List of 31et rank two temperaments by badness

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Below are listed rank-two temperaments supported by the 31edo 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.

1 <<1 4 4]] Meantone 7.381 81/80
2 <<15 -2 -38]] Luna 20.576 274877906944/274658203125
3 <<8 1 -17]] Würschmidt 40.603 393216/390625
4 <<7 -3 -21]] Orson 40.807 2109375/2097152

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE badness times 1000 for 19 temperaments with badness less than 0.06.

Rank Wedgie Name Badness Commas
1 <<22 -5 3 -59 -57 21]] Tertiaseptal 12.995 2401/2400 65625/65536
2 <<1 4 10 4 13 12]] Meantone 13.707 81/80 126/125
3 <<6 -7 -2 -25 -20 15]] Miracle 16.742 225/224 1029/1024
4 <<16 2 5 -34 -37 6]] Hemiwürschmidt 20.307 2401/2400 3136/3125
5 <<7 -3 8 -21 -7 27]] Orwell 20.735 225/224 1728/1715
6 <<10 9 7 -9 -17 -9]] Myna 27.044 126/125 1728/1715
7 <<9 5 -3 -13 -30 -21]] Valentine 31.056 126/125 1029/1024
8 <<38 -3 8 -93 -94 27]] Quasiorwell 35.832 2401/2400 29360128/29296875
9 <<3 12 -1 12 -10 -36]] Mothra/Cynder 37.146 81/80 1029/1024
10 <<15 -2 -5 -38 -50 -6]] Hemithirds 44.284 1029/1024 3136/3125
11 <<60 -8 11 -152 -151 48]] Subneutral 45.792 2401/2400 274877906944/274658203125
12 <<4 16 9 16 3 -24]] Squares 45.993 81/80 2401/2400
13 <<5 -11 -12 -29 -33 3]] Tritonic 47.578 225/224 50421/50000
14 <<11 13 17 -5 -4 3]] Nusecond 50.389 126/125 2430/2401
15 <<17 6 15 -30 -24 18]] Semisept 50.472 1728/1715 3136/3125
16 <<8 1 18 -17 6 39]] Würschmidt 50.776 225/224 8748/8575
17 <<23 -1 13 -55 -44 33]] Grendel 51.834 6144/6125 16875/16807
18 <<2 8 -11 8 -23 -48]] Mohajira 55.714 81/80 6144/6125
19 <<13 -10 6 -46 -27 42]] Slender 56.934 225/224 589824/588245

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 68 temperaments with badness less than 0.05.

