List of 37et rank two temperaments by badness

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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