Mirkwai clan

Temperaments of the mirkwai clan temper out the mirkwai comma, [0 3 4 -5⟩ = 16875/16807, a no-twos comma. Members of the clan include grendel, kwai, pluto, mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer considered below, as well as these considered elsewhere:

• Octokaidecal, {28/27, 50/49} → Trienstonic clan
• Meantritone, {81/80, 16875/16807} → Meantone family
• Nusecond, {126/125, 2430/2401} → Starling temperaments
• Miracle, {225/224, 1029/1024} → Gamelismic clan
• Bohpier, {245/243, 3125/3087} → Sensamagic clan
• Semisept, {1728/1715, 3136/3125} → Hemimean clan
• Octoid, {4375/4374, 16875/16807} → Ragismic microtemperaments
• Sqrtphi, {15625/15552, 16875/16807} → Kleismic family
• Quanharuk, {16875/16807, 32805/32768} → Schismatic family
• Familia, {16875/16807, 1600000/1594323} → Amity family
• Rainwell, {16875/16807, 2100875/2097152} → Semicomma family

Canopus

Main article: Canopus

Subgroup: 3.5.7

Comma list: 16875/16807

Sval mapping: [⟨1 3 3], ⟨0 -5 -4]]

Sval mapping generators: ~3, ~7/5

POTE generator: ~7/5 = 583.9584

Optimal ET sequence: b13, b62, b75, b88, b101, b114, b355, b469, b583, b697

Grendel

Subgroup: 2.3.5.7

Comma list: 6144/6125, 16875/16807

Mapping: [⟨1 9 2 7], ⟨0 -23 1 -13]]

Wedgie: ⟨⟨23 -1 13 -55 -44 33]]

POTE generator: ~5/4 = 386.863

Optimal ET sequence: 31, 90, 121, 152, 335d

Badness: 0.051834

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 5632/5625

Mapping: [⟨1 9 2 7 17], ⟨0 -23 1 -13 -42]]

POTE generator: ~5/4 = 386.856

Optimal ET sequence: 31, 90e, 121, 152, 335d, 487d

Badness: 0.019845

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 625/624, 1375/1372

Mapping: [⟨1 9 2 7 17 -5], ⟨0 -23 1 -13 -42 27]]

POTE generator: ~5/4 = 386.826

Optimal ET sequence: 31, 121, 152f, 425deff

Badness: 0.024839

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 9 2 7 17 -5 -3], ⟨0 -23 1 -13 -42 27 22]]

POTE generator: ~5/4 = 386.812

Optimal ET sequence: 31, 121, 273defgg

Badness: 0.021400

19-limit

Subgroup: 2.3.5.7.11.13.17.19

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

POTE generator: ~5/4 = 386.819

Mapping: [⟨1 9 2 7 17 -5 -3 -8], ⟨0 -23 1 -13 -42 27 22 38]]

Optimal ET sequence: 31, 121, 152fg, 273defgg

Badness: 0.018413

Kwai

For the 5-limit version of this temperament, see High badness temperaments #Kwai.

Subgroup: 2.3.5.7

Comma list: 5120/5103, 16875/16807

Mapping: [⟨1 0 -50 -40], ⟨0 1 33 27]]

Wedgie: ⟨⟨1 33 27 50 40 -30]]

POTE generator: ~3/2 = 702.616

Optimal ET sequence: 41, 111, 152, 345, 497d

Badness: 0.054476

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 5120/5103

Mapping: [⟨1 0 -50 -40 32], ⟨0 1 33 27 -18]]

POTE generator: ~3/2 = 702.623

Optimal ET sequence: 29cd, 41, 111, 152

Badness: 0.026219

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 729/728, 1375/1372

Mapping: [⟨1 0 -50 -40 32 27], ⟨0 1 33 27 -18 -21]]

POTE generator: ~3/2 = 702.644

Optimal ET sequence: 29cd, 41, 111, 152f

Badness: 0.024555

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 0 -50 -40 32 27 58], ⟨0 1 33 27 -18 -21 -34]]

POTE generator: ~3/2 = 702.660

Optimal ET sequence: 29cdg, 41, 111, 152fg, 263dfg

Badness: 0.021950

19-limit

Subgroup: 2.3.5.7.11.13.17.19

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

Mapping: [⟨1 0 -50 -40 32 27 58 -56], ⟨0 1 33 27 -18 -21 -34 38]]

