Hemifamity temperaments

The hemifamity temperaments temper out the hemifamity comma, |10 -6 1 -1> = 5120/5103. Belonging to it and considered below are buzzard, undecental, leapday, mystery, quanic and ketchup. Other hemifamity temperaments are dominant, garibaldi, hemififths, amity, misty, rodan, countercata and kwai.

Buzzard

Commas: 1728/1715, 5120/5103

POTE generator: ~320/243 = 475.636

Map: [<1 0 -6 4|, <0 4 21 -3|]

Wedgie: <<4 21 -3 24 -16 -66||

EDOs: 48, 53, 111, 164d, 275d

Badness: 0.0480

11-limit

Commas: 176/175, 540/539, 5120/5103

POTE generator: ~320/243 = 475.700

Map: [<1 0 -6 4 -12|, <0 4 21 -3 39|]

EDOs: 53, 58, 111, 280cd, 391cd

Badness: 0.0345

13-limit

Commas: 176/175, 351/350, 540/539, 676/675

POTE generator: ~320/243 = 475.697

Map: [<1 0 -6 4 -12 -7|, <0 4 21 -3 39 27|]

EDOs: 53, 58, 111, 280cdf, 391cdf

Badness: 0.0188

17-limit

Commas: 176/175, 256/255, 351/350, 442/441, 540/539

POTE generator: ~320/243 = 475.692

Map: [<1 0 -6 4 -12 -7 14|, <0 4 21 -3 39 27 -25|]

EDOs: 53, 58, 111, 321cdfg

Badness: 0.0184

19-limit

Commas: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539

POTE generator: ~320/243 = 475.679

Map: [<1 0 -6 4 -12 -7 14 -12|, <0 4 21 -3 39 27 -25 41|]

EDOs: 53, 58h, 111

Badness: 0.0156

Buteo

Commas: 99/98, 385/384, 2200/2187

POTE generator: ~21/16 = 475.436

Map: [<1 0 -6 4 9|, <0 4 21 -3 -14|]

EDOs: 5, 48, 53

Badness: 0.0602

13-limit

Commas: 99/98, 275/273, 385/384, 572/567

POTE generator: ~21/16 = 475.464

Map: [<1 0 -6 4 9 -7|, <0 4 21 -3 -14 27|]

EDOs: 5, 53

Badness: 0.0390

Undecental

Commas: 5120/5103, 235298/234375

POTE generator: ~3/2 = 703.039

Map: [<1 0 61 71|, <0 1 -37 -43|]

Wedgie: <<1 -37 -43 -61 -71 4||

EDOs: 12, 29, 70, 99

Leapday

Comma: 10737418240/10460353203

POTE generator: ~3/2 = 704.179

Map: [<1 0 -31|, <0 1 21|]

EDOs: 29, 46, 121, 167, 455bc, 622bc

Badness: 0.5232

7-limit

Commas: 686/675, 5120/5103

POTE generator: ~3/2 = 704.263

Map: [<1 0 -31 -21|, <0 1 21 15|]

Wedgie: <<1 21 15 31 21 -24||

EDOs: 29, 46, 305

Badness: 0.0961

11-limit

Commas: 121/120, 441/440, 686/675

POTE generator: ~3/2 = 704.250

Map: [<1 0 -31 -21 -14|, <0 1 21 15 11|]

EDOs: 29, 46, 259

Badness: 0.0386

13-limit

Commas: 91/90, 121/120, 169/168, 441/440

POTE generator: ~3/2 = 704.214

Map: [<1 0 -31 -21 -14 -9|, <0 1 21 15 11 8|]

EDOs: 29, 46, 167, 213, 380

Badness: 0.0247

17-limit

Commas: 91/90, 121/120, 136/135, 154/153, 169/168

POTE generator: ~3/2 = 704.229

[<1 0 -31 -21 -14 -9 -34|, <0 1 21 15 11 8 24|]

EDOs: 29g, 46, 121defg, 167defg, 213defg

Badness: 0.0179

19-limit

Commas: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168

POTE generator: ~3/2 = 704.135

Map: [<1 0 -31 -21 -14 -9 -34 9|, <0 1 21 15 11 8 24 -3|]

EDOs: 29g, 46, 75dfgh, 121defgh

Badness: 0.0174

Leapling

Commas: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168

POTE generator: ~3/2 = 704.123

Map: [<1 0 -31 -21 -14 -9 -34 -37|, <0 1 21 15 11 8 24 26|]

EDOs: 29g, 46h, 75dfg

Badness: 0.0191

Mystery

Commas: 5120/5103, 50421/50000

POTE generator: ~5/4 = 388.646

Map: [<29 46 0 14|, <0 0 1 1|]

Wedgie: <<0 29 29 46 46 -14||

EDOs: 29, 58, 87, 145

Badness: 0.1037

11-limit

Commas: 441/440, 896/891, 3388/3375

POTE generator: ~5/4 = 388.460

Map: [<29 46 0 14 33|, <0 0 1 1 1|]

EDOs: 29, 58, 87, 145

Badness: 0.0343

13-limit

Commas: 196/195, 352/351, 364/363, 676/675

POTE generator: ~5/4 = 388.354

Map: [<29 46 0 14 33 40|, <0 0 1 1 1 1|]

