List of 12et rank two temperaments by badness
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Below are listed rank-2 temperaments supported by the 12et patent val, below the indicated cutoff in TE logflat 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 | Comma List |
---|---|---|---|---|
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 | Comma List |
---|---|---|---|---|
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 | 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 | Comma List |
---|---|---|---|---|
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]] | Andromeda | 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]] | Catnip | 34.478 | 56/55 81/80 128/125 |
18 | ⟨⟨4 -20 -44 -72 -41 -81 -128 -46 -98 -50]] | Undim | 34.837 | 1375/1372 5120/5103 5632/5625 |
19 | ⟨⟨1 -8 -14 -30 -15 -25 -51 -10 -42 -36]] | Helenus | 35.637 | 99/98 176/175 3125/3087 |
20 | ⟨⟨3 -12 -30 -42 -26 -56 -77 -36 -56 -14]] | Misty | 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]] | Bimeantone | 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]] | Bidia | 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]] | Passion | 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 |