POTE generator: ~3/2 = 702.657

Optimal ET sequence: 29cdgh, 41, 111, 152fg, 263dfgh

Badness: 0.016957

Hemikwai

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 676/675, 1375/1372, 5120/5103

Mapping: [⟨1 2 16 14 -4 18], ⟨0 -2 -66 -54 36 -69]]

POTE generator: ~15/13 = 248.686

Optimal ET sequence: 82, 111, 193, 304d

Badness: 0.044108

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 442/441, 540/539, 676/675, 715/714, 5120/5103

Mapping: [⟨1 2 16 14 -4 18 13], ⟨0 -2 -66 -54 36 -69 -43]]

POTE generator: ~15/13 = 248.686

Optimal ET sequence: 82, 111, 193, 304d

Badness: 0.025806

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 400/399, 442/441, 540/539, 676/675, 715/714, 1445/1444

Mapping: [⟨1 2 16 14 -4 18 13 20], ⟨0 -2 -66 -54 36 -69 -43 -76]]

POTE generator: ~15/13 = 248.687

Optimal ET sequence: 82, 111, 193, 304dh

Badness: 0.019146

Pluto

Subgroup: 2.3.5.7

Comma list: 4000/3969, 10976/10935

Mapping: [⟨1 5 15 15], ⟨0 -7 -26 -25]]

Wedgie: ⟨⟨7 26 25 25 20 -15]]

POTE generator: ~7/5 = 585.147

Optimal ET sequence: 39d, 41, 80, 121, 404bd

Badness: 0.057514

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 896/891, 1375/1372

Mapping: [⟨1 5 15 15 2], ⟨0 -7 -26 -25 3]]

POTE generator: ~7/5 = 585.114

Optimal ET sequence: 39d, 41, 80, 121

Badness: 0.029844

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 364/363, 540/539

Mapping: [⟨1 5 15 15 2 -8], ⟨0 -7 -26 -25 3 24]]

POTE generator: ~7/5 = 585.123

Optimal ET sequence: 39d, 41, 80, 121

Badness: 0.025717

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 5 15 15 2 -8 -12], ⟨0 -7 -26 -25 3 24 33]]

POTE generator: ~7/5 = 585.116

Optimal ET sequence: 39d, 41, 80, 121

Badness: 0.021463

19-limit

Subgroup: 2.3.5.7.11.13.17.19

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

Mapping: [⟨1 5 15 15 2 -8 -12 14], ⟨0 -7 -26 -25 3 24 33 -20]]

POTE generator: ~7/5 = 585.109

Optimal ET sequence: 39d, 41, 80, 121

Badness: 0.017650

Orcus

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 196/195, 275/273, 896/891

Mapping: [⟨1 5 15 15 2 12], ⟨0 -7 -26 -25 3 -17]]

POTE generator: ~7/5 = 585.111

Optimal ET sequence: 41, 80f, 121ff

Badness: 0.033441

Plutino

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242, 10976/10935

Mapping: [⟨1 5 15 15 22], ⟨0 -7 -26 -25 -38]]

POTE generator: ~7/5 = 585.283

Optimal ET sequence: 39dee, 41

Badness: 0.057966

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 196/195, 245/242, 729/728

Mapping: [⟨1 5 15 15 22 12], ⟨0 -7 -26 -25 -38 -17]]

POTE generator: ~7/5 = 585.232

Optimal ET sequence: 39deef, 41

Badness: 0.040182

Mirkat

Subgroup: 2.3.5.7

Comma list: 16875/16807, 19683/19600

Mapping: [⟨3 2 1 2], ⟨0 6 13 14]]

Wedgie: ⟨⟨18 39 42 20 16 -12]]

POTE generator: ~10/9 = 183.539

Optimal ET sequence: 39d, 72, 111, 183, 255

Badness: 0.059376

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 8019/8000

Mapping: [⟨3 2 1 2 9], ⟨0 6 13 14 3]]

POTE generator: ~10/9 = 183.528

Optimal ET sequence: 39d, 72, 111, 183, 255

Badness: 0.022126

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 676/675, 1375/1372

Mapping: [⟨3 2 1 2 9 1], ⟨0 6 13 14 3 22]]

