-limit

Subgroup: 2.5.7.11.13.17.23.31.37

Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 1925/1924, 105644/105625, 50575/50531

Mapping: [⟨1 -10 30 40 101 146 -1 115 -53], ⟨0 29 -64 -86 -229 -334 13 -259 137]]

POTE generator: ~1375/1024 = 509.8657

Optimal ET sequence: 233, 659, 892

Badness: 1.535

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

239 & 683

Subgroup: 2.5.11.17.23.29

Comma list: 69632/69575, 1048576/1047625, 107648/107525, 244338688/244140625

Mapping: [⟨1 2 1 4 10 6], ⟨0 11 84 3 -187 -39]]

POTE generator: ~638/625 = 35.1399

Optimal ET sequence: 205i, 239, 444i, 683, 1605egi

Badness: 1.628

31-limit

Subgroup: 2.5.11.17.23.29.31

Comma list: 69632/69575, 5800/5797, 14384/14375, 1048576/1047625, 12111616/12109375

Mapping: [⟨1 2 1 4 10 6 8], ⟨0 11 84 3 -187 -39 -104]]

POTE generator: ~253/248 = 35.1400

Optimal ET sequence: 205i, 239, 444i, 683, 1605egik

Badness: 1.106

37-limit

Subgroup: 2.5.11.17.23.29.31.37

Comma list: 69632/69575, 5800/5797, 14384/14375, 4625/4624, 1048576/1047625, 1647536/1646875

Mapping: [⟨1 2 1 4 10 6 8 6], ⟨0 11 84 3 -187 -39 -104 -27]]

POTE generator: 253/248 = 35.1400

Optimal ET sequence: 205i, 239, 444i, 683, 1605egik

Badness: 0.988

239 & 1063

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 1953125/1951488, 322102/321489

Mapping: [⟨1 47 34 30 87], ⟨0 -162 -113 -97 -298]]

POTE generator: ~175/144 = 336.4071

Optimal ET sequence: 107bee, 239, 585e, 824e, 1887e

Badness: 4.796

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

Focus (307 & 743)

Subgroup: 2.5.7.11.13.17

Comma list: 140800/140777, 40898/40817, 102487/102400, 184960/184877

Mapping: [⟨1 -69 -22 -26 -37 -37], ⟨0 184 64 76 105 106]]

POTE generator: ~17/13 = 465.1430

Optimal ET sequence: 129c, 178c, 307, 743, 1050

Badness: 2.436

19-limit

Subgroup: 2.5.7.11.13.17.19

Comma list: 10241/10240, 1331/1330, 140800/140777, 64220/64141, 5491/5488

Mapping: [⟨1 -69 -22 -26 -37 -37 12], ⟨0 184 64 76 105 106 -20]]

POTE generator: ~17/13 = 465.1425

Optimal ET sequence: 129c, 178c, 307, 743, 1050

Badness: 1.878

23-limit

Subgroup: 2.5.7.11.13.17.19.23

Comma list: 10241/10240, 140800/140777, 27209/27200, 4807/4802, 31603/31556, 608000/607453

Mapping: [⟨1 -69 -22 -26 -37 -37 12 -73], ⟨0 184 64 76 105 106 -20 200]]

POTE generator: ~17/13 = 465.1422

Optimal ET sequence: 129ci, 307, 743, 1050

Badness: 1.538

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 & 701

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 22478848/22460625, 1395654656/1395032625

Mapping: [⟨1 -13 40 18 -17], ⟨0 72 -186 -75 101]]

POTE generator: ~405/352 = 243.0836

Optimal ET sequence: 79c, 311, 701, 1012, 1323, 2335, 3658

Badness: 2.442

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 4096/4095, 2401/2400, 6656/6655, 1574640/1574573

Mapping: [⟨1 -13 40 18 -17 -20], ⟨0 72 -186 -75 101 117]]

POTE generator: ~405/352 = 243.0835

Optimal ET sequence: 79c, 311, 701, 1012, 1323, 2335

Badness: 1.383

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

311 & 1193

Subgroup: 2.3.5.7

Comma list: 2401/2400, [36 -16 -7 2⟩

Mapping: [⟨1 11 -22 -7], ⟨0 -48 124 50]]

POTE generator: ~8/7 = 235.3744

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: 3025/3024, 2401/2400, 3637837299712/3632067084375

Mapping: [⟨1 11 -22 -7 37], ⟨0 -48 124 50 -171]]

POTE generator: ~55/48 = 235.3736

Optimal ET sequence: 51e, 260, 311, 571, 882, 2075

Badness: 2.441

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 3025/3024, 4096/4095, 2401/2400, 492128/492075

Mapping: [⟨1 11 -22 -7 37 19], ⟨0 -48 124 50 -171 -78]]

