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This tempers out the mirkwai comma, |0 3 4 -5> = 16875/16807, a no-twos comma. Members of the clan include grendel, kwai, pluto and mirkat considered below, as well as miracle, octokaidecal, nusecond, semisept and bohpier, considered elsewhere.

Grendel

Commas: 6144/6125, 16875/16807

POTE generator: 386.863

Map: [<1 9 2 7|, <0 -23 1 -13|]
Wedgie: <<23 -1 13 -55 -44 33||
EDOs: 31, 90, 121, 152, 335

11-limit

Commas: 540/539, 1375/1372, 5632/5625

POTE generator: 386.856

Map: [<1 9 2 7 17|, <0 -23 1 -13 -42|]
EDOs: 31, 90, 121, 152, 335, 487

13-limit

Commas: 352/351, 540/539, 625/624, 1375/1372

POTE generator: 386.826

Map: [<1 9 2 7 17 -5|, <0 -23 1 -13 -42 27|]
EDOs: 31, 121, 152, 425

17-limit

Commas: 256/255, 352/351, 625/624, 715/714, 1275/1274

POTE generator: 386.812

Map: [<1 9 2 7 17 -5 -3|, <0 -23 1 -13 -42 27 22|]
EDOs: 31, 121, 273

19-limit

Commas: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714

POTE generator: 386.819

Map: [<1 9 2 7 17 -5 -3|, <0 -23 1 -13 -42 27 22|]
EDOs: 31, 121, 152, 273

Kwai

Commas: 5120/5103, 16875/16807

POTE generator: 702.616

Map: [<1 0 -50 -40|, <0 1 33 27|]
Wedgie: <<1 33 27 50 40 -30||
EDOs: 41, 111, 152, 345, 497

11-limit

Commas: 540/539, 1375/1372, 16384/16335

POTE generator: 702.623

Map: [<1 0 -50 -40 32|, <0 1 33 27 -18|]
EDOs: 29, 41, 111, 152

13-limit

Commas: 352/351, 540/539, 729/728, 1375/1372

POTE generator: 702.644

Map: [<1 0 -50 -40 32 27|, <0 1 33 27 -18 -21|]
EDOs: 29, 41, 111, 152

17-limit

Commas: 256/255, 352/351, 540/539, 715/714, 1089/1088

POTE generator: 702.660

Map: [<1 0 -50 -40 32 27 58|, <0 1 33 27 -18 -21 -34|]
EDOs: 29, 41, 111, 152, 263

19-limit

Commas: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845

POTE generator: 702.657

Map: [<1 0 -50 -40 32 27 58 -56|, <0 1 33 27 -18 -21 -34 38|]
EDOs: 29, 41, 111, 152, 263

Pluto

Commas: 4000/3969, 10976/10935

POTE generator: 585.147

Map: [<1 5 15 15|, <0 -7 -26 -25|]
Wedgie: <<7 26 25 25 20 -15||
EDOs: 39, 41, 80, 121, 404

11-limit

Commas: 540/539, 896/891, 1375/1372

POTE generator: 585.114

Map: [<1 5 15 15 2|, <0 -7 -26 -25 3|]
EDOs: 39, 41, 80, 121

13-limit

Commas: 325/324, 352/351, 364/363, 540/539

POTE generator: 585.123

Map: [<1 5 15 15 2 -8|, <0 -7 -26 -25 3 24|]
EDOs: 39, 41, 80, 121

17-limit

Commas: 256/255, 325/324, 352/351, 364/363, 540/539

POTE generator: 585.116

Map: [<1 5 15 15 2 -8 -12|, <0 -7 -26 -25 3 24 33|]
EDOs: 39, 41, 80, 121

19-limit

Commas: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594

POTE generator: 585.109

Map: [<1 5 15 15 2 -8 -12 14|, <0 -7 -26 -25 3 24 33 -20|]
EDOs: 39, 41, 80, 121, 564, 685

Orcus

Commas: 144/143, 196/195, 275/273, 896/891

POTE generator: ~7/5 = 585.111

Map: [<1 5 15 15 2 12|, <0 -7 -26 -25 3 -17|]
EDOs: 41, 80f, 121f
Badness: 0.0334

Plutino

Commas: 100/99, 245/242, 16875/16807

POTE generator: ~7/5 = 585.283

Map: [<1 5 15 15 22|, <0 -7 -26 -25 -38|]
EDOs: 41, 123c
Badness: 0.0580

13-limit

Commas: 100/99, 196/195, 245/242, 729/728

POTE generator: ~7/5 = 585.232

Map: [<1 5 15 15 22 12|, <0 -7 -26 -25 -38 -17|]
EDOs: 41, 121ef
Badness: 0.0402

Eris

Commas: 16875/16807, 65625/65536

POTE generator: ~60/49 = 348.216

Map: [<1 10 0 6|, <0 -29 8 -11|]
Wedgie: <<29 -8 11 -80 -64 48}}
EDOs: 31, 131, 162, 193, 224, 1823cd, 2271cd
Badness: 0.0747

11-limit

Commas: 540/539, 1375/1372, 65625/65536

POTE generator: ~11/9 = 348.219

Map: [<1 10 0 6 20|, <0 -29 8 -11 -57|]
EDOs: 31, 193, 224, 703, 927d, 1151cd
Badness: 0.0276

Mirkat

Commas: 16875/16807, 19683/19600

POTE generator: ~10/9 = 183.539

Map: [<3 2 1 2|, <0 6 13 14|]
Wedgie: <<18 39 42 20 16 -12||
EDOs: 39d, 72, 111, 183, 255
Badness: 0.0594

11-limit

Commas: 540/539, 1375/1372, 8019/8000

POTE generator: ~10/9 = 183.528

Map: [<3 2 1 2 9|, <0 6 13 14 3|]
EDOs: 39d, 72, 111, 183, 255
Badness: 0.0221

13-limit

Commas: 351/350, 540/539, 676/675, 1375/1372

POTE generator: ~10/9 = 183.577

Map: [<3 2 1 2 9 1|, <0 6 13 14 3 22|]
EDOs: 39df, 72, 111, 183, 255f
Badness: 0.0186

17-limit

Commas: 351/350, 442/441, 540/539, 561/560, 715/714

POTE generator: ~10/9 = 183.579

Map: [<3 2 1 2 9 1 4|, <0 6 13 14 3 22 18|]
EDOs: 39dfg, 72, 111, 183, 255f

Subsemifourth

Commas: 16875/16807, 26873856/26796875

POTE generator: ~144/125 = 244.719

Map: [<1 39 27 45|, <0 -47 -31 -53|]
Wedgie: <<47 31 53 -60 -48 36||
EDOs: 49, 103, 152, 255, 407
Badness: 0.1352

11-limit

Commas: 540/539, 1375/1372, 234375/234256

POTE generator: ~121/105 = 244.719

Map: [<1 39 27 45 56|, <0 -47 -31 -53 -66|]
EDOs: 49, 103, 152, 255, 407, 966d
Badness: 0.0343

13-limit

Commas: 540/539, 847/845, 1375/1372, 1575/1573

POTE generator: ~15/13 = 244.714

Map: [<1 39 27 45 56 65|, <0 -47 -31 -53 -66 -77|]
EDOs: 103, 152f, 255, 407f, 662df
Badness: 0.0284