Canopic 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 and mirkat considered below, as well as these considered elsewhere:
- octokaidecal, {28/27, 50/49} → Trienstonic clan #Octokaidecal
- nusecond, {126/125, 2430/2401} → Starling temperaments #Nusecond
- miracle, {225/224, 1029/1024} → Gamelismic clan #Miracle
- bohpier, {245/243, 3125/3087} → Sensamagic clan #Bohpier
- semisept, {1728/1715, 3136/3125} → Hemimean clan #Semisept
- octoid, {4375/4374, 16875/16807} → Ragismic microtemperaments #Octoid
- sqrtphi, {15625/15552, 16875/16807} → Kleismic family #Sqrtphi
- quanharuk, {16875/16807, 32805/32768} → Schismatic family #Quanharuk
- familia, {16875/16807, 1600000/1594323} → Amity family #Familia
- rainwell, {16875/16807, 2100875/2097152} → Semicomma family #Rainwell
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
Vals: 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
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
Vals: Template:Val list
Badness: 0.019845
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 625/624, 1375/1372
Map: [⟨1 9 2 7 17 -5], ⟨0 -23 1 -13 -42 27]]
POTE generator: ~5/4 = 386.826
Vals: Template:Val list
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
Vals: Template:Val list
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]]
Vals: Template:Val list
Badness: 0.018413
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
Badness: 0.054476
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 16384/16335
Mapping: [⟨1 0 -50 -40 32], ⟨0 1 33 27 -18]]
POTE generator: ~3/2 = 702.623
Vals: Template:Val list
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
Vals: Template:Val list
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
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.016957
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
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
Vals: Template:Val list
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
Vals: Template:Val list
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
Vals: Template:Val list
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
Vals: Template:Val list
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
Vals: Template:Val list
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
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.040182
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
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
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.025137
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
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
Vals: Template:Val list
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
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.011775
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
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
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.028387