List of 16et rank two temperaments by badness

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Below are listed rank-two temperaments supported by the 16edo patent val, below the indicated cutoff in TE badness.

5-limit temperaments with badness below 0.1

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

Rank Wedgie Name Badness Commas
1 <<14 6 -23]] Vishnu 31.181 6115295232/6103515625
2 <<5 1 -10]] Magic 39.163 3125/3072
3 <<1 -3 -7]] Mavila 39.556 135/128
4 <<4 4 -3]] Diminished 47.231 648/625

7-limit temperaments with badness below 0.06

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

1 <<4 4 4 -3 -5 -2]] Diminished 22.401 36/35 50/49
2 <<9 5 -3 -13 -30 -21]] Valentine 31.056 126/125 1029/1024
3 <<1 -3 5 -7 5 20]] Armodue 49.038 36/35 135/128
4 <<5 1 -7 -10 -25 -19]] Muggles 56.206 126/125 525/512

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 18 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 <<4 4 4 12 -3 -5 5 -2 14 20]] Demolished 26.574 36/35 45/44 50/49
3 <<1 -3 5 -1 -7 5 -5 20 8 -20]] Armodue 27.211 33/32 36/35 45/44
4 <<2 -6 -6 -2 -14 -15 -10 3 16 15]] Bipelog 35.694 33/32 45/44 50/49
5 <<24 8 -8 24 -43 -80 -45 -41 28 95]] 37.220 385/384 441/440 9375/9317
6 <<10 2 2 6 -20 -25 -25 -1 7 10]] 39.151 50/49 121/120 176/175
7 <<4 4 4 -4 -3 -5 -20 -2 -23 -25]] 39.912 33/32 36/35 50/49
8 <<33 13 -11 31 -56 -110 -65 -62 27 125]] 40.785 385/384 441/440 234375/234256
9 <<6 -2 -2 10 -17 -20 -5 1 30 35]] 41.563 45/44 50/49 385/384
10 <<1 -3 -11 -1 -7 -20 -5 -17 8 35]] 42.049 33/32 45/44 126/125
11 <<13 9 1 19 -16 -35 -15 -23 13 50]] 43.336 126/125 176/175 864/847
12 <<8 8 8 8 -6 -10 -15 -4 -9 -5]] 43.387 36/35 50/49 121/120
13 <<15 3 -5 17 -30 -50 -25 -20 29 65]] 45.623 385/384 441/440 625/616
14 <<3 7 -1 -3 4 -10 -15 -22 -31 -5]] 46.385 33/32 36/35 352/343
15 <<5 1 9 11 -10 0 0 18 22 0]] 46.775 36/35 45/44 363/343
16 <<5 1 -7 -5 -10 -25 -25 -19 -15 10]] 46.970 33/32 126/125 176/175
17 <<5 1 -7 11 -10 -25 0 -19 22 55]] 48.038 45/44 126/125 385/384
18 <<3 7 -1 13 4 -10 10 -22 6 40]] 49.500 36/35 45/44 1029/1024

13-limit temperaments with badness below 0.04

Listed is the wedgie and the TE badness times 1000 for 32 temperaments with badness less than 0.04.