Rank Wedgie Name Badness Commas
1 <<6 -7 -2 15 -25 -20 3 15 59 49]] Miracle 10.684 225/224 243/242 441/440
2 <<7 -3 8 2 -21 -7 -21 27 15 -22]] Orwell 15.231 99/98 121/120 176/175
3 <<44 -10 6 79 -118 -114 -27 42 218 201]] Hemitert 15.633 2401/2400 3025/3024 65625/65536
4 <<9 5 -3 7 -13 -30 -20 -21 -1 30]] Valentine 16.687 121/120 126/125 176/175
5 <<10 9 7 25 -9 -17 5 -9 27 46]] Myna 16.842 126/125 176/175 243/242
6 <<1 4 10 18 4 13 25 12 28 16]] Meantone 17.027 81/80 99/98 126/125
7 <<38 -3 8 64 -93 -94 -30 27 159 152]] Quasiorwell 17.540 2401/2400 3025/3024 5632/5625
8 <<15 -2 -5 22 -38 -50 -17 -6 58 79]] Hemithirds 19.003 385/384 441/440 3136/3125
9 <<23 -1 13 42 -55 -44 -13 33 101 73]] Grendel 19.845 540/539 1375/1372 5632/5625
10 <<16 2 5 40 -34 -37 8 6 86 95]] Hemiwürschmidt 21.069 243/242 441/440 3136/3125
11 <<1 4 10 -13 4 13 -24 12 -44 -71]] Meanpop 21.543 81/80 126/125 540/539
12 <<4 16 9 10 16 3 2 -24 -32 -3]] Squares 21.636 81/80 99/98 121/120
13 <<17 6 15 27 -30 -24 -16 18 42 24]] Semisept 22.476 176/175 540/539 1331/1323
14 <<5 -11 -12 -3 -29 -33 -22 3 31 33]] Tritonic 23.659 121/120 225/224 441/440
15 <<8 1 18 20 -17 6 4 39 43 -6]] Würschmidt 24.413 99/98 176/175 243/242
16 <<13 -10 6 17 -46 -27 -18 42 74 27]] Slender 25.342 225/224 385/384 1331/1323
17 <<2 8 20 5 8 26 1 24 -16 -55]] Migration 25.516 81/80 121/120 126/125
18 <<11 13 17 12 -5 -4 -19 3 -17 -25]] Nusecond 25.621 99/98 121/120 126/125
19 <<3 12 -1 -8 12 -10 -23 -36 -60 -19]] Mothra 25.642 81/80 99/98 385/384
20 <<2 8 -11 5 8 -23 1 -48 -16 52]] Mohajira 26.064 81/80 121/120 176/175
21 <<29 -8 11 57 -80 -64 -10 48 160 122]] Eris 27.621 540/539 1375/1372 65625/65536
22 <<16 2 5 9 -34 -37 -41 6 14 8]] Hemiwur 29.270 121/120 176/175 1375/1372
23 <<21 -9 -7 37 -63 -70 -14 9 117 128]] Triwell 29.807 385/384 441/440 456533/455625
24 <<22 -5 3 24 -59 -57 -38 21 73 57]] Tertia 30.171 385/384 1331/1323 1375/1372
25 <<82 -13 14 143 -211 -208 -57 69 377 353]] 30.609 2401/2400 3025/3024 369140625/369098752
26 <<3 12 -1 23 12 -10 26 -36 12 68]] 31.334 81/80 540/539 1029/1024
27 <<7 -3 8 33 -21 -7 28 27 87 65]] 31.438 225/224 441/440 1728/1715
28 <<67 -11 19 121 -173 -158 -40 75 319 274]] 32.121 3025/3024 180224/180075 703125/702464
29 <<6 -7 -2 -16 -25 -20 -46 15 -13 -38]] 32.946 99/98 176/175 1029/1024
30 <<10 9 7 -6 -9 -17 -44 -9 -45 -41]] 33.434 99/98 126/125 385/384
31 <<8 1 -13 20 -17 -43 4 -33 43 101]] 33.436 126/125 243/242 385/384
32 <<32 4 10 49 -68 -74 -33 12 100 103]] 34.814 2401/2400 3025/3024 3136/3125
33 <<22 -5 3 55 -59 -57 11 21 145 144]] 35.576 243/242 441/440 703125/702464