POTE generator: ~10/9 = 183.577

Optimal ET sequence: 39df, 72, 111, 183

Badness: 0.018632

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨3 2 1 2 9 1 4], ⟨0 6 13 14 3 22 18]]

POTE generator: ~10/9 = 183.579

Optimal ET sequence: 39dfg, 72, 111, 183

Badness: 0.011775

Eris

Subgroup: 2.3.5.7

Comma list: 16875/16807, 65625/65536

Mapping: [⟨1 10 0 6], ⟨0 -29 8 -11]]

Wedgie: ⟨⟨29 -8 11 -80 -64 48]]

POTE generator: ~60/49 = 348.216

Optimal ET sequence: 31, 131, 162, 193, 224, 1823cd, 2271cd

Badness: 0.074719

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 65625/65536

Mapping: [⟨1 10 0 6 20], ⟨0 -29 8 -11 -57]]

POTE generator: ~11/9 = 348.219

Optimal ET sequence: 31, 193, 224, 703, 927d, 1151cd

Badness: 0.027621

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 625/624, 1375/1372, 4096/4095

Mapping: [⟨1 10 0 6 20 -14], ⟨0 -29 8 -11 -57 61]]

POTE generator: ~11/9 = 348.213

Optimal ET sequence: 31, 193, 224

Badness: 0.025137

Subsemifourth

Subgroup: 2.3.5.7

Comma list: 16875/16807, 26873856/26796875

Mapping: [⟨1 -8 -4 -8], ⟨0 47 31 53]]

Wedgie: ⟨⟨47 31 53 -60 -48 36]]

POTE generator: ~144/125 = 244.719

Optimal ET sequence: 49, 103, 152, 255, 407

Badness: 0.135173

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 234375/234256

Mapping: [⟨1 -8 -4 -8 -10], ⟨0 47 31 53 66]]

POTE generator: ~121/105 = 244.719

Optimal ET sequence: 49, 103, 152, 255, 407, 966d

Badness: 0.034276

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 847/845, 1375/1372, 1575/1573

Mapping: [⟨1 -8 -4 -8 -10 -12], ⟨0 47 31 53 66 77]]

POTE generator: ~15/13 = 244.714

Optimal ET sequence: 49f, 103, 152f, 255, 407f, 662df

Badness: 0.028387

Septendesemi

The name septendesemi means a septendecimal semitone (17/16). The septendesemi temperament (80&103) tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma, zotritrigu) in the 7-limit. 183EDO provides an excellent tuning for 7, 11, 13, and 17-limit septendesemi.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 1959552/1953125

Mapping: [⟨1 -2 -1 -2], ⟨0 41 38 55]]

Wedgie: ⟨⟨41 38 55 -35 -28 21]]

POTE generator: ~343/324 = 104.916

Optimal ET sequence: 80, 103, 183

Badness: 0.146795

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 43923/43750

Mapping: [⟨1 -2 -1 -2 -1], ⟨0 41 38 55 51]]

POTE generator: ~35/33 = 104.916

Optimal ET sequence: 80, 103, 183

Badness: 0.041554

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 1375/1372, 4225/4224

Mapping: [⟨1 -2 -1 -2 -1 3], ⟨0 41 38 55 51 8]]

POTE generator: ~35/33 = 104.908

Optimal ET sequence: 80, 103, 183, 469f, 652def

Badness: 0.027908

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224

Mapping: [⟨1 -2 -1 -2 -1 3 4], ⟨0 41 38 55 51 8 1]]

POTE generator: ~17/16 = 104.909

Optimal ET sequence: 80, 103, 183, 469f, 652def

Badness: 0.020128

Gaster

For the 5-limit version of this temperament, see Very high accuracy temperaments #Gaster.