Rank Wedgie Name Badness Commas
1 <<1 -3 5 -1 3 -7 5 -5 1 20 8 18 -20 -10 14]] Armodue 19.351 27/26 33/32 36/35 45/44
2 <<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
3 <<33 13 -11 31 19 -56 -110 -65 -92 -62 27 -4 125 94 -49]] 21.636 385/384 441/440 625/624 847/845
4 <<4 4 4 12 12 -3 -5 5 4 -2 14 13 20 19 -3]] 22.837 27/26 36/35 45/44 50/49
5 <<6 -2 -2 10 2 -17 -20 -5 -19 1 30 12 35 13 -30]] Lemba 25.477 45/44 50/49 65/64 78/77
6 <<8 8 8 8 8 -6 -10 -15 -17 -4 -9 -11 -5 -7 -2]] 27.514 36/35 50/49 66/65 143/140
7 <<5 1 -7 -5 -1 -10 -25 -25 -20 -19 -15 -6 10 23 15]] 28.732 33/32 65/64 105/104 126/125
8 <<13 9 1 19 7 -16 -35 -15 -37 -23 13 -17 50 16 -46]] 28.920 78/77 126/125 144/143 176/175
9 <<24 8 -8 24 8 -43 -80 -45 -76 -41 28 -11 95 52 -61]] 29.407 169/168 385/384 441/440 625/624
10 <<2 -6 -6 -2 -10 -14 -15 -10 -23 3 16 -1 15 -6 -27]] 29.418 33/32 45/44 50/49 78/77
11 <<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
12 <<19 7 -1 13 9 -33 -55 -45 -56 -22 6 -5 40 29 -17]] 32.564 121/120 169/168 176/175 275/273
13 <<11 -1 -9 5 1 -27 -45 -30 -39 -18 15 6 45 36 -15]] 32.611 65/64 105/104 121/120 275/273
14 <<3 7 -1 13 9 4 -10 10 3 -22 6 -5 40 29 -17]] 32.664 27/26 36/35 45/44 507/500
15 <<18 10 -6 14 6 -26 -60 -40 -57 -42 -2 -23 60 39 -31]] 32.749 121/120 126/125 169/168 176/175
16 <<15 3 -5 17 13 -30 -50 -25 -35 -20 29 19 65 55 -18]] 33.081 105/104 144/143 275/273 625/616
17 <<7 11 3 9 5 1 -15 -10 -18 -24 -17 -29 15 3 -16]] 33.102 36/35 66/65 143/140 352/343
18 <<4 4 4 -4 -4 -3 -5 -20 -21 -2 -23 -24 -25 -26 1]] 33.195 33/32 36/35 50/49 65/64
19 <<22 14 -2 26 18 -29 -65 -35 -53 -44 12 -10 80 58 -34]] 33.792 126/125 144/143 176/175 847/845
20 <<4 4 4 12 -4 -3 -5 5 -21 -2 14 -24 20 -26 -58]] 33.951 36/35 45/44 50/49 65/64
21 <<1 -3 -11 -1 3 -7 -20 -5 1 -17 8 18 35 49 14]] 34.043 27/26 33/32 45/44 126/125
22 <<9 5 -3 7 -5 -13 -30 -20 -41 -21 -1 -30 30 -3 -43]] 34.114 65/64 78/77 121/120 126/125
23 <<10 2 2 6 -2 -20 -25 -25 -40 -1 7 -12 10 -13 -29]] 34.376 50/49 65/64 78/77 121/120
24 <<10 2 2 6 14 -20 -25 -25 -15 -1 7 25 10 32 26]] 35.284 50/49 66/65 105/104 121/120
25 <<6 -2 -2 -6 2 -17 -20 -30 -19 1 -7 12 -10 13 29]] 35.324 33/32 50/49 65/64 105/104
26 <<14 6 6 18 10 -23 -30 -20 -36 -3 21 1 30 6 -32]] 35.525 50/49 78/77 144/143 176/175
27 <<3 7 -1 -3 9 4 -10 -15 3 -22 -31 -5 -5 29 42]] 35.582 27/26 33/32 36/35 275/273
28 <<2 -6 -6 -2 6 -14 -15 -10 2 3 16 36 15 39 28]] 35.956 27/26 33/32 45/44 50/49
29 <<4 4 4 -4 12 -3 -5 -20 4 -2 -23 13 -25 19 56]] 36.915 27/26 33/32 36/35 50/49
30 <<1 -3 -11 -1 -13 -7 -20 -5 -24 -17 8 -19 35 4 -41]] 37.545 33/32 45/44 78/77 126/125
31 <<5 1 9 11 15 -10 0 0 5 18 22 31 0 9 11]] 38.328 27/26 36/35 45/44 363/343
32 <<5 1 9 11 -1 -10 0 0 -20 18 22 -6 0 -36 -44]] 38.808 36/35 45/44 65/64 275/273