34 <<28 -12 1 39 -84 -77 -35 36 132 106]] 36.493 385/384 1375/1372 14641/14580
35 <<14 -6 16 35 -42 -14 7 54 102 43]] 38.377 225/224 243/242 2420/2401
36 <<25 7 2 47 -47 -67 -12 -15 85 125]] 39.162 441/440 3388/3375 6144/6125
37 <<4 -15 9 10 -33 3 2 63 75 -3]] 39.595 99/98 243/242 385/384
38 <<31 0 0 62 -72 -87 -9 0 144 174]] 39.9210 441/440 3136/3125 41503/41472
39 <<3 -19 -1 -8 -37 -10 -23 51 47 -19]] 40.217 99/98 121/120 1029/1024
40 <<19 14 4 32 -22 -47 -15 -30 26 76]] 40.539 126/125 176/175 14641/14580
41 <<54 -1 13 104 -127 -131 -22 33 245 247]] 41.496 2401/2400 5632/5625 46656/46585
42 <<8 1 -13 -11 -17 -43 -45 -33 -29 14]] 41.680 126/125 176/175 14641/14406
43 <<9 5 -3 38 -13 -30 29 -21 71 117]] 42.204 126/125 540/539 1029/1024
44 <<12 -14 -4 -1 -50 -40 -43 30 46 11]] 42.687 121/120 225/224 1029/1024
45 <<12 17 27 30 -1 9 6 15 11 -9]] 42.719 99/98 126/125 243/242
46 <<5 20 19 28 20 16 27 -12 -4 13]] 42.869 81/80 99/98 2541/2500
47 <<0 0 0 31 0 0 49 0 72 87]] 42.959 81/80 126/125 1029/1024
48 <<11 -18 -14 12 -54 -53 -19 18 90 82]] 44.005 225/224 441/440 9317/9216
49 <<11 13 17 43 -5 -4 30 3 55 62]] 44.041 126/125 176/175 2430/2401
50 <<13 21 6 17 3 -27 -18 -45 -33 27]] 44.186 121/120 441/440 891/875
51 <<26 11 12 34 -43 -54 -36 -3 41 54]] 44.660 176/175 1331/1323 2401/2400
52 <<61 -4 21 106 -148 -138 -43 60 260 225]] 44.729 3025/3024 5632/5625 825000/823543
53 <<60 -8 11 119 -152 -151 -19 48 304 296]] 44.888 2401/2400 46656/46585 172032/171875
54 <<19 -17 4 32 -71 -47 -15 57 133 76]] 45.168 225/224 385/384 585640/583443
55 <<5 -11 -12 28 -29 -33 27 3 103 120]] 45.456 225/224 385/384 27783/27500
56 <<5 20 19 -3 20 16 -22 -12 -76 -74]] 45.466 81/80 540/539 1375/1372
57 <<1 4 -21 -13 4 -36 -24 -60 -44 36]] 45.509 81/80 176/175 1331/1323
58 <<18 10 25 45 -26 -11 9 30 70 40]] 45.7950 176/175 243/242 1375/1372
59 <<39 1 18 82 -89 -81 -5 39 187 168]] 45.928 540/539 5632/5625 151263/151250
60 <<2 -23 -11 5 -41 -23 1 39 91 52]] 46.181 243/242 441/440 1815/1792
61 <<4 -15 -22 10 -33 -46 2 -9 75 104]] 46.462 225/224 243/242 1617/1600
62 <<9 5 28 7 -13 19 -20 51 -1 -77]] 47.885 121/120 225/224 891/875
63 <<33 8 20 67 -64 -61 -8 24 128 119]] 48.088 540/539 3136/3125 15488/15435
64 <<14 -6 -15 4 -42 -63 -42 -18 30 63]] 48.150 121/120 441/440 3136/3125
65 <<8 1 18 -11 -17 6 -45 39 -29 -93]] 48.186 225/224 385/384 891/875
66 <<50 -17 4 94 -143 -134 -24 57 277 250]] 48.798 2401/2400 3025/3024 1265625/1261568
67 <<7 -3 -23 2 -21 -56 -21 -45 15 85]] 49.572 121/120 126/125 2079/2048
68 <<20 18 14 19 -18 -34 -39 -18 -18 5]] 49.917 121/120 126/125 1728/1715

