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
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
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
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
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