List of 19et rank two temperaments by badness

From Xenharmonic Wiki
Jump to: navigation, search

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 with badness below 0.1

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

Rank Wedgie Name Badness Commas
1 <<1 4 4]] Meantone 7.381 81/80
2 <<6 5 -6]] Hanson 13.234 15625/15552
3 <<7 9 -2]] Sensipent 35.22 78732/78125
4 <<5 1 -10]] Magic 39.163 3125/3072
5 <<51 52 -36]] Egads 41.819 |-36 -52 51>
6 <<13 14 -8]] Parakleismic 43.279 1224440064/1220703125
7 <<19 19 -14]] Enneadecal 47.845 19073486328125/19042491875328
8 <<4 -3 -14]] Negri 86.856 16875/16384

7-limit temperaments with badness below 0.06

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

Rank Wedgie Name Badness Commas
1 <<19 19 57 -14 37 79]] Enneadecal 10.954 4375/4374 703125/702464
2 <<1 4 10 4 13 12]] Meantone 13.707 81/80 126/125
3 <<5 1 12 -10 5 25]] Magic 18.918 225/224 245/243
4 <<6 5 22 -6 18 37]] Catakleismic 21.501 225/224 4375/4374
5 <<7 9 13 -2 1 5]] Sensi 25.622 126/125 245/243
6 <<4 -3 2 -14 -8 13]] Negri 26.483 49/48 225/224
7 <<2 8 1 8 -4 -20]] Godzilla 26.747 49/48 81/80
8 <<6 5 3 -6 -12 -7]] Keemun 27.408 49/48 126/125
9 <<13 14 35 -8 19 42]] Parakleismic 27.431 3136/3125 4375/4374
10 <<1 4 -9 4 -17 -32]] Flattone 38.553 81/80 525/512
11 <<8 13 23 2 14 17]] Unicorn 40.913 126/125 10976/10935
12 <<3 12 11 12 9 -8]] Liese 46.706 81/80 686/675
13 <<12 10 25 -12 6 30]] Clyde 47.261 245/243 3136/3125
14 <<14 18 45 -4 32 54]] Subpental 54.303 3136/3125 19683/19600
15 <<32 33 92 -22 56 121]] Acrokleismic 56.184 4375/4374 2202927104/2197265625
16 <<5 1 -7 -10 -25 -19]] Muggles 56.206 126/125 525/512
17 <<7 9 32 -2 31 49]] Sensei 59.218 225/224 78732/78125
18 <<3 -7 -8 -18 -21 1]] Triton 59.245 225/224 1029/1000

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 2 temperaments with badness less than 0.05.

Rank Wedgie Name Badness Commas
1 <<5 1 12 -8 -10 5 -30 25 -22 -64]] Magic 20.352 100/99 225/224 245/243
2 <<1 4 10 6 4 13 6 12 0 -18]] Meanenneadecal 21.423 45/44 56/55 81/80
3 <<1 4 10 -13 4 13 -24 12 -44 -71]] Meanpop 21.543 81/80 126/125 540/539
4 <<6 5 22 -21 -6 18 -54 37 -66 -135]] Catakleismic 21.849 225/224 385/384 4375/4374
5 <<4 -3 2 5 -14 -8 -6 13 22 7]] Negri 26.190 45/44 49/48 56/55
6 <<6 5 3 -2 -6 -12 -24 -7 -22 -16]] Keemun 27.410 49/48 56/55 100/99
7 <<7 9 13 4 -2 1 -18 5 -22 -34]] Sensis 28.680 56/55 100/99 245/243
8 <<2 8 1 12 8 -4 12 -20 0 30]] Godzilla 28.947 45/44 49/48 81/80
9 <<1 4 -9 6 4 -17 6 -32 0 48]] Flattone 33.839 45/44 81/80 385/384
10 <<2 8 1 -7 8 -4 -18 -20 -44 -23]] Baragon 35.673 49/48 56/55 81/80
11 <<0 0 0 19 0 0 30 0 44 53]] Undevigintone 36.387 49/48 81/80 126/125
12 <<32 33 92 -74 -22 56 -228 121 -286 -526]] Acrokleismic 36.878 4375/4374 41503/41472 172032/171875
13 <<7 9 13 -15 -2 1 -48 5 -66 -87]] Sensor 37.942 126/125 245/243 385/384
14 <<4 -3 2 -14 -14 -8 -36 13 -22 -46]] Negril 38.679 49/48 100/99 225/224
15 <<8 13 23 -9 2 14 -42 17 -66 -105]] Alicorn 39.156 126/125 540/539 896/891
16 <<5 1 12 11 -10 5 0 25 22 -11]] Charisma 39.282 45/44 56/55 245/243
17 <<38 38 114 -95 -28 74 -282 158 -352 -661]] 39.701 4375/4374 41503/41472 703125/702464
18 <<6 5 3 17 -6 -12 6 -7 22 37]] 40.056 45/44 49/48 126/125
19 <<3 12 11 -1 12 9 -12 -8 -44 -41]] 40.7210 56/55 81/80 540/539
20 <<13 14 35 -17 -8 19 -72 42 -88 -169]] 41.720 540/539 896/891 3136/3125
21 <<19 19 57 -38 -14 37 -126 79 -154 -304]] 43.734 540/539 4375/4374 16384/16335
22 <<6 5 22 -2 -6 18 -24 37 -22 -82]] 44.3350 100/99 225/224 864/847
23 <<14 18 45 -30 -4 32 -96 54 -132 -240]] 45.352 540/539 3136/3125 8019/8
24 <<3 -7 -8 -1 -18 -21 -12 1 22 25]] 45.675 45/44 56/55 1029/1000
25 <<12 10 25 -23 -12 6 -78 30 -88 -151]] 47.417 245/243 385/384 3136/3125
26 <<5 1 -7 11 -10 -25 0 -19 22 55]] 48.038 45/44 126/125 385/384
27 <<2 8 20 -7 8 26 -18 24 -44 -89]] 49.303 81/80 126/125 864/847
28 <<13 14 35 -36 -8 19 -102 42 -132 -222]] 49.711 385/384 3136/3125 4375/4374

