List of 15et rank two temperaments by badness

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Below are listed rank-two temperaments supported by the 15edo patent val, below the indicated cutoff in TE badness.

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE badness times 1000 for 15 temperaments with badness less than 0.06.

Rank Wedgie Name Badness Commas
1 <<3 0 -6 -7 -18 -14]] Augene 24.816 64/63 126/125
2 <<0 5 0 8 0 -14]] Blacksmith 25.640 28/27 49/48
3 <<6 5 3 -6 -12 -7]] Keemun 27.408 49/48 126/125
4 <<9 5 -3 -13 -30 -21]] Valentine 31.056 126/125 1029/1024
5 <<3 5 9 1 6 7]] Opossum 40.650 28/27 126/125
6 <<3 5 -6 1 -18 -28]] Porcupine 41.057 64/63 250/243
7 <<21 15 -12 -25 -78 -70]] Nessafof 45.048 6144/6125 250047/250000
8 <<39 30 -18 -43 -138 -126]] Pnict 45.660 250047/250000 2100875/2097152
9 <<9 10 -3 -5 -30 -35]] Superkleismic 47.932 875/864 1029/1024
10 <<12 10 -9 -12 -48 -49]] Hemikleismic 52.054 4000/3969 6144/6125
11 <<3 0 9 -7 6 21]] Inflated 54.729 28/27 128/125
12 <<6 0 3 -14 -12 7]] Triforce 54.988 49/48 128/125
13 <<18 15 -6 -18 -60 -56]] Tritikleismic 56.337 1029/1024 15625/15552
14 <<6 10 3 2 -12 -21]] Nautilus 57.420 49/48 250/243
15 <<60 45 -30 -68 -216 -196]] 58.002 250047/250000 12884901888/12867859375

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 33 temperaments with badness less than 0.05.