POTE generator: ~55/48 = 235.3738

Optimal ET sequence: 51e, 260, 311, 571, 882, 2075f

Badness: 1.528

311 & 1759

Subgroup: 2.3.5.7.11.13

Comma list: 3025/3024, 4225/4224, 4100625/4100096, 1664000/1663893

Mapping: [⟨1 -34 40 36 -71 -89], ⟨0 119 -126 -111 249 310]]

POTE generator: ~315/256 = 358.8399

Optimal ET sequence: 311, 826f, 1137, 1448, 4655cef, 6103cef, 7551ceeff, 8999cceeff

Badness: 1.405

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 3025/3024, 2500/2499, 4225/4224, 56595/56576, 4100625/4100096

Mapping: [⟨1 -34 40 36 -71 -89 124], ⟨0 119 -126 -111 249 310 -401]]

POTE generator: ~315/256 = 358.8402

Optimal ET sequence: 311, 1137g, 1448, 1759

Badness: 1.903

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 1549184/1549125

Mapping: [⟨1 -34 40 36 -71 -89 124 50], ⟨0 119 -126 -111 249 310 -401 -153]]

POTE generator: ~315/256 = 358.8402

Optimal ET sequence: 311, 1137g, 1448, 1759

Badness: 1.418

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 76545/76544

Mapping: [⟨1 -34 40 36 -71 -89 124 50 -81], ⟨0 119 -126 -111 249 310 -401 -153 286]]

POTE generator: ~315/256 = 358.8402

Optimal ET sequence: 311, 1137g, 1448, 1759

Badness: 1.239

29-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544

Mapping: [⟨1 -34 40 36 -71 -89 124 50 -81 -101], ⟨0 119 -126 -111 249 310 -401 -153 286 354]]

POTE generator: ~315/256 = 358.8402

Badness: 1.159

31-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31

Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075

Mapping: [⟨1 -34 40 36 -71 -89 124 50 -81 -101 -164], ⟨0 119 -126 -111 249 310 -401 -153 286 354 565]]

POTE generator: ~315/256 = 358.8403

Badness: 1.303

37-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075, 5625/5624

Mapping: [⟨1 -34 40 36 -71 -89 124 50 -81 -101 -164 39], ⟨0 119 -126 -111 249 310 -401 -153 286 354 565 -113]]

POTE generator: ~315/256 = 358.8402

Badness: 1.301

41-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41

Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075, 5625/5624, 2625/2624

Mapping: [⟨1 -34 40 36 -71 -89 124 50 -81 -101 -164 39 116], ⟨0 119 -126 -111 249 310 -401 -153 286 354 565 -113 -370]]

POTE generator: ~315/256 = 358.8403

Badness: 1.360

373 & 727

Subgroup: 2.3.5.7.11

Comma list: 24057/24010, 137781/137500, 496125/495616

Mapping: [⟨1 18 20 55 115], ⟨0 -39 -42 -124 -265]]

POTE generator: ~75/56 = 505.0903

Optimal ET sequence: 19e, 335dee, 354, 373, 727, 1100, 1827b

Badness: 3.365

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 729/728, 1716/1715, 78975/78848, 34398/34375

Mapping: [⟨1 18 20 55 115 50], ⟨0 -39 -42 -124 -265 -110]]

POTE generator: ~75/56 = 505.0903

Optimal ET sequence: 19e, 335dee, 354, 373, 727, 1100, 1827bf

Badness: 1.677

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

487 & 691

Subgroup: 2.3.5.11.17.19

Comma list: 374000/373977, 500000/499851, 632225/632043, 116640/116603

Mapping: [⟨1 30 59 65 79 55], ⟨0 -187 -373 -405 -493 -334]]

POTE generator: ~10/9 = 182.3424

Optimal ET sequence: 204cegh, 283ceggh, 487, 1178, 1665

Badness: 1.522

31-limit

Subgroup: 2.3.5.11.17.19.31

Comma list: 6480/6479, 374000/373977, 500000/499851, 6138/6137, 242000/241893

Mapping: [⟨1 30 59 65 79 55 63], ⟨0 -187 -373 -405 -493 -334 -382]]

POTE generator: ~10/9 = 182.3424

Optimal ET sequence: 204ceghk, 283cegghk, 487, 1178, 1665

Badness: 1.045

Shortcrust (677 & 761)

Subgroup: 2.3.5

Comma list: [159 33 -91⟩

Mapping: [⟨1 20 9], ⟨0 -91 -33]]

POTE generator: ~48828125/42467328 = 242.8354

Optimal ET sequence: 84, 341b, 425, 509, 593, 677, 1947, 2624, 8549c

Badness: 94.681