List of 19et rank two temperaments by badness

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Below are listed rank-two temperaments supported by the 19edo patent val, below the indicated cutoff in TE badness.

See also List of 19et rank two temperaments by complexity.

5-limit temperaments

Listed is the TE logflat badness times 1000 for six temperaments with badness less than 0.1.

# Name Badness Comma list
1 Meantone 7.381 81/80
2 Hanson 13.234 15625/15552
3 Sensipent 35.22 78732/78125
4 Magic 39.163 3125/3072
5 Egads 41.819 [-36 -52 51
6 Parakleismic 43.279 1224440064/1220703125
7 Enneadecal 47.845 19073486328125/19042491875328
8 Negri 86.856 16875/16384

7-limit temperaments

Listed is the TE badness times 1000 for 18 temperaments with badness less than 0.06.

# Name Badness Commas
1 Enneadecal 10.954 4375/4374 703125/702464
2 Meantone 13.707 81/80 126/125
3 Magic 18.918 225/224 245/243
4 Catakleismic 21.501 225/224 4375/4374
5 Sensi 25.622 126/125 245/243
6 Negri 26.483 49/48 225/224
7 Godzilla 26.747 49/48 81/80
8 Keemun 27.408 49/48 126/125
9 Parakleismic 27.431 3136/3125 4375/4374
10 Flattone 38.553 81/80 525/512
11 Unicorn 40.913 126/125 10976/10935
12 Liese 46.706 81/80 686/675
13 Clyde 47.261 245/243 3136/3125
14 Subpental 54.303 3136/3125 19683/19600
15 Acrokleismic 56.184 4375/4374 2202927104/2197265625
16 Muggles 56.206 126/125 525/512
17 Sensei 59.218 225/224 78732/78125
18 Triton 59.245 225/224 1029/1000

11-limit temperaments

Listed is the TE badness times 1000 for 28 temperaments with badness less than 0.05.

# Name Badness Comma list
1 Magic 20.352 100/99 225/224 245/243
2 Meanenneadecal 21.423 45/44 56/55 81/80
3 Meanpop 21.543 81/80 126/125 540/539
4 Catakleismic 21.849 225/224 385/384 4375/4374
5 Negri 26.190 45/44 49/48 56/55
6 Keemun 27.410 49/48 56/55 100/99
7 Sensis 28.680 56/55 100/99 245/243
8 Godzilla 28.947 45/44 49/48 81/80
9 Flattone 33.839 45/44 81/80 385/384
10 Baragon 35.673 49/48 56/55 81/80
11 Undevigintone 36.387 49/48 81/80 126/125
12 Acrokleismic 36.878 4375/4374 41503/41472 172032/171875
13 Sensor 37.942 126/125 245/243 385/384
14 Negril 38.679 49/48 100/99 225/224
15 Alicorn 39.156 126/125 540/539 896/891
16 Horcrux 39.282 45/44 56/55 245/243
18 Qeema 40.056 45/44 49/48 126/125
19 Liesel 40.721 56/55 81/80 540/539
20 Paradigmic 41.720 540/539 896/891 3136/3125
21 Enneadecal 43.734 540/539 4375/4374 16384/16335
22 Cataleptic 44.335 100/99 225/224 864/847
23 Subpental 45.352 540/539 3136/3125 8019/8000
24 Triton 45.675 45/44 56/55 1029/1000
25 Clyde 47.417 245/243 385/384 3136/3125
26 Muggles 48.038 45/44 126/125 385/384
28 Parakleismic 49.711 385/384 3136/3125 4375/4374

13-limit temperaments

Listed is the TE badness times 1000 for 46 temperaments with badness less than 0.04.

# Name Badness Comma list
1 Catakleismic 16.883 169/168 225/224 325/324 385/384
2 Negri 17.833 45/44 49/48 56/55 78/77
3 Sensis 20.017 56/55 78/77 91/90 100/99
4 Meanpop 20.883 81/80 105/104 144/143 196/195
5 Meanenneadecal 21.182 45/44 56/55 78/77 81/80
6 Magic 21.509 100/99 105/104 144/143 196/195
7 Flattone 22.260 45/44 65/64 78/77 81/80
8 Godzilla 22.503 45/44 49/48 78/77 81/80
9 Kema 22.749 49/48 56/55 91/90 100/99
10 Undevigintone 22.933 49/48 65/64 81/80 91/90
11 Alicorn 23.667 126/125 144/143 196/195 676/675
12 Negril 24.383 49/48 65/64 91/90 875/858
13 Vincenzo 24.763 45/44 56/55 65/64 81/80
14 Sensor 25.575 91/90 126/125 169/168 385/384
15 Sorcery 25.829 65/64 78/77 91/90 100/99
17 Liesel 27.304 56/55 78/77 81/80 91/90
18 Cataleptic 27.343 78/77 100/99 144/143 676/675
19 Meanplop 27.666 65/64 81/80 126/125 169/165
20 Qeema 29.419 45/44 49/48 78/77 126/125
21 Keemun 29.749 49/48 56/55 78/77 100/99
22 Muggles 30.386 45/44 65/64 78/77 126/125
24 Horcrux 31.938 45/44 56/55 78/77 875/864
27 Glamour 33.317 45/44 56/55 65/64 507/500
29 Sycamore 34.295 91/90 100/99 169/168 385/384
34 Paradigmic 35.781 169/168 325/324 540/539 832/825
35 Lisa 36.144 45/44 81/80 91/88 147/143
45 Rhinoceros 39.343 49/48 78/77 100/99 126/121