Below are listed rank-two temperaments supported by the 37edo 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 two temperaments with badness less than 0.1.
| 1
|
<<3 5 1]]
|
Porcupine
|
30.778
|
250/243
|
| 2
|
<<8 1 -17]]
|
Würschmidt
|
40.603
|
393216/390625
|
7-limit temperaments with badness below 0.06
Listed is the wedgie and the TE badness times 1000 for four temperaments with badness less than 0.06.
| Rank
|
Wedgie
|
Name
|
Badness
|
Commas
|
| 1
|
<<16 2 5 -34 -37 6]]
|
Hemiwürschmidt
|
20.307
|
2401/2400 3136/3125
|
| 2
|
<<3 5 -6 1 -18 -28]]
|
Porcupine
|
41.057
|
64/63 250/243
|
| 3
|
<<2 -9 -4 -19 -12 16]]
|
Beatles
|
45.872
|
64/63 686/675
|
| 4
|
<<78 19 29 -151 -173 14]]
|
|
56.890
|
2401/2400 133590662774784/133514404296875
|
11-limit temperaments with badness below 0.05
Listed is the wedgie and the TE badness times 1000 for nine temperaments with badness less than 0.05.
| Rank
|
Wedgie
|
Name
|
Badness
|
Commas
|
| 1
|
<<3 5 -6 4 1 -18 -4 -28 -8 32]]
|
Porcupine
|
21.562
|
55/54 64/63 100/99
|
| 2
|
<<16 2 5 9 -34 -37 -41 6 14 8]]
|
Hemiwur
|
29.270
|
121/120 176/175 1375/1372
|
| 3
|
<<30 13 14 3 -49 -62 -99 -4 -38 -40]]
|
Cotritone
|
32.225
|
385/384 1375/1372 4000/3993
|
| 4
|
<<13 -3 11 5 -35 -19 -37 34 22 -24]]
|
Twothirdtonic
|
40.768
|
121/120 176/175 686/675
|
| 5
|
<<5 -4 -10 -18 -18 -30 -46 -12 -28 -16]]
|
Passion
|
40.809
|
64/63 100/99 1375/1372
|
| 6
|
<<94 21 34 2 -185 -210 -322 20 -68 -112]]
|
|
43.106
|
2401/2400 43923/43904 172032/171875
|
| 7
|
<<14 11 9 -6 -15 -25 -58 -10 -52 -48]]
|
Quasitemp
|
43.209
|
100/99 385/384 1375/1372
|
| 8
|
<<2 -9 -4 -22 -19 -12 -42 16 -20 -48]]
|
Beatles
|
45.639
|
64/63 100/99 686/675
|
| 9
|
<<9 15 19 12 3 5 -12 2 -24 -32]]
|
Ammonite
|
45.694
|
55/54 100/99 686/675
|
13-limit temperaments with badness below 0.04
Listed is the wedgie and the TE badness times 1000 for 22 temperaments with badness less than 0.04.
| Rank
|
Wedgie
|
Name
|
Badness
|
Commas
|
| 1
|
[3 5 -6 4 17 1 -18 -4 16 -28 -8 21 32 70 44]
|
Porcupinefish
|
25.314
|
55/54 64/63 91/90 100/99
|
| 2
|
[13 -3 11 5 12 -35 -19 -37 -29 34 22 39 -24 -7 23]
|
Twothirdtonic
|
25.941
|
91/90 121/120 169/168 176/175
|
| 3
|
[94 21 34 2 27 -185 -210 -322 -305 20 -68 -15 -112 -50 86]
|
|
26.829
|
1001/1000 1716/1715 4225/4224 6656/6655
|
| 4
|
[9 15 19 12 14 3 5 -12 -11 2 -24 -23 -32 -31 4]
|
Ammonite
|
27.168
|
55/54 91/90 100/99 169/168
|
| 5
|
[46 15 19 12 14 -83 -99 -140 -148 2 -24 -23 -32 -31 4]
|
|
27.429
|
385/384 625/624 847/845 1375/1372
|
| 6
|
[16 2 5 9 -8 -34 -37 -41 -72 6 14 -26 8 -41 -61]
|
Hemiwur
|
28.432
|
121/120 176/175 196/195 275/273
|
| 7
|
[30 13 14 3 22 -49 -62 -99 -76 -4 -38 3 -40 10 65]
|
Cotritone
|
28.683
|
169/168 364/363 1001/1000 1716/1715
|
| 8
|
[27 8 20 -1 5 -50 -44 -95 -92 24 -30 -18 -72 -60 21]
|
Emka
|
29.741
|
196/195 364/363 385/384 625/624
|
| 9
|
[2 -9 -4 -22 -1 -19 -12 -42 -9 16 -20 31 -48 12 78]
|
Beatles
|
30.161
|
64/63 91/90 100/99 169/168
|
| 10
|
[5 -4 -10 -18 -21 -18 -30 -46 -52 -12 -28 -34 -16 -22 -6]
|
Passion
|
30.886
|
64/63 100/99 196/195 275/273
|
| 11
|
[18 -7 1 -13 -9 -53 -49 -83 -81 22 -6 5 -40 -29 17]
|
|
32.205
|
176/175 196/195 364/363 512/507
|
| 12
|
[19 7 -1 13 9 -33 -55 -45 -56 -22 6 -5 40 29 -17]
|
Semaja
|
32.564
|
121/120 169/168 176/175 275/273
|
| 13
|
[14 11 9 -6 -7 -15 -25 -58 -63 -10 -52 -57 -48 -53 -2]
|
|
32.913
|
100/99 196/195 275/273 385/384
|
| 14
|
[11 6 15 27 13 -16 -7 5 -20 18 42 8 24 -19 -55]
|
|
33.562
|
55/54 91/90 169/168 176/175
|
| 15
|
[2 -9 -4 15 -1 -19 -12 17 -9 16 66 31 56 12 -59]
|
|
33.971
|
55/54 64/63 91/90 169/168
|
| 16
|
[11 6 15 -10 13 -16 -7 -54 -20 18 -44 8 -80 -19 82]
|
|
34.295
|
91/90 100/99 169/168 385/384
|
| 17
|
[3 5 -6 4 -20 1 -18 -4 -43 -28 -8 -65 32 -34 -84]
|
|
35.130
|
55/54 64/63 100/99 196/195
|
| 18
|
[48 6 15 -10 13 -102 -111 -182 -157 18 -44 8 -80-19 82]
|
|
35.398
|
364/363 1001/1000 1716/1715 3136/3125
|
| 19
|
[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
|
| 20
|
[21 -2 -5 -9 8 -52 -67 -87 -65 -6 -14 26 -8 41 61]
|
|
37.577
|
169/168 176/175 364/363 640/637
|
| 21
|
[8 1 -16 -14 -4 -17 -48 -50 -36 -40 -36 -13 16 48 38]
|
|
37.834
|
64/63 100/99 169/168 275/273
|
| 22
|
[35 9 4 -15 1 -67 -92 -145 -128 -16 -66 -31 -56 -12 59]
|
|
39.533
|
364/363 625/624 1375/1372 2200/2197
|