13-limit temperaments with badness below 0.04

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

Rank Wedgie Name Badness Commas
1 <<6 5 22 -21 14 -6 18 -54 0 37 -66 14 -135 -42 126]] Catakleismic 16.883 169/168 225/224 325/324 385/384
2 <<4 -3 2 5 3 -14 -8 -6 -10 13 22 18 7 1 -8]] Negri 17.833 45/44 49/48 56/55 78/77
3 <<7 9 13 4 10 -2 1 -18 -10 5 -22 -10 -34 -20 20]] Sensis 20.017 56/55 78/77 91/90 100/99
4 <<1 4 10 -13 15 4 13 -24 20 12 -44 20 -71 5 100]] Meanpop 20.883 81/80 105/104 144/143 196/195
5 <<1 4 10 6 15 4 13 6 20 12 0 20 -18 5 30]] Meanenneadecal 21.182 45/44 56/55 78/77 81/80
6 <<5 1 12 -8 18 -10 5 -30 10 25 -22 38 -64 6 92]] Magic 21.509 100/99 105/104 144/143 196/195
7 <<1 4 -9 6 -4 4 -17 6 -10 -32 0 -24 48 22 -36]] Flattone 22.260 45/44 65/64 78/77 81/80
8 <<2 8 1 12 11 8 -4 12 10 -20 0 -4 30 27 -6]] 22.503 45/44 49/48 78/77 81/80
9 <<6 5 3 -2 14 -6 -12 -24 0 -7 -22 14 -16 28 56]] Keema 22.749 49/48 56/55 91/90 625/624
10 <<0 0 0 19 0 0 0 30 0 0 44 0 53 0 -70]] 22.933 49/48 65/64 81/80 91/90
11 <<8 13 23 -9 25 2 14 -42 10 17 -66 10 -105 -15 120]] Alicorn 23.667 126/125 144/143 196/195 676/675
12 <<4 -3 2 -14 3 -14 -8 -36 -10 13 -22 18 -46 1 62]] Negril 24.383 49/48 65/64 91/90 875/858
13 <<1 4 10 6 -4 4 13 6 -10 12 0 -24 -18 -48 -36]] 24.763 45/44 56/55 65/64 81/80
14 <<7 9 13 -15 10 -2 1 -48 -10 5 -66 -10 -87 -20 90]] Sensor 25.575 91/90 126/125 169/168 385/384
15 <<5 1 12 -8 -1 -10 5 -30 -20 25 -22 -6 -64 -47 26]] 25.829 65/64 78/77 91/90 100/99
16 <<2 8 1 -7 11 8 -4 -18 10 -20 -44 -4 -23 27 64]] 26.703 49/48 56/55 81/80 91/90
17 <<3 12 11 -1 7 12 9 -12 0 -8 -44 -28 -41 -21 28]] 27.304 56/55 78/77 81/80 91/90
18 <<6 5 22 -2 14 -6 18 -24 0 37 -22 14 -82 -42 56]] 27.343 78/77 100/99 144/143 676/675
19 <<1 4 10 -13 -4 4 13 -24 -10 12 -44 -24 -71 -48 34]] 27.666 65/64 81/80 126/125 169/165
20 <<6 5 3 17 14 -6 -12 6 0 -7 22 14 37 28 -14]] 29.419 45/44 49/48 78/77 126/125
21 <<6 5 3 -2 -5 -6 -12 -24 -30 -7 -22 -30 -16 -25 -10]] 29.749 49/48 56/55 78/77 100/99
22 <<5 1 -7 11 -1 -10 -25 0 -20 -19 22 -6 55 23 -44]] 30.386 45/44 65/64 78/77 126/125