Rank Wedgie Name Badness Commas
1 <<9 5 -3 7 -13 -30 -20 -21 -1 30]] Valentine 16.687 121/120 126/125 176/175
2 <<18 15 -6 9 -18 -60 -48 -56 -31 46]] Tritikleismic 19.333 385/384 441/440 4000/3993
3 <<3 0 -6 -6 -7 -18 -20 -14 -14 4]] Augene 19.613 56/55 64/63 100/99
4 <<3 5 -6 4 1 -18 -4 -28 -8 32]] Porcupine 21.562 55/54 64/63 100/99
5 <<3 5 9 4 1 6 -4 7 -8 -20]] Opossum 22.325 28/27 55/54 77/75
6 <<0 5 0 -5 8 0 -8 -14 -29 -14]] Blacksmith 24.641 28/27 49/48 55/54
7 <<9 10 -3 2 -5 -30 -28 -35 -30 16]] Superkleismic 25.659 100/99 245/242 385/384
8 <<6 10 3 8 2 -12 -8 -21 -16 12]] Nautilus 26.023 49/48 55/54 100/99
9 <<6 0 3 3 -14 -12 -16 7 7 -2]] Triforce 26.152 49/48 56/55 77/75
10 <<6 5 3 -2 -6 -12 -24 -7 -22 -16]] Keemun 27.41 49/48 56/55 100/99
11 <<6 5 3 13 -6 -12 0 -7 13 26]] Darjeeling 27.648 49/48 55/54 77/75
12 <<0 5 0 10 8 0 16 -14 6 28]] Ferrier 29.2 28/27 49/48 77/75
13 <<3 -5 -6 -1 -15 -18 -12 0 15 18]] Progress 31.036 56/55 64/63 77/75
14 <<3 0 9 9 -7 6 4 21 21 -6]] Inflated 31.171 28/27 55/54 128/125
15 <<12 5 -9 1 -20 -48 -40 -35 -15 34]] Thuja 33.078 126/125 176/175 1344/1331
16 <<27 20 -9 16 -31 -90 -68 -77 -32 76]] Tritriple 35.350 385/384 441/440 43923/43750
17 <<3 0 -6 9 -7 -18 4 -14 21 46]] 35.554 55/54 64/63 77/75
18 <<6 5 -12 -2 -6 -36 -24 -42 -22 36]] 36.894 64/63 100/99 1331/1323
19 <<12 10 -9 11 -12 -48 -24 -49 -9 62]] 38.230 121/120 176/175 4000/3969
20 <<12 10 6 11 -12 -24 -24 -14 -9 10]] 42.696 49/48 121/120 126/125
21 <<3 10 9 14 9 6 12 -7 -2 8]] 43.195 28/27 77/75 245/242
22 <<15 10 -15 5 -19 -66 -44 -63 -23 66]] 43.508 176/175 1331/1323 4000/3969
23 <<33 25 -21 14 -37 -126 -92 -119 -54 112]] 43.743 3025/3024 4000/3993 6144/6125
24 <<15 15 0 15 -11 -42 -28 -42 -17 42]] 44.405 121/120 441/440 875/864
25 <<6 0 -12 3 -14 -36 -16 -28 7 50]] 44.448 64/63 121/120 126/125
26 <<15 10 0 5 -19 -42 -44 -28 -23 14]] 45.070 126/125 245/242 385/384
27 <<0 10 0 5 16 0 8 -28 -23 14]] 45.972 28/27 49/48 121/120
28 <<30 20 -15 10 -38 -108 -88 -91 -46 80]] 47.990 441/440 4000/3993 6144/6125
29 <<9 0 -3 -3 -21 -30 -36 -7 -7 2]] 48.345 56/55 128/125 2541/2500
30 <<3 0 9 -6 -7 6 -20 21 -14 -48]] 48.744 28/27 77/75 128/125
31 <<21 15 -12 3 -25 -78 -68 -70 -45 50]] 48.836 441/440 1344/1331 4375/4356
32 <<0 5 15 10 8 24 16 21 6 -24]] 49.486 56/55 100/99 256/243
33 <<3 10 -6 -1 9 -18 -12 -42 -37 18]] 49.863 55/54 64/63 245/242

13-limit temperaments with badness below 0.04

Listed is the wedgie and the TE badness times 1000 for 59 temperaments with badness less than 0.04.

