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Below are listed rank-two temperaments supported by the 22edo 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
<<16 -10 -53]]
Kwazy
14.091
9010162353515625/9007199254740992
2
<<2 -4 -11]]
Srutal
19.915
2048/2025
3
<<3 5 1]]
Porcupine
30.778
250/243
4
<<5 1 -10]]
Magic
39.163
3125/3072
5
<<7 -3 -21]]
Orson
40.807
2109375/2097152
6
<<9 -7 -32]]
Escapade
83.778
4294967296/4271484375

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE badness times 1000 for 14 temperaments with badness less than 0.06.
Rank
Wedgie
Name
Badness
Commas
1
<<5 1 12 -10 5 25]]
Magic
18.918
225/224 245/243
2
<<2 -4 -4 -11 -12 2]]
Pajara
20.033
50/49 64/63
3
<<7 -3 8 -21 -7 27]]
Orwell
20.735
225/224 1728/1715
4
<<23 -13 42 -74 2 134]]
Fifthplus
25.840
65625/65536 420175/419904
5
<<1 9 -2 12 -6 -30]]
Superpyth
32.318
64/63 245/243
6
<<12 -2 20 -31 -2 52]]
Wizard
40.846
225/224 118098/117649
7
<<3 5 -6 1 -18 -28]]
Porcupine
41.057
64/63 250/243
8
<<11 -11 22 -43 4 82]]
Hendecatonic
41.081
6144/6125 10976/10935
9
<<8 6 6 -9 -13 -3]]
Doublewide
43.462
50/49 875/864
10
<<6 10 10 2 -1 -5]]
Hedgehog
43.983
50/49 245/243
11
<<4 -8 14 -22 11 55]]
Shrutar
47.377
245/243 2048/2025
12
<<3 5 16 1 17 23]]
Porky
54.389
225/224 250/243
13
<<6 -12 10 -33 -1 57]]
Echidna
58.033
1728/1715 2048/2025
14
<<18 -14 30 -64 -3 109]]
Septisuperfourth
59.241
6144/6125 118098/117649

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 38 temperaments with badness less than 0.05.
Rank
Wedgie
Name
Badness
Commas
1
<<7 -3 8 2 -21 -7 -21 27 15 -22]]
Orwell
15.231
99/98 121/120 176/175
2
<<12 -2 20 -6 -31 -2 -51 52 -7 -86]]
Wizard
18.539
225/224 385/384 4000/3993
3
<<2 -4 -4 -12 -11 -12 -26 2 -14 -20]]
Pajara
20.343
50/49 64/63 99/98
4
<<5 1 12 -8 -10 5 -30 25 -22 -64]]
Magic
20.352
100/99 225/224 245/243
5
<<3 5 -6 4 1 -18 -4 -28 -8 32]]
Porcupine
21.562
55/54 64/63 100/99
6
<<6 10 10 8 2 -1 -8 -5 -16 -12]]
Hedgehog
23.095
50/49 55/54 99/98
7
<<18 -14 30 -20 -64 -3 -94 109 2 -160]]
Septisuperfourth
24.619
540/539 4000/3993 5632/5625
8
<<1 9 -2 16 12 -6 22 -30 6 52]]
Superpyth
24.976
64/63 100/99 245/243
9
<<6 -12 10 -14 -33 -1 -43 57 9 -74]]
Echidna
25.987
176/175 540/539 896/891
10
<<4 -8 14 -2 -22 11 -17 55 23 -54]]
Shrutar
26.489
121/120 176/175 245/243
11
<<5 1 12 14 -10 5 5 25 29 -2]]
Telepathy
27.109
55/54 99/98 176/175
12
<<3 5 16 4 1 17 -4 23 -8 -44]]
Porky
27.268
55/54 100/99 225/224
13
<<46 -26 84 -34 -148 4 -213 268 11 -386]]

27.785
9801/9800 41503/41472 65625/65536
14
<<2 -4 -4 10 -11 -12 9 2 37 42]]
Pajarous
28.349
50/49 55/54 64/63
15
<<34 -24 64 -28 -117 6 -162 216 18 -300]]

28.943
5632/5625 9801/9800 41503/41472
16
<<8 6 6 -4 -9 -13 -34 -3 -30 -32]]
Doublewide
32.058
50/49 99/98 875/864
17
<<16 -10 34 -8 -53 9 -68 107 16 -140]]
Bisupermajor
32.080
385/384 3388/3375 9801/9800
18
<<1 -13 -2 -6 -23 -6 -13 32 31 -10]]
Quasisupra
32.203
64/63 99/98 121/120
19
<<1 9 -2 -6 12 -6 -13 -30 -45 -10]]
Suprapyth
32.768
55/54 64/63 99/98
20
<<8 6 6 18 -9 -13 1 -3 21 30]]
Fleetwood
35.202
50/49 55/54 176/175
21
<<9 -7 26 -10 -32 16 -47 80 1 -118]]
Sensa
35.844
245/243 385/384 4000/3993
22
<<10 2 24 6 -20 10 -25 50 7 -66]]
Divination
35.864
121/120 225/224 245/243
23
<<9 -7 4 -10 -32 -19 -47 29 1 -42]]

