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
|