List of 26et rank two temperaments by badness
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Below are listed rank-two temperaments supported by the 26edo 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 three temperaments with badness less than 0.1.
Rank | Wedgie | Name | Badness | Commas |
1 | <<1 4 4]] | Meantone | 7.381 | 81/80 |
2 | <<35 62 17]] | Senior | 21.22 | |-17 62 -35> |
3 | <<12 22 7]] | Unidec | 82.423 | 31381059609/31250000000 |
7-limit temperaments with badness below 0.06
Listed is the wedgie and the TE badness times 1000 for ten temperaments with badness less than 0.06.
Rank | Wedgie | Name | Badness | Commas |
1 | <<2 8 8 8 7 -4]] | Injera | 31.130 | 50/49 81/80 |
2 | <<3 12 -1 12 -10 -36]] | Mothra/Cynder | 37.146 | 81/80 1029/1024 |
3 | <<23 40 1 10 -63 -110]] | Gamera | 37.648 | 4375/4374 589824/588245 |
4 | <<12 22 -4 7 -40 -71]] | Unidec | 38.393 | 1029/1024 4375/4374 |
5 | <<1 4 -9 4 -17 -32]] | Flattone | 38.553 | 81/80 525/512 |
6 | <<58 102 -2 27 -166 -291]] | Orga | 40.236 | 4375/4374 54975581388800/54936068900769 |
7 | <<11 18 5 3 -23 -39]] | Quartonic | 42.632 | 1728/1715 4000/3969 |
8 | <<8 6 6 -9 -13 -3]] | Doublewide | 43.462 | 50/49 875/864 |
9 | <<35 62 -3 17 -103 -181]] | Seniority | 44.877 | 4375/4374 201768035/201326592 |
10 | <<9 10 -3 -5 -30 -35]] | Superkleismic | 47.932 | 875/864 1029/1024 |
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 | <<12 22 -4 -6 7 -40 -51 -71 -90 -3]] | Unidec | 15.479 | 385/384 441/440 4375/4374 |
2 | <<58 102 -2 -16 27 -166 -226 -291 -390 -38]] | Orga | 16.188 | 3025/3024 4375/4374 5767168/5764801 |
3 | <<2 8 8 12 8 7 12 -4 0 6]] | Injera | 23.124 | 45/44 50/49 99/98 |
4 | <<3 12 -1 -8 12 -10 -23 -36 -60 -19]] | Mothra | 25.642 | 81/80 99/98 385/384 |
5 | <<9 10 -3 2 -5 -30 -28 -35 -30 16]] | Superkleismic | 25.659 | 100/99 245/242 385/384 |
6 | <<8 6 6 -4 -9 -13 -34 -3 -30 -32]] | Doublewide | 32.058 | 50/49 99/98 875/864 |
7 | <<1 4 -9 6 4 -17 6 -32 0 48]] | Flattone | 33.839 | 45/44 81/80 385/384 |
8 | <<10 14 14 8 -1 -6 -22 -7 -30 -26]] | Crepuscular | 40.758 | 50/49 99/98 1944/1925 |
9 | <<46 80 2 -10 20 -126 -175 -220 -300 -35]] | Hemigamera | 40.955 | 3025/3024 4375/4374 202397184/201768035 |
10 | <<6 -2 -2 10 -17 -20 -5 1 30 35]] | Lemba | 41.563 | 45/44 50/49 385/384 |
11 | <<11 18 5 14 3 -23 -16 -39 -30 22]] | Quarto | 41.786 | 100/99 245/242 864/847 |
12 | <<5 -6 7 4 -21 -3 -11 33 30 -13]] | Secund | 42.562 | 45/44 99/98 385/384 |
13 | <<70 124 -6 -22 34 -206 -277 -362 -480 -41]] | 45.479 | 3025/3024 4375/4374 23737807549715/23706377367552 | |
14 | <<1 4 17 6 4 24 6 28 0 -42]] | 46.139 | 45/44 81/80 1375/1344 | |
15 | <<1 4 -9 -20 4 -17 -35 -32 -60 -25]] | 46.294 | 81/80 99/98 525/512 | |
16 | <<14 30 4 6 15 -33 -39 -75 -90 3]] | 46.373 | 441/440 1344/1331 1728/1715 | |
17 | <<5 20 7 4 20 -3 -11 -40 -60 -13]] | 47.915 | 81/80 99/98 864/847 | |
18 | <<7 2 15 16 -13 4 1 29 30 -7]] | 49.066 | 45/44 99/98 875/864 |
13-limit temperaments with badness below 0.04
Listed is the wedgie and the TE badness times 1000 for 40 temperaments with badness less than 0.04.