23 <<2 8 20 -7 11 8 26 -18 10 24 -44 -4 -89 -43 64]] 30.438 78/77 126/125 144/143 676/675
24 <<5 1 12 11 18 -10 5 0 10 25 22 38 -11 6 22]] 31.938 45/44 56/55 78/77 875/864
25 <<2 8 1 12 -8 8 -4 12 -20 -20 0 -48 30 -26 -72]] 32.878 45/44 49/48 65/64 81/80
26 <<12 10 25 -4 28 -12 6 -48 0 30 -44 28 -98 -14 112]] 32.989 100/99 144/143 196/195 2197/2187
27 <<5 1 12 11 -1 -10 5 0 -20 25 22 -6 -11 -47 -44]] 33.317 45/44 56/55 65/64 507/500
28 <<3 -7 -8 -1 -12 -18 -21 -12 -30 1 22 -2 25 -4 -38]] 33.858 45/44 56/55 78/77 507/500
29 <<11 6 15 -10 13 -16 -7 -54 -20 18 -44 8 -80 -19 82]] 34.295 91/90 100/99 169/168 385/384
30 <<1 4 -9 25 -4 4 -17 36 -10 -32 44 -24 101 22 -106]] 34.640 65/64 81/80 105/104 625/616
31 <<2 8 1 -7 -8 8 -4 -18 -20 -20 -44 -48 -23 -26 -2]] 35.063 49/48 56/55 65/64 81/80
32 <<5 1 -7 -8 -1 -10 -25 -30 -20 -19 -22 -6 2 23 26]] 35.188 56/55 65/64 100/99 105/104
33 <<0 0 0 0 19 0 0 0 30 0 0 44 0 53 66]] 35.286 45/44 49/48 56/55 81/80
34 <<13 14 35 -17 24 -8 19 -72 -10 42 -88 4 -169 -62 146]] 35.781 169/168 325/324 540/539 832/825
35 <<3 12 11 18 7 12 9 18 0 -8 0 -28 12 -21 -42]] 36.144 45/44 81/80 91/88 147/143
36 <<11 6 15 9 13 -16 -7 -24 -20 18 0 8 -27 -19 12]] 37.127 56/55 78/77 91/90 125/121
37 <<10 2 24 -16 17 -20 10 -60 -10 50 -44 32 -128 -41 118]] 37.146 100/99 169/168 225/224 245/243
38 <<6 5 3 17 -5 -6 -12 6 -30 -7 22 -30 37 -25 -80]] 37.435 45/44 49/48 65/64 126/125
39 <<3 -7 11 -1 7 -18 9 -12 0 45 22 42 -41 -21 28]] 37.666 45/44 65/64 78/77 245/243
40 <<1 4 -9 -13 -4 4 -17 -24 -10 -32 -44 -24 -5 22 34]] 37.680 56/55 65/64 81/80 105/104
41 <<7 9 13 4 29 -2 1 -18 20 5 -22 34 -34 33 86]] 38.025 56/55 100/99 105/104 245/243
42 <<2 -11 1 -7 -8 -22 -4 -18 -20 33 22 22 -23 -26 -2]] 38.389 45/44 49/48 78/77 896/891
43 <<3 -7 -8 -1 7 -18 -21 -12 0 1 22 42 25 49 28]] 38.573 45/44 56/55 65/64 1323/1280
44 <<8 13 23 10 25 2 14 -12 10 17 -22 10 -52 -15 50]] 39.090 56/55 78/77 100/99 729/715
45 <<8 13 4 10 6 2 -16 -12 -20 -27 -22 -34 14 2 -16]] 39.343 49/48 78/77 100/99 126/121
46 <<7 9 13 23 10 -2 1 12 -10 5 22 -10 19 -20 -50]] 39.653 45/44 91/88 126/125 147/143