Rank Wedgie Name Badness Commas
1 <<18 15 -6 9 42 -18 -60 -48 0 -56 -31 42 46 140 112]] Tritikleismic 15.652 325/324 364/363 441/440 625/624
2 <<3 5 9 4 2 1 6 -4 -8 7 -8 -14 -20 -28 -8]] Opossum 19.389 28/27 40/39 55/54 66/65
3 <<6 0 3 3 9 -14 -12 -16 -8 7 7 21 -2 14 20]] Triforce 20.248 49/48 56/55 66/65 77/75
4 <<0 5 0 -5 5 8 0 -8 8 -14 -29 -7 -14 14 36]] Blacksmith 20.498 28/27 40/39 49/48 55/54
5 <<3 0 -6 -6 -3 -7 -18 -20 -16 -14 -14 -7 4 14 12]] Augene 20.785 40/39 56/55 64/63 66/65
6 <<3 5 -6 4 2 1 -18 -4 -8 -28 -8 -14 32 28 -8]] Porcupine 21.276 40/39 55/54 64/63 66/65
7 <<9 5 -3 7 11 -13 -30 -20 -16 -21 -1 7 30 42 12]] Lupercalia 21.328 66/65 105/104 121/120 126/125
8 <<6 5 3 13 14 -6 -12 0 0 -7 13 14 26 28 0]] 21.445 49/48 55/54 66/65 77/75
9 <<9 10 -3 2 16 -5 -30 -28 -8 -35 -30 0 16 56 48]] Superkleismic 21.478 100/99 105/104 245/242 1188/1183
10 <<6 10 3 8 19 2 -12 -8 8 -21 -16 7 12 42 36]] Nautilus 22.285 49/48 55/54 91/90 100/99
11 <<0 5 0 10 5 8 0 16 8 -14 6 -7 28 14 -20]] 22.325 28/27 40/39 49/48 66/65
12 <<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
13 <<12 5 -9 1 23 -20 -48 -40 -8 -35 -15 35 34 98 76]] Thuja 22.838 126/125 144/143 176/175 364/363
14 <<3 0 -6 -6 12 -7 -18 -20 8 -14 -14 28 4 56 64]] 22.890 56/55 64/63 91/90 100/99
15 <<9 5 -3 7 26 -13 -30 -20 8 -21 -1 42 30 84 64]] Dwynwen 23.461 91/90 121/120 126/125 176/175
16 <<3 5 -6 4 17 1 -18 -4 16 -28 -8 21 32 70 44]] Porcupinefish 25.314 55/54 64/63 91/90 100/99
17 <<12 10 -9 11 28 -12 -48 -24 0 -49 -9 28 62 112 56]] Hemikleismic 26.005 121/120 176/175 275/273 325/324
18 <<3 -5 -6 -1 7 -15 -18 -12 0 0 15 35 18 42 28]] Progress 26.214 56/55 64/63 66/65 77/75
19 <<6 5 -12 -2 14 -6 -36 -24 0 -42 -22 14 36 84 56]] 26.336 64/63 100/99 144/143 275/273
20 <<3 0 9 9 12 -7 6 4 8 21 21 28 -6 0 8]] 28.940 28/27 55/54 66/65 147/143
21 <<0 0 0 0 15 0 0 0 24 0 0 35 0 42 52]] 28.944 28/27 49/48 55/54 77/75
22 <<3 0 9 9 -3 -7 6 4 -16 21 21 -7 -6 -42 -44]] 29.443 28/27 40/39 55/54 245/242
23 <<3 5 9 4 17 1 6 -4 16 7 -8 21 -20 14 44]] 29.806 28/27 55/54 77/75 105/104
24 <<6 10 3 8 4 2 -12 -8 -16 -21 -16 -28 12 0 -16]] 29.816 40/39 49/48 55/54 66/65
25 <<30 20 -15 10 65 -38 -108 -88 -8 -91 -46 77 80 238 188]] 29.837 364/363 441/440 676/675 40824/40625
26 <<3 0 -6 9 12 -7 -18 4 8 -14 21 28 46 56 8]] 29.922 55/54 64/63 66/65 77/75
27 <<27 20 -9 16 53 -31 -90 -68 -16 -77 -32 49 76 182 124]] 30.930 385/384 441/440 625/624 1188/1183
28 <<6 5 3 -2 -1 -6 -12 -24 -24 -7 -22 -21 -16 -14 4]] 31.633 40/39 49/48 56/55 66/65
29 <<3 -5 -6 -1 -8 -15 -18 -12 -24 0 15 0 18 0 -24]] 32.217 40/39 56/55 64/63 77/75
30 <<0 5 0 -5 -10 8 0 -8 -16 -14 -29 -42 -14 -28 -16]] 32.301 28/27 49/48 55/54 66/65
