Hemimean clan
The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as meantone, hemiwürschmidt, parakleismic, hemithirds, clyde, bischismic, passion, hexe and sycamore considered elsewhere.
Didacus
Subgroup: 2.5.7
Comma list: 3136/3125
Sval mapping: [⟨1 0 -3], ⟨0 2 5]]
Mapping generators: ~2, ~28/25
Gencom mapping: [⟨1 0 0 -3], ⟨0 0 2 5]]
Gencom: [2 28/25; 3136/3125]
POTE generator: ~28/25 = 193.772
Misty
Comma list: 3136/3125, 5120/5103
Mapping: [⟨3 0 26 56], ⟨0 1 -4 -10]]
Wedgie: ⟨⟨ 3 -12 -30 -26 -56 -36 ]]
POTE generator: ~3/2 = 703.021
11-limit
Comma list: 441/440, 3136/3125, 4375/4356
Mapping: [⟨3 0 26 56 77], ⟨0 1 -4 -10 -14]]
POTE generator: ~3/2 = 703.210
13-limit
Comma list: 196/195, 352/351, 364/363, 625/624
Mapping: [⟨3 0 26 56 77 92], ⟨0 1 -4 -10 -14 -17]]
POTE generator: ~3/2 = 703.303
17-limit
Comma list: 196/195, 352/351, 364/363, 375/374, 595/594
Mapping: [⟨3 0 26 56 77 92 -2], ⟨0 1 -4 -10 -14 -17 3]]
POTE generator: ~3/2 = 703.233
19-limit
Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594
Mapping: [⟨3 0 26 56 77 92 -2 8], ⟨0 1 -4 -10 -14 -17 3 1]]
POTE generator: ~3/2 = 703.253
Mystic
Comma list: 325/324, 441/440, 896/891, 1001/1000
Mapping: [⟨3 0 26 56 77 -46], ⟨0 1 -4 -10 -14 12]]
POTE generator: ~3/2 = 703.311
Hemimist
Comma list: 3136/3125, 5120/5103, 3025/3024
Mapping: [⟨3 0 26 56 8], ⟨0 2 -8 -20 1]]
POTE generator: ~11/8 = 551.527
Badness: 0.0474
13-limit
Comma list: 352/351, 676/675, 847/845, 3025/3024
Mapping: [⟨3 0 26 56 8 23], ⟨0 2 -8 -20 1 -5]]
POTE generator: ~11/8 = 551.525
Badness: 0.0229
Semisept
5-limit
Comma list: 782757789696/762939453125
Mapping: [⟨1 12 6], ⟨0 -17 -6]]
POTE generator: ~192/125 = 735.146
Badness: 0.6306
7-limit
Comma list: 3136/3125, 1728/1715
Mapping: [⟨1 12 6 12], ⟨0 -17 -6 -15]]
Wedgie: ⟨⟨ 17 6 15 -30 -24 18 ]]
POTE generator: ~75/49 = 735.155
11-limit
Comma list: 176/175, 540/539, 1331/1323
Mapping: [⟨1 12 6 12 20], ⟨0 -17 -6 -15 -27]]
POTE generator: ~55/36 = 735.125
Badness: 0.0225
13-limit
Comma list: 176/175, 351/350, 540/539, 1375/1372
Mapping: [⟨1 12 6 12 20 -11], ⟨0 -17 -6 -15 -27 24]]
POTE generator: ~55/36 = 735.126
Badness: 0.0252
17-limit
Comma list: 176/175, 256/255, 351/350, 640/637, 715/714
Mapping: [⟨1 12 6 12 20 -11 -10], ⟨0 -17 -6 -15 -27 24 23]]
POTE generator: ~26/17 = 735.125
19-limit
Comma list: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323
Mapping: [⟨1 12 6 12 20 -11 -10 -8], ⟨0 -17 -6 -15 -27 24 23 20]]
POTE generator: ~26/17 = 735.116
23-limit
Comma list: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459
Mapping: [{{val| 1 12 6 12 20 -11 -10 -8 18|, ⟨0 -17 -6 -15 -27 24 23 20 -22]]
POTE generator: ~26/17 = 735.106
Semishly
Comma list: 144/143, 176/175, 196/195, 275/273
Mapping: [⟨1 12 6 12 20 8], ⟨0 -17 -6 -15 -27 -7]]
POTE generator: ~13/10 = 464.980
Badness: 0.0284
Sengagen
Commas: 3136/3125, 420175/419904
POTE generator: ~686/675 = 24.217
Map: [<1 1 2 2|, <0 29 16 40|]
Wedgie: <<29 16 40 -42 -18 48||
EDOs: 49, 50, 99, 248, 347, 446
Badness: 0.0580
Subpental
Commas: 3136/3125, 19683/19600
POTE generator: ~56/45 = 378.467
Map: [<1 6 8 17|, <0 -14 -18 -45|]
Wedgie: <<14 18 45 -4 32 54||
EDOs: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc
Badness: 0.0543
11-limit
Commas: 540/539, 3136/3125, 8019/8000
POTE generator: ~56/45 = 378.440
Map: [<1 6 8 17 -6|, <0 -14 -18 -45 30|]
EDOs: 19, 111, 130, 241, 371ce, 501cde, 872cde
Badness: 0.0453
13-limit
Commas: 351/350, 540/539, 676/675, 3136/3125
POTE generator: ~56/45 = 378.437
Map: [<1 6 8 17 -6 16|, <0 -14 -18 -45 30 -39|]
EDOs: 19, 111, 130, 241, 371ce
Badness: 0.0239
Arch
Commas: 3136/3125, 5250987/5242880
POTE generator: ~64/63 = 27.668
Map: [<1 2 2 2|, <0 -18 14 35|]
Wedgie: <<18 -14 -35 -64 -106 -42||
EDOs: 43, 87, 130, 217, 347, 824c, 1171c, 1518cd
Badness: 0.0943
11-limit
Commas: 441/440, 3136/3125, 4000/3993
POTE generator: ~64/63 = 27.663
Map: [<1 2 2 2 3|, <0 -18 14 35 20|]
EDOs: 43, 87, 130, 217, 347e, 911cde
Badness: 0.0365
13-limit
Commas: 364/363, 441/440, 676/675, 3136/3125
POTE generator: ~64/63 = 27.660
Map: [<1 2 2 2 3 4|, <0 -18 14 35 20 -13|]
EDOs: 43, 87, 130, 217, 347e, 564e
Badness: 0.0195
Emka
Commas: 3136/3125, 84035/82944
POTE generator: ~48/35 = 551.782
Map: [<1 14 6 12|, <0 -27 -8 -20|]
EDOs: 37, 50, 87, 137d, 224d
Badness: 0.1443
11-limit
Commas: 385/384, 2401/2376, 3136/3125
POTE generator: ~11/8 = 551.765
Map: [<1 14 6 12 3|, <0 -27 -8 -20 1|]
EDOs: 37, 50, 87, 224d, 311d
Badness: 0.0547
13-limit
Commas: 196/195, 364/363, 385/384, 625/624
POTE generator: ~11/8 = 551.758
Map: [<1 14 6 12 3 6|, <0 -27 -8 -20 1 -5|]
EDOs: 37, 50, 87, 224d, 311d, 398d
Badness: 0.0297