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, hemischismic, passion, hexe and sycamore considered elsewhere.

2.5.7-limit

Comma: 3136/3125

No-threes POTE generator (~28/25): 193.772

Map: [<1 0 0 -3|, <0 0 2 5|]

EDOs: 6, 12, 19, 31, 68, 80, 87, 99, 130, 217, 229, 328, 347, 446, 545c, 675

Misty

Commas: 3136/3125, 5120/5103

POTE generator: 703.021

Map: [<3 0 26 56|, <0 1 -4 -10|]

Wedgie: <<3 -12 -30 -26 -56 -36||

EDOs: 12, 87, 99

11-limit

Commas: 441/440, 3136/3125, 4375/4356

POTE generator: 703.210

Map: [<3 0 26 56 77|, <0 1 -4 -10 -14|]

EDOs: 12, 87, 99e, 186e

13-limit

Commas: 196/195, 352/351, 364/363, 625/624

POTE generator: 703.303

Map: [<3 0 26 56 77 92|, <0 1 -4 -10 -14 -17|]

EDOs: 12, 87, 186ef, 273ef

Mystic

Commas: 325/324, 441/440, 896/891, 1001/1000

POTE generator: 703.311

Map: [<3 0 26 56 77 -46|, <0 1 -4 -10 -14 12|]

EDOs: 12, 87, 186e, 273e, 633bde

17-limit

Commas: 196/195, 352/351, 364/363, 625/624

POTE generator: 703.233

Map: [<3 0 26 56 77 92 -2|, <0 1 -4 -10 -14 -17 3|]

EDOs: 87, 186ef, 273ef

19-limit

Commas: 154/153, 196/195, 245/243, 273/272, 286/285, 325/324

POTE generator: 703.253

Map: [<3 0 26 56 77 92 -2 8|, <0 1 -4 -10 -14 -17 3 1|]

EDOs: 46, 87, 133, 326de, 413degh

Semisept

Comma: 782757789696/762939453125

POTE generator: ~192/125 = 735.146

Map: [<1 12 6|, <0 -17 -6|]

EDOs: 18, 31, 80, 111

Badness: 0.6306

7-limit

Commas: 3136/3125, 1728/1715

POTE generator: (~75/49) 735.155

Map: [<1 12 6 12|, <0 -17 -6 -15|]

Wedgie: <<17 6 15 -30 -24 18||

EDOs: 18, 31, 80, 111

11-limit

Commas: 176/175, 540/539, 1331/1323

POTE generator: (~55/36) 735.125

Map: [<1 12 6 12 20|, <0 -17 -6 -15 -27|]

EDOs: 18e, 31, 80, 111, 364cd,

Badness: 0.0225

Semishly

Commas: 144/143, 176/175, 196/195, 275/273

POTE generator: ~13/10 = 464.980

Map: [<1 12 6 12 20 8|, <0 -17 -6 -15 -27 -7|]

EDOs: 31, 49f, 80f

Badness: 0.0284

13-limit

Commas: 176/175, 351/350, 540/539, 1375/1372

POTE generator: 735.126

Map: [<1 12 6 12 20 -11|, <0 -17 -6 -15 -27 24|]

EDOs: 31, 80, 111

Badness: 0.0252

17-limit

Commas: 176/175, 256/255, 351/350, 640/637, 715/714

POTE generator: (~26/17) 735.125

Map: [<1 12 6 12 20 -11 -10|, <0 -17 -6 -15 -27 24 23|]

EDOs: 31, 80, 111

19-limit

Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323

POTE generator: 735.116

Map: [<1 12 6 12 20 -11 -10 -8|, <0 -17 -6 -15 -27 24 23 20|]

EDOs: 31, 80, 111

23-limit

Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459

POTE generator: 435.106

Map: [<1 12 6 12 20 -11 -10 -8 18|,

<0 -17 -6 -15 -27 24 23 20 -22|]

EDOs: 31, 80, 111, 191cdh, 302cdgh

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