Hemifamity temperaments

The hemifamity temperaments temper out the hemifamity comma, [10 -6 1 -1⟩ = 5120/5103, dividing an exact or approximate septimal diesis, [2 2 -1 -1⟩ = 36/35 into two equal steps. 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

Map: [<1 2 2 0 3|, <0 -9 7 61 10|]

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

Semiseptiquarter

Commas: 5120/5103, 9801/9800, 14641/14580

POTE generators: ~121/105 = 242.4511

Map: [<2 6 20 4 15|, <0 -7 -38 4 -20|]

EDOs: 94, 198, 292, 490

Badness: 0.0642

13-limit

Commas: 352/351, 847/845, 1716/1715, 14641/14580

POTE generators: ~121/105 = 242.4448

Map: [<2 6 20 4 15 7|, <0 -7 -38 4 -20 1|]

EDOs: 94, 198, 490f

Badness: 0.0348

Tricot

The generator for tricot temperament is the real cube root of third harmonic, 3^1/3, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&70 temperament, tempering out the tricot comma, [39 -29 3⟩ in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit.

5-limit

Comma: [39 -29 3⟩ = 68719476736000/68630377364883

POTE generator: ~59049/40960 = 634.012

Map: [<1 0 -13|, <0 3 29|]

Wedgie: <<3 29 39||

EDOs: 53, 229, 282, 335, 388, 441, 1376, 1817, 2258

Badness: 0.0461

7-limit

Commas: 2430/2401, 5120/5103

POTE generator: ~81/56 = 634.026

Map: [<1 0 -13 -3|, <0 3 29 11|]

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

EDOs: 17c, 36c, 53, 229dd, 282dd

Badness: 0.1001

11-limit

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

POTE generator: ~63/44 = 634.027

Map: [<1 0 -13 -3 -5|, <0 3 29 11 16|]

EDOs: 17c, 36ce, 53, 176de

Badness: 0.0561

13-limit

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

POTE generator: ~13/9 = 634.012

Map: [<1 0 -13 -3 -5 0|, <0 3 29 11 16 7|]

EDOs: 17c, 36ce, 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