Rank | Wedgie | Name | Badness | Commas |
1 | <<12 22 -4 -6 4 7 -40 -51 -38 -71 -90 -72 -3 26 36]] | Hendec | 17.707 | 169/168 325/324 364/363 1716/1715 |
2 | <<46 80 2 -10 50 20 -126 -175 -91 -220 -300 -180 -35 133 210]] | Hemigamera | 20.416 | 1716/1715 2080/2079 2200/2197 3025/3024 |
3 | <<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 |
4 | <<2 8 8 12 18 8 7 12 21 -4 0 12 6 21 18]] | Injera | 21.565 | 45/44 50/49 78/77 99/98 |
5 | <<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 |
6 | <<3 12 -1 -8 14 12 -10 -23 11 -36 -60 -12 -19 43 78]] | Mothra | 23.954 | 81/80 99/98 105/104 144/143 |
7 | <<10 14 14 8 12 -1 -6 -22 -18 -7 -30 -24 -26 -18 12]] | Crepuscular | 24.368 | 50/49 78/77 99/98 144/143 |
8 | <<14 30 4 6 22 15 -33 -39 -17 -75 -90 -60 3 47 54]] | Secant | 25.035 | 144/143 351/350 364/363 441/440 |
9 | <<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 |
10 | <<5 -6 7 4 6 -21 -3 -11 -9 33 30 36 -13 -9 6]] | 26.212 | 45/44 65/64 78/77 99/98 | |
11 | <<1 4 -9 -20 -4 4 -17 -35 -10 -32 -60 -24 -25 22 60]] | 26.566 | 65/64 81/80 99/98 105/104 | |
12 | <<11 18 5 14 8 3 -23 -16 -28 -39 -30 -48 22 4 -24]] | 27.692 | 78/77 100/99 144/143 245/242 | |
13 | <<21 32 -7 -4 20 2 -70 -79 -46 -106 -120 -72 13 82 84]] | 28.393 | 325/324 364/363 441/440 2200/2197 | |
14 | <<11 18 5 -12 8 3 -23 -57 -28 -39 -90 -48 -51 4 72]] | 28.818 | 99/98 169/168 275/273 385/384 | |
15 | <<5 20 7 4 6 20 -3 -11 -9 -40 -60 -60 -13 -9 6]] | 29.285 | 78/77 81/80 99/98 144/143 | |
16 | <<8 6 6 -4 -6 -9 -13 -34 -39 -3 -30 -36 -32 -39 -6]] | 29.481 | 50/49 78/77 99/98 875/864 | |
17 | <<7 2 -11 -10 -2 -13 -37 -40 -29 -31 -30 -12 10 35 30]] | 30.043 | 65/64 100/99 105/104 245/242 | |
18 | <<8 6 6 -4 20 -9 -13 -34 2 -3 -30 24 -32 34 84]] | 30.921 | 50/49 99/98 105/104 144/143 | |
19 | <<15 34 -5 -14 18 19 -50 -74 -27 -107 -150 -84 -22 69 114]] | 30.934 | 351/350 385/384 441/440 1188/1183 | |
20 | <<4 16 -10 -2 10 16 -27 -17 1 -68 -60 -36 29 65 42]] | 31.039 | 81/80 105/104 144/143 245/242 | |
21 | <<2 8 8 12 -8 8 7 12 -20 -4 0 -48 6 -52 -72]] | 31.589 | 45/44 50/49 65/64 99/98 | |
22 | <<3 12 -1 -8 -12 12 -10 -23 -30 -36 -60 -72 -19 -30 -12]] | 32.520 | 65/64 78/77 81/80 99/98 | |
23 | <<26 52 0 0 26 22 -73 -90 -55 -146 -180 -132 0 73 90]] | 32.946 | 351/350 364/363 441/440 15379/15360 | |
24 | <<3 12 -1 18 14 12 -10 18 11 -36 0 -12 54 43 -18]] | 34.124 | 45/44 78/77 81/80 640/637 | |
25 | <<20 28 2 -10 24 -2 -53 -85 -36 -74 -120 -48 -35 60 120]] | 34.179 | 275/273 325/324 385/384 1573/1568 | |
26 | <<6 -2 -2 -16 2 -17 -20 -46 -19 1 -30 12 -38 13 66]] | 34.689 | 50/49 65/64 99/98 105/104 | |
27 | <<8 6 6 22 20 -9 -13 7 2 -3 30 24 41 34 -12]] | 35.040 | 45/44 50/49 78/77 325/324 | |
28 | <<1 4 17 6 -4 4 24 6 -10 28 0 -24 -42 -74 -36]] | 35.184 | 45/44 65/64 81/80 1188/1183 | |
29 | <<17 16 3 -2 10 -14 -43 -62 -47 -38 -60 -36 -16 17 42]] | 35.724 | 100/99 169/168 275/273 385/384 | |
30 | <<9 10 -3 2 -10 -5 -30 -28 -49 -35 -30 -60 16 -17 -42]] | 36.254 | 65/64 78/77 100/99 245/242 | |
31 | <<32 50 -2 -16 28 5 -93 -136 -74 -145 -210 -120 -38 86 156]] | 36.996 | 325/324 385/384 1573/1568 2200/2197 | |
32 | <<2 8 -18 -14 -8 8 -34 -29 -20 -64 -60 -48 23 44 24]] | 37.031 | 65/64 81/80 105/104 245/242 | |
33 | <<13 26 13 0 26 11 -16 -45 -7 -43 -90 -36 -45 25 90]] | 37.851 | 99/98 144/143 275/273 1040/1029 | |
34 | <<19 24 11 10 28 -6 -36 -50 -26 -42 -60 -24 -10 38 60]] | 38.179 | 100/99 144/143 275/273 1040/1029 | |
35 | <<7 2 15 16 24 -13 4 1 12 29 30 48 -7 12 24]] | 38.402 | 45/44 78/77 99/98 325/324 | |
36 | <<7 2 15 16 -2 -13 4 1 -29 29 30 -12 -7 -61 -66]] | 39.063 | 45/44 65/64 99/98 275/273 | |
37 | <<25 48 9 -6 30 18 -56 -96 -45 -114 -180 -108 -48 51 126]] | 39.183 | 351/350 640/637 1188/1183 1573/1568 | |
38 | <<1 4 17 6 22 4 24 6 31 28 0 36 -42 -1 54]] | 39.550 | 45/44 78/77 81/80 1344/1331 | |
39 | <<2 8 8 -14 -8 8 7 -29 -20 -4 -60 -48 -67 -52 24]] | 39.744 | 50/49 65/64 78/77 81/80 | |
40 | <<22 36 10 2 16 6 -46 -73 -56 -78 -120 -96 -29 8 48]] | 39.891 | 169/168 325/324 364/363 640/637 |