13-limit temperaments with badness below 0.04

Listed is the wedgie and the TE badness times 1000 for 64 temperaments with badness less than 0.04.

Rank Wedgie Name Badness Commas
1 <<6 -7 -2 15 -34 -25 -20 3 -76 15 59 -53 49 -88 -173]] Benediction 15.715 225/224 243/242 351/350 441/440
2 <<10 9 7 25 -5 -9 -17 5 -45 -9 27 -45 46 -40 -110]] Myna 17.125 126/125 144/143 176/175 196/195
3 <<1 4 10 18 15 4 13 25 20 12 28 20 16 5 -15]] Meantone 18.048 66/65 81/80 99/98 105/104
4 <<6 -7 -2 15 -3 -25 -20 3 -27 15 59 19 49 -1 -66]] Miraculous 18.669 105/104 144/143 196/195 275/273
5 <<7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73]] Orwell 19.718 99/98 121/120 176/175 275/273
6 <<7 -3 8 2 12 -21 -7 -21 -7 27 15 39 -22 4 34]] Winston 19.931 66/65 99/98 105/104 121/120
7 <<9 5 -3 7 -20 -13 -30 -20 -65 -21 -1 -65 30 -45 -95]] Valentino 20.665 121/120 126/125 176/175 196/195
8 <<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
9 <<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
10 <<15 -2 -5 22 -23 -38 -50 -17 -92 -6 58 -46 79 -46 -161]] Hemithirds 21.738 196/195 352/351 1001/1000 1029/1024
11 <<5 -11 -12 -3 -18 -29 -33 -22 -47 3 31 -1 33 -6 -51]] Tritonic 22.993 105/104 121/120 196/195 275/273
12 <<16 2 5 40 -39 -34 -37 8 -121 6 86 -98 95 -128 -283]] Hemiwürschmidt 23.074 243/242 351/350 441/440 3584/3575
13 <<11 13 17 12 10 -5 -4 -19 -25 3 -17 -25 -25 -35 -10]] Nusecond 23.323 66/65 99/98 121/120 126/125
14 <<2 8 -11 5 -1 8 -23 1 -9 -48 -16 -32 52 38 -22]] Mohajira 23.388 66/65 105/104 121/120 512/507
15 <<8 1 18 20 -4 -17 6 4 -36 39 43 -13 -6 -78 -88]] Würschmidt 23.593 99/98 144/143 176/175 275/273
16 <<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
17 <<4 16 9 10 29 16 3 2 31 -24 -32 8 -3 48 63]] Agora 24.522 81/80 99/98 105/104 121/120
18 <<23 -1 13 42 -27 -55 -44 -13 -128 33 101 -59 73 -124 -249]] Grendel 24.839 352/351 540/539 625/624 1375/1372
19 <<17 6 15 27 -24 -30 -24 -16 -101 18 42 -78 24 -123 -183]] 25.204 176/175 351/350 540/539 1375/1372
20 <<0 0 0 0 31 0 0 0 49 0 0 72 0 87 107]] Gallium 25.484 81/80 99/98 121/120 126/125
21 <<4 16 9 10 -2 16 3 2 -18 -24 -32 -64 -3 -39 -44]] Squares 25.514 66/65 81/80 99/98 121/120
22 <<1 4 10 18 -16 4 13 25 -29 12 28 -52 16 -82 -122]] Grosstone 25.899 81/80 99/98 126/125 144/143
23 <<13 -10 6 17 -22 -46 -27 -18 -83 42 74 -14 27 -84 -139]] Slender 25.913 225/224 275/273 385/384 1331/1323
24 <<21 -9 -7 37 -57 -63 -70 -14 -168 9 117 -99 128 -134 -334]] 27.405 385/384 441/440 625/624 13720/13689
25 <<2 8 20 5 30 8 26 1 40 24 -16 40 -55 10 85]] 27.835 81/80 105/104 121/120 196/195
26 <<2 8 20 5 -1 8 26 1 -9 24 -16 -32 -55 -77 -22]] Migration 28.071 66/65 121/120 126/125 1215/1183
27 <<22 -5 3 24 -42 -59 -57 -38 -148 21 73 -79 57 -129 -234]] 28.384 352/351 385/384 625/624 1331/1323
28 <<17 6 15 27 7 -30 -24 -16 -52 18 42 -6 24 -36 -76]] 28.408 144/143 176/175 196/195 275/273
29 <<16 2 5 9 -8 -34 -37 -41 -72 6 14 -26 8 -41 -61]] 28.432 121/120 176/175 196/195 275/273
30 <<3 12 -1 23 14 12 -10 26 11 -36 12 -12 68 43 -37]] 29.207 66/65 81/80 105/104 1001/1000
31 <<6 -7 -2 -16 -3 -25 -20 -46 -27 15 -13 19 -38 -1 49]] 29.452 66/65 99/98 105/104 1001/1000