Main article: Gaster temperament

The gaster temperament (111&113) tempers out [-70 72 -19⟩ (quadbila-negu) in the 5-limit; mirkwai comma (16875/16807) and skeetsma (14348907/14336000) in the 7-limit. The word "gaster" means abdomen or stomach, but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals 111, 113 and 224 support it even in the 41-limit.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 14348907/14336000

Mapping: [⟨1 11 38 37], ⟨0 -19 -72 -69]]

Wedgie: ⟨⟨19 72 69 70 56 -42]]

POTE generator: ~800/567 = 594.641

Optimal ET sequence: 111, 224

Badness: 0.154521

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 14348907/14336000

Mapping: [⟨1 11 38 37 -1], ⟨0 -19 -72 -69 9]]

POTE generator: ~512/363 = 594.639

Optimal ET sequence: 111, 224, 783d, 1007d, 1231dd

Badness: 0.054060

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1375/1372, 2200/2197

Mapping: [⟨1 11 38 37 -1 26], ⟨0 -19 -72 -69 9 -45]]

POTE generator: ~55/39 = 594.639

Optimal ET sequence: 111, 224, 783df, 1007df, 1231ddf

Badness: 0.024882

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197

Mapping: [⟨1 11 38 37 -1 26 14], ⟨0 -19 -72 -69 9 -45 -20]]

POTE generator: ~24/17 = 594.636

Optimal ET sequence: 111, 224, 559dgg

Badness: 0.021436

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444

Mapping: [⟨1 11 38 37 -1 26 14 32], ⟨0 -19 -72 -69 9 -45 -20 -56]]

POTE generator: ~24/17 = 594.636

Optimal ET sequence: 111, 224

Badness: 0.018370

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714

Mapping: [⟨1 11 38 37 -1 26 14 32 7], ⟨0 -19 -72 -69 9 -45 -20 -56 -5]]

POTE generator: ~24/17 = 594.641

Optimal ET sequence: 111, 224

Badness: 0.017619

29-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714

Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32]]

POTE generator: ~24/17 = 594.646

Optimal ET sequence: 111, 113, 224

Badness: 0.016815

31-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31

Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714

Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11 0], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10]]

POTE generator: ~24/17 = 594.644

Optimal ET sequence: 111, 113, 224

Badness: 0.014790

37-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714

Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11 0 -27], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65]]

POTE generator: ~24/17 = 594.644

Optimal ET sequence: 111, 113, 224

Badness: 0.014377

41-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41

Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666

Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11 0 -27 45], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80]]

POTE generator: ~24/17 = 594.643

Optimal ET sequence: 111, 113, 224

Badness: 0.012858

Subsedia

The generator for subsedia (10&111) is 0.5 cents flat of 15/14-wide semitone and tempers out the mirkwai comma and 65536/64827 (buzzardisma, saquadru comma). In this temperament, three generators makes ~16/13, five of them equals ~24/17, twelve of them equals ~16/7, sixteen of them equals ~3/1, and 45 of them equals ~22/1.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 65536/64827

Mapping: [⟨1 0 5 4], ⟨0 16 -27 -12]]

Wedgie: ⟨⟨16 -27 -12 -80 -64 48]]

POTE generator: ~15/14 = 118.965

Optimal ET sequence: 10, 101, 111, 121, 232d

Badness: 0.157658

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 65536/64827

Mapping: [⟨1 0 5 4 -1], ⟨0 16 -27 -12 45]]

POTE generator: ~15/14 = 118.968

Optimal ET sequence: 10, 101, 111, 121, 232d

Badness: 0.066838

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 676/675, 1375/1372

Mapping: [⟨1 0 5 4 -1 4], ⟨0 16 -27 -12 45 -3]]

POTE generator: ~15/14 = 118.968

Optimal ET sequence: 10, 101, 111, 121, 232d

Badness: 0.031635

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 256/255, 352/351, 442/441, 540/539, 715/714

Mapping: [⟨1 0 5 4 -1 4 3], ⟨0 16 -27 -12 45 -3 11]]

POTE generator: ~15/14 = 118.968

Optimal ET sequence: 10, 101, 111, 121, 232dg

Badness: 0.019707

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714

Mapping: [⟨1 0 5 4 -1 4 3 10], ⟨0 16 -27 -12 45 -3 11 -58]]

POTE generator: ~15/14 = 118.964

Optimal ET sequence: 10, 101h, 111, 121, 232dg

Badness: 0.017935

Hemiseptisix

The name hemiseptisix means a half of septimal major sixth (12/7). The hemiseptisix temperament (103&121) tempers out the mirkwai comma and 95703125/95551488 (pontiqak comma, lazozotritriyo) in the 7-limit. 224EDO provides an excellent tuning for 7, 11, and 13-limit hemiseptisix.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 95703125/95551488