EDOs: 29, 58, 87, 145, 232, 377

Badness: 0.0186

Quanic

Commas: 5120/5103, 5832000/5764801

POTE generator: ~160/147 = 140.493

Map: [<1 1 -4 0|, <0 5 54 24|]

EDOs: 94, 111, 205

Badness: 0.1795

11-limit

Commas: 540/539, 1331/1323, 5120/5103

POTE generator: ~88/81 = 140.489

Map: [<1 1 -4 0 1|, <0 5 54 24 21|]

EDOs: 94, 111, 205

Badness: 0.0587

13-limit

Commas: 352/351, 540/539, 729/728, 1331/1323

POTE generator: ~13/12 = 140.496

Map: [<1 1 -4 0 1 3|, <0 5 54 24 21 6|]

EDOs: 94, 111, 205

Badness: 0.0325

17-limit

Commas: 352/351, 442/441, 540/539, 715/714, 847/845

POTE generator: ~13/12 = 140.497

Map: [<1 1 -4 0 1 3 -2|, <0 5 54 24 21 6 52|]

EDOs: 94, 111, 205

Badness: 0.0211

19-limit

Commas: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714

POTE generator: ~13/12 = 140.496

Map: [<1 1 -4 0 1 3 -2 -5|, <0 5 54 24 21 6 52 79|]

EDOs: 94, 111, 205

Badness: 0.0173

Supers

Commas: 5120/5103, 118098/117649

POTE generator: ~9/7 = 434.218

Map: [<2 1 -12 2|, <0 3 23 5|]

Wedgie: <<6 46 10 59 -1 -106||

EDOs: 58, 94, 152

Badness: 92.748

11-limit

Commas: 540/539, 4000/3993, 5120/5103

POTE generator: ~9/7 = 434.217

Map: [<2 1 -12 2 -9|, <0 3 23 5 22|]

EDOs: 58, 94, 152

Badness: 0.0282

13-limit

Commas: 352/351, 540/539, 729/728, 1575/1573

POTE generator: ~9/7 = 434.221

Map: [<2 1 -12 2 -9 -2|, <0 3 23 5 22 13|]

EDOs: 58, 94, 152f

Badness: 0.0216

Alphaquarter

Commas: 5120/5103, 29360128/29296875

POTE generator: ~16128/15625 = 55.243

Map: [<1 2 2 0|, <0 -9 7 61|]

Wedgie: <<9 -7 -61 -32 -122 -122||

EDOs: 87, 152, 239, 391

Badness: 0.1166

11-limit

Commas: 3025/3024, 4000/3993, 5120/5103

POTE generator: ~33/32 = 55.243

EDOs: 87, 152, 239, 391

Badness: 0.0296

Septiquarter

Commas: 5120/5103, 420175/419904

POTE generator: ~147/128 = 242.453

Map: [<1 3 10 2|, <0 -7 -38 4|]

Wedgie: <<7 38 -4 44 -26 -116||

EDOs: 94, 99, 292, 391, 881bd, 1272bcd

Badness: 0.0538

Tricot

Commas: 2430/2401, 5120/5103

POTE generator: ~81/56 = 634.026

Map: [[< 3 16 8|, <0 -3 -29 -11|]

Wedgie: <<3 29 11 39 9 -56||

EDOs: 53, 229d, 282d

Badness: 0.1001

11-limit

Commas: 99/98, 121/120, 5120/5103

POTE generator: ~63/44 = 634.027

Map: [[< 3 16 8 11|, <0 -3 -29 -11 -16|]

EDOs: 53, 176de, 229

Badness: 0.0561

13-limit

Commas: 99/98, 121/120, 169/168, 352/351

POTE generator: ~13/9 = 634.012

Map: [[< 3 16 8 11 7|, <0 -3 -29 -11 -16 -7|]

EDOs: 53

Badness: 0.0321

Ketchup

Commas: 5120/5103, 1071875/1062882

POTE generator: ~64/63 = ~81/80 = 25.719

Map: [<2 3 4 6|, <0 4 15 -9|]

EDOS: 46, 94, 140

Badness: 0.0845

11-limit

Commas: 385/384, 1331/1323, 2200/2187

POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.693

Map: [<2 3 4 6 7|, <0 4 15 -9 -2|]

EDOs: 46, 94, 140

Badness: 0.0396

13-limit

Commas: 325/324, 352/351, 847/845, 1331/1323

POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.697

Map: [<2 3 4 6 7 8|, <0 4 15 -9 -2 -14|]

EDOs: 46, 94, 140

Badness: 0.0248

17-limit

Commas: 289/288, 325/324, 352/351, 385/384, 561/560

POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.701

Map: [<2 3 4 6 7 8 8|, <0 4 15 -9 -2 -14 4|]

EDOs: 46, 94, 140

Badness: 0.0166

19-limit

Commas: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560

POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.660

Map: [<2 3 4 6 7 8 8 9|, <0 4 15 -9 -2 -14 4 -12|]

EDOs: 46, 94, 140h, 234eh

Badness: 0.0182

23-limit

Commas: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384

POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.661

Map: [<2 3 4 6 7 8 8 9 9|, <0 4 15 -9 -2 -14 4 -12 1|]

EDOs: 46, 94, 140h, 234ehi

Badness: 0.0140