31 <<15 15 0 15 30 -11 -42 -28 -8 -42 -17 14 42 84 48]] 32.378 105/104 121/120 275/273 325/324
32 <<6 0 -12 3 9 -14 -36 -16 -8 -28 7 21 50 70 20]] 32.379 64/63 66/65 121/120 676/675
33 <<3 10 9 14 7 9 6 12 0 -7 -2 -21 8 -14 -28]] 32.653 28/27 40/39 77/75 147/143
34 <<12 10 6 11 28 -12 -24 -24 0 -14 -9 28 10 56 56]] 32.900 49/48 91/90 121/120 126/125
35 <<15 10 0 5 25 -19 -42 -44 -16 -28 -23 21 14 70 68]] 33.410 105/104 126/125 144/143 245/242
36 <<3 0 -6 9 -3 -7 -18 4 -16 -14 21 -7 46 14 -44]] 33.779 40/39 55/54 64/63 77/75
37 <<18 10 -6 14 37 -26 -60 -40 -8 -42 -2 49 60 126 76]] 34.916 121/120 126/125 176/175 676/675
38 <<0 10 0 5 10 16 0 8 16 -28 -23 -14 14 28 16]] 35.251 28/27 40/39 49/48 121/117
39 <<30 25 -15 20 70 -30 -108 -72 0 -105 -40 70 108 252 168]] 35.285 325/324 385/384 625/624 1331/1323
40 <<9 10 -3 2 31 -5 -30 -28 16 -35 -30 35 16 98 100]] 36.091 91/90 100/99 245/242 625/624
41 <<0 5 15 10 5 8 24 16 8 21 6 -7 -24 -42 -20]] 36.155 40/39 56/55 66/65 256/243
42 <<3 10 -6 -1 7 9 -18 -12 0 -42 -37 -21 18 42 28]] 36.463 40/39 55/54 64/63 245/242
43 <<0 0 0 15 0 0 0 24 0 0 35 0 42 0 -56]] 36.794 28/27 40/39 49/48 126/125
44 <<6 5 3 13 -1 -6 -12 0 -24 -7 13 -21 26 -14 -52]] 36.933 40/39 55/54 77/75 147/143
45 <<3 5 -6 -11 2 1 -18 -28 -8 -28 -43 -14 -10 28 48]] 37.036 40/39 56/55 64/63 250/243
46 <<21 15 -12 3 39 -25 -78 -68 -16 -70 -45 35 50 154 124]] 37.409 144/143 364/363 441/440 625/624
47 <<3 10 9 -1 7 9 6 -12 0 -7 -37 -21 -34 -14 28]] 37.431 28/27 40/39 55/54 539/507
48 <<21 20 -12 13 44 -17 -78 -52 -8 -84 -39 28 78 168 104]] 37.468 275/273 325/324 385/384 1331/1323
49 <<3 0 9 -6 -3 -7 6 -20 -16 21 -14 -7 -48 -42 12]] 37.500 28/27 40/39 66/65 385/384
50 <<6 0 3 3 -6 -14 -12 -16 -32 7 7 -14 -2 -28 -32]] 37.775 40/39 49/48 56/55 121/117
51 <<12 10 -9 -4 28 -12 -48 -48 0 -49 -44 28 20 112 112]] 37.792 100/99 144/143 245/242 625/624
52 <<15 10 -15 5 40 -19 -66 -44 8 -63 -23 56 66 168 120]] 38.006 176/175 325/324 364/363 640/637
53 <<12 15 -9 6 33 -4 -48 -32 8 -63 -38 21 48 126 92]] 38.228 100/99 275/273 385/384 572/567
54 <<9 0 -3 -3 6 -21 -30 -36 -24 -7 -7 14 2 28 32]] 38.535 56/55 66/65 105/104 637/625
55 <<24 15 -18 12 51 -32 -96 -64 -8 -84 -24 63 96 210 132]] 38.616 176/175 640/637 676/675 1331/1323
56 <<24 20 -18 7 56 -24 -96 -72 0 -98 -53 56 82 224 168]] 38.844 325/324 364/363 625/624 640/637
57 <<0 0 15 0 0 0 24 0 0 35 0 0 -52 -56 0]] 38.991 40/39 55/54 66/65 256/243
58 <<33 25 -21 14 67 -37 -126 -92 -16 -119 -54 63 112 266 180]] 39. 625/624 640/637 1188/1183 1575/1573
59 <<9 10 12 17 16 -5 -6 -4 -8 0 5 0 6 0 -8]] 39.006 55/54 66/65 77/75 147/143