Mapping: [⟨1 -19 -7 -17], ⟨0 53 24 51]]

Wedgie: ⟨⟨53 24 51 -85 -68 51]]

POTE generator: ~98/75 = 466.071

Optimal ET sequence: 18, 103, 121, 224

Badness: 0.162826

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 2734375/2725888

Mapping: [⟨1 -19 -7 -17 -28], ⟨0 53 24 51 81]]

POTE generator: ~55/42 = 466.070

Optimal ET sequence: 103, 121, 224

Badness: 0.043381

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 625/624, 1375/1372, 2200/2197

Mapping: [⟨1 -19 -7 -17 -28 -13], ⟨0 53 24 51 81 43]]

POTE generator: ~55/42 = 466.071

Optimal ET sequence: 103, 121, 224

Badness: 0.021127

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 375/374, 540/539, 625/624, 715/714, 2200/2197

Mapping: [⟨1 -19 -7 -17 -28 -13 -13], ⟨0 53 24 51 81 43 44]]

POTE generator: ~17/13 = 466.074

Optimal ET sequence: 103, 121, 224

Badness: 0.018611

Browser

See also: Sensipent family

Subgroup: 2.3.5.7

Comma list: 16875/16807, 78732/78125

Mapping: [⟨1 6 8 10], ⟨0 -35 -45 -57]]

Wedgie: ⟨⟨35 45 57 -10 -8 6]]

POTE generator: ~49/45 = 151.399

Optimal ET sequence: 103, 111, 214

Badness: 0.180645

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 78732/78125

Mapping: [⟨1 6 8 10 8], ⟨0 -35 -45 -57 -36]]

POTE generator: ~12/11 = 151.405

Optimal ET sequence: 103, 214

Badness: 0.057634

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 847/845, 1375/1372

Mapping: [⟨1 6 8 10 8 9], ⟨0 -35 -45 -57 -36 -42]]

POTE generator: ~12/11 = 151.403

Optimal ET sequence: 103, 111, 214

Badness: 0.028822

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 351/350, 540/539, 561/560, 715/714, 847/845

Mapping: [⟨1 6 8 10 8 9 8], ⟨0 -35 -45 -57 -36 -42 -31]]

POTE generator: ~12/11 = 151.397

Optimal ET sequence: 103, 111, 214

Badness: 0.020384

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 324/323, 351/350, 456/455, 495/494, 540/539, 715/714

Mapping: [⟨1 6 8 10 8 9 8 18], ⟨0 -35 -45 -57 -36 -42 -31 -109]]

POTE generator: ~12/11 = 151.396

Optimal ET sequence: 103h, 111, 214

Badness: 0.017570

Grazer

Subgroup: 2.3.5.7

Comma list: 16875/16807, 1071875/1062882

Mapping: [⟨1 -3 -4 -5], ⟨0 37 51 63]]

Wedgie: ⟨⟨37 51 63 -5 -4 3]]

POTE generator: ~49/45 = 148.719

Optimal ET sequence: 113, 121, 234

Badness: 0.217166

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 218750/216513

Mapping: [⟨1 -3 -4 -5 -1], ⟨0 37 51 63 36]]

POTE generator: ~12/11 = 148.729

Optimal ET sequence: 113, 121, 234, 355e, 589cee

Badness: 0.076062

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 364/363, 540/539, 2200/2197

Mapping: [⟨1 -3 -4 -5 -1 -2], ⟨0 37 51 63 36 46]]

POTE generator: ~12/11 = 148.729

Optimal ET sequence: 113, 121, 234, 355e, 589cee

Badness: 0.036248

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 325/324, 364/363, 540/539, 595/594, 2000/1989

Mapping: [⟨1 -3 -4 -5 -1 -2 0], ⟨0 37 51 63 36 46 33]]

POTE generator: ~12/11 = 148.735

Optimal ET sequence: 113, 121, 234g, 355eg

Badness: 0.025410

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 325/324, 364/363, 400/399, 540/539, 595/594, 665/663

Mapping: [⟨1 -3 -4 -5 -1 -2 0 4], ⟨0 37 51 63 36 46 33 2]]

POTE generator: ~12/11 = 148.727

Optimal ET sequence: 113, 121, 234g, 355eg, 589ceegg

Badness: 0.022574