List of 12et rank two temperaments by badness

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Below are listed rank-two temperaments supported by the 12et 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 six temperaments with badness less than 0.1.

Rank Wedgie Name Badness Commas
1 <<12 -84 -161]] Atomic 3.802 |161 -84 -12>
2 <<1 -8 -15]] Helmholtz 4.259 32805/32768
3 <<1 4 4]] Meantone 7.381 81/80
4 <<2 -4 -11]] Srutal 19.915 2048/2025
5 <<3 0 -7]] Augmented 22.315 128/125
6 <<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 18 temperaments with badness less than 0.06.

Rank Wedgie Name Badness Commas
1 <<1 4 10 4 13 12]] Meantone 13.707 81/80 126/125
2 <<3 -24 -54 -45 -94 -58]] Term 19.950 32805/32768 250047/250000
3 <<2 -4 -4 -11 -12 2]] Pajara 20.033 50/49 64/63
4 <<1 4 -2 4 -6 -16]] Dominant 20.690 36/35 64/63
5 <<1 -8 -14 -15 -25 -10]] Garibaldi 21.644 225/224 3125/3087
6 <<4 4 4 -3 -5 -2]] Diminished 22.401 36/35 50/49
7 <<3 0 -6 -7 -18 -14]] Augene 24.816 64/63 126/125
8 <<3 0 6 -7 1 14]] August 26.459 36/35 128/125
9 <<2 8 8 8 7 -4]] Injera 31.130 50/49 81/80
10 <<0 12 24 19 38 22]] Compton/Waage 35.686 225/224 250047/250000
11 <<3 -12 -30 -26 -56 -36]] Misty 36.802 3136/3125 5120/5103
12 <<2 -4 -16 -11 -31 -26]] Diaschismic 37.914 126/125 2048/2025
13 <<0 0 12 0 19 28]] Catler 50.297 81/80 128/125
14 <<2 -16 -40 -30 -69 -48]] Bischismic 54.744 3136/3125 32805/32768
15 <<4 -8 -20 -22 -43 -24]] Bidia 56.474 2048/2025 3136/3125
16 <<1 -8 -2 -15 -6 18]] Schism 56.648 64/63 360/343
17 <<6 0 0 -14 -17 0]] Hexe 57.730 50/49 128/125
18 <<5 8 2 1 -11 -18]] Ripple 59.735 36/35 2560/2401

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 40 temperaments with badness less than 0.05.

Rank Wedgie Name Badness Commas
1 <<1 4 10 18 4 13 25 12 28 16]] Meantone 17.027 81/80 99/98 126/125
2 <<3 0 -6 -6 -7 -18 -20 -14 -14 4]] Augene 19.613 56/55 64/63 100/99
3 <<3 0 6 6 -7 1 -1 14 14 -4]] August 20.191 36/35 45/44 56/55
4 <<2 -4 -4 -12 -11 -12 -26 2 -14 -20]] Pajara 20.343 50/49 64/63 99/98
5 <<1 4 10 6 4 13 6 12 0 -18]] Meanenneadecal 21.423 45/44 56/55 81/80
6 <<1 4 -2 6 4 -6 6 -16 0 24]] Domineering 21.978 36/35 45/44 64/63
7 <<4 4 4 0 -3 -5 -14 -2 -14 -14]] Diminished 22.132 36/35 50/49 56/55
8 <<0 12 24 36 19 38 57 22 42 18]] Compton 22.235 225/224 441/440 4375/4356
9 <<2 8 8 12 8 7 12 -4 0 6]] Injera 23.124 45/44 50/49 99/98
10 <<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]] Cassandra 23.556 100/99 225/224 245/242
11 <<2 -4 -4 0 -11 -12 -7 2 14 14]] Pajaric 23.798 45/44 50/49 56/55
12 <<1 4 -2 -6 4 -6 -13 -16 -28 -10]] Dominant 24.18 36/35 56/55 64/63
13 <<2 -4 -16 -24 -11 -31 -45 -26 -42 -12]] Diaschismic 25.034 126/125 176/175 5488/5445
14 <<4 4 4 12 -3 -5 5 -2 14 20]] Demolished 26.574 36/35 45/44 50/49
15 <<2 -16 -40 -60 -30 -69 -102 -48 -84 -30]] Bischismic 28.160 441/440 3136/3125 8019/8000
16 <<0 0 0 12 0 0 19 0 28 34]] Duodecim 30.536 36/35 50/49 64/63
17 <<0 0 12 12 0 19 19 28 28 -8]] Catcall 34.478 56/55 81/80 128/125
18 <<4 -20 -44 -72 -41 -81 -128 -46 -98 -50]] 34.837 1375/1372 5120/5103 5632/5625
19 <<1 -8 -14 -30 -15 -25 -51 -10 -42 -36]] 35.637 99/98 176/175 3125/3087
20 <<3 -12 -30 -42 -26 -56 -77 -36 -56 -14]] 35.932 441/440 3136/3125 4375/4356
21 <<1 -8 -2 -6 -15 -6 -13 18 14 -10]] 37.482 45/44 64/63 99/98
22 <<2 8 20 24 8 26 31 24 28 -2]] 38.122 81/80 126/125 245/242
23 <<6 0 0 0 -14 -17 -21 0 0 0]] 38.412 50/49 56/55 125/121
24 <<5 8 2 6 1 -11 -8 -18 -14 10]] 38.811 36/35 80/77 126/121
25 <<3 0 6 -6 -7 1 -20 14 -14 -38]] 39.764 36/35 80/77 128/125
26 <<4 -8 -20 -36 -22 -43 -71 -24 -56 -32]] 40.191 176/175 896/891 1375/1372
27 <<5 8 14 18 1 8 11 10 14 2]] 40.347 45/44 99/98 126/125
28 <<5 -4 -10 -18 -18 -30 -46 -12 -28 -16]] 40.809 64/63 100/99 1375/1372
29 <<3 0 -6 -18 -7 -18 -39 -14 -42 -30]] 40.832 64/63 99/98 126/125
30 <<2 8 8 0 8 7 -7 -4 -28 -28]] 43.062 50/49 56/55 81/77
31 <<3 0 -6 6 -7 -18 -1 -14 14 38]] 44.048 45/44 64/63 126/125
32 <<4 -32 -68 -108 -60 -119 -185 -68 -140 -68]] 45.738 1375/1372 6250/6237 496125/495616
33 <<3 12 18 30 12 20 37 8 28 22]] 46.794 81/80 99/98 625/616
34 <<2 -4 8 0 -11 7 -7 30 14 -28]] 47.882 36/35 45/44 128/121
35 <<2 -4 -16 -12 -11 -31 -26 -26 -14 22]] 48.070 56/55 100/99 2048/2025
36 <<2 -16 -28 -48 -30 -50 -83 -20 -56 -38]] 48.712 225/224 2420/2401 3125/3087
37 <<2 8 8 24 8 7 31 -4 28 40]] 48.739 50/49 81/80 176/175
38 <<1 -8 -26 -42 -15 -44 -70 -38 -70 -28]] 48.887 126/125 176/175 539055/537824
39 <<1 16 34 54 23 51 82 34 70 34]] 49.725 225/224 441/440 78408/78125
40 <<7 4 10 6 -10 -4 -15 12 0 -18]] 49.914 36/35 56/55 125/121