32 <<10 9 7 25 26 -9 -17 5 4 -9 27 27 46 47 -3]] 29.868 66/65 105/104 126/125 540/539
33 <<7 -3 8 33 -19 -21 -7 28 -56 27 87 -33 65 -83 -188]] 30.237 144/143 225/224 351/350 441/440
34 <<16 2 5 40 -8 -34 -37 8 -72 6 86 -26 95 -41 -176]] Hemithir 31.199 144/143 196/195 243/242 625/624
35 <<32 4 10 49 -47 -68 -74 -33 -193 12 100 -124 103 -169 -344]] 31.732 352/351 1001/1000 1716/1715 3025/3024
36 <<10 9 7 -6 -5 -9 -17 -44 -45 -9 -45 -45 -41 -40 5]] 31.850 66/65 99/98 126/125 385/384
37 <<15 -2 -5 22 -54 -38 -50 -17 -141 -6 58 -118 79 -133 -268]] 31.990 351/350 385/384 441/440 3146/3125
38 <<23 -1 13 42 -58 -55 -44 -13 -177 33 101 -131 73 -211 -356]] 32.359 351/350 540/539 1375/1372 5632/5625
39 <<1 4 10 -13 -16 4 13 -24 -29 12 -44 -52 -71 -82 -7]] 33.007 66/65 81/80 126/125 385/384
40 <<12 -14 -4 30 -37 -50 -40 6 -103 30 118 -34 98 -89 -239]] 33.451 225/224 243/242 441/440 1875/1859
41 <<8 1 18 20 27 -17 6 4 13 39 43 59 -6 9 19]] 34.382 66/65 99/98 105/104 243/242
42 <<8 1 -13 20 -4 -17 -43 4 -36 -33 43 -13 101 37 -88]] 34.458 105/104 126/125 144/143 243/242
43 <<3 -19 -1 -8 -17 -37 -10 -23 -38 51 47 31 -19 -44 -29]] 35.530 99/98 105/104 121/120 640/637
44 <<8 1 -13 20 -35 -17 -43 4 -85 -33 43 -85 101 -50 -195]] 35.585 126/125 196/195 385/384 1575/1573
45 <<3 12 -1 -8 -17 12 -10 -23 -38 -36 -60 -84 -19 -44 -29]] 36.239 66/65 81/80 99/98 385/384
46 <<8 1 -13 -11 -4 -17 -43 -45 -36 -33 -29 -13 14 37 27]] 36.331 66/65 105/104 126/125 512/507
47 <<5 -11 -12 -3 -49 -29 -33 -22 -96 3 31 -73 33 -93 -158]] 36.533 121/120 225/224 351/350 441/440
48 <<10 9 7 -6 26 -9 -17 -44 4 -9 -45 27 -41 47 112]] 36.656 99/98 105/104 126/125 144/143
49 <<3 12 -1 23 -17 12 -10 26 -38 -36 12 -84 68 -44 -144]] 36.857 81/80 144/143 176/175 1029/1024
50 <<22 -5 3 55 -42 -59 -57 11 -148 21 145 -79 144 -129 -349]] 36.876 243/242 441/440 625/624 3584/3575
51 <<5 20 19 28 13 20 16 27 2 -12 -4 -44 13 -34 -59]] 37.382 66/65 81/80 99/98 1001/1000
52 <<4 -15 9 10 -2 -33 3 2 -18 63 75 51 -3 -39 -44]] 37.408 99/98 105/104 144/143 243/242
53 <<13 -10 6 17 -53 -46 -27 -18 -132 42 74 -86 27 -171 -246]] 37.732 225/224 351/350 385/384 1331/1323
54 <<12 17 27 30 25 -1 9 6 -5 15 11 -5 -9 -30 -25]] 37.849 66/65 99/98 126/125 243/242
55 <<0 0 0 31 0 0 0 49 0 0 72 0 87 0 -115]] 37.885 81/80 105/104 196/195 512/507
56 <<13 21 6 17 9 3 -27 -18 -34 -45 -33 -57 27 3 -32]] 38.116 66/65 121/120 343/338 441/440
57 <<10 9 7 25 -36 -9 -17 5 -94 -9 27 -117 46 -127 -217]] 38.811 126/125 176/175 243/242 1573/1568
58 <<7 -3 8 33 12 -21 -7 28 -7 27 87 39 65 4 -81]] 38.812 105/104 196/195 275/273 648/637
59 <<9 5 -3 38 -20 -13 -30 29 -65 -21 71 -65 117 -45 -210]] 39.221 126/125 144/143 196/195 1029/1024
60 <<25 7 2 47 -28 -47 -67 -12 -137 -15 85 -91 125 -86 -271]] 39.271 196/195 352/351 1001/1000 6144/6125
61 <<14 -6 16 35 -38 -42 -14 7 -112 54 102 -66 43 -166 -261]] 39.531 225/224 243/242 351/350 2420/2401
62 <<11 13 17 12 41 -5 -4 -19 24 3 -17 47 -25 52 97]] 39.576 99/98 105/104 121/120 126/125
63 <<11 13 17 43 10 -5 -4 30 -25 3 55 -25 62 -35 -125]] 39.707 126/125 176/175 196/195 648/637
64 <<16 2 5 9 -39 -34 -37 -41 -121 6 14 -98 8 -128 -168]] 39.907 121/120 176/175 351/350 1375/1372