36.700
99/98 176/175 2560/2541
24
<<11 -11 22 -22 -43 4 -73 82 -13 -138]]

38.042
540/539 896/891 4375/4356
25
<<4 -8 -8 -2 -22 -24 -17 4 23 22]]
Hemipaj
38.890
50/49 64/63 121/120
26
<<10 2 2 6 -20 -25 -25 -1 7 10]]
Astrology
39.151
50/49 121/120 176/175
27
<<19 -5 28 -4 -52 -9 -72 79 8 -108]]

40.603
225/224 385/384 43923/43750
28
<<13 7 18 10 -19 -8 -29 22 -1 -34]]

41.282
99/98 121/120 625/616
29
<<30 -16 50 -26 -95 -5 -145 161 -5 -246]]

42.972
540/539 4000/3993 65625/65536
30
<<13 -15 18 -12 -54 -8 -64 84 24 -96]]

43.309
176/175 540/539 16384/16335
31
<<4 14 14 20 13 11 18 -7 -2 8]]

45.052
50/49 99/98 2662/2625
32
<<2 -4 18 -12 -11 23 -26 53 -14 -96]]

45.270
100/99 385/384 1232/1215
33
<<7 -3 8 -20 -21 -7 -56 27 -36 -84]]

45.950
100/99 225/224 1728/1715
34
<<11 -11 22 0 -43 4 -38 82 38 -76]]

46.088
121/120 176/175 10976/10935
35
<<5 1 -10 -8 -10 -30 -30 -26 -22 12]]

47.379
64/63 100/99 605/588
36
<<28 -12 54 -14 -84 7 -119 159 9 -226]]

47.776
385/384 9801/9800 456533/455625
37
<<0 0 0 22 0 0 35 0 51 62]]

48.372
50/49 64/63 245/243
38
<<25 -17 38 -18 -85 -10 -115 136 17 -182]]

49.466
540/539 5632/5625 35937/35840

13-limit temperaments with badness below 0.04

Listed is the wedgie and the TE badness times 1000 for 40 temperaments with badness less than 0.04.
Rank
Wedgie
Name
Badness
Commas
1
<<7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73]]
Orwell
19.718
99/98 121/120 176/175 275/273
2
<<6 10 10 8 12 2 -1 -8 -3 -5 -16 -9 -12 -3 12]]
Hedgehog
21.516
50/49 55/54 65/63 99/98
3
<<12 -2 20 -6 -20 -31 -2 -51 -76 52 -7 -39 -86 -130 -47]]
Lizard
21.781
225/224 351/350 364/363 385/384
4
<<2 -4 -4 -12 -18 -11 -12 -26 -36 2 -14 -27 -20 -36 -18]]
Pajara
22.327
50/49 64/63 99/98 975/968
5
<<7 -3 8 2 3 -21 -7 -21 -21 27 15 18 -22 -21 3]]
Blair
23.086
65/64 78/77 91/90 99/98
6
<<6 -12 10 -14 -32 -33 -1 -43 -73 57 9 -30 -74 -127 -59]]
Echidna
23.679
176/175 351/350 364/363 540/539
7
<<1 9 -2 16 13 12 -6 22 17 -30 6 -3 52 44 -14]]
Superpyth
24.673
64/63 78/77 91/90 100/99
8
<<2 -4 -4 10 4 -11 -12 9 -1 2 37 24 42 26 -23]]
Pajarous
25.176
50/49 55/54 64/63 65/63
9
<<5 1 12 -8 -23 -10 5 -30 -55 25 -22 -57 -64 -109 -50]]
Necromancy
25.275
100/99 225/224 245/243 275/273
10
<<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
11
<<5 1 12 14 -1 -10 5 5 -20 25 29 -6 -2 -47 -55]]
Telepathy
25.522
55/54 65/64 91/90 99/98
12
<<5 1 12 -8 -1 -10 5 -30 -20 25 -22 -6 -64 -47 26]]
Sorcery
25.829
65/64 78/77 91/90 100/99
13
<<3 5 -6 4 -5 1 -18 -4 -19 -28 -8 -30 32 8 -32]]
Porkpie
26.043
55/54 64/63 65/63 100/99
14
<<4 -8 14 -2 -14 -22 11 -17 -37 55 23 -3 -54 -91 -41]]
Srutar
26.069
91/90 121/120 176/175 245/243
15
<<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]]

26.543
55/54 65/64 91/90 100/99
16
<<2 -4 -4 -12 4 -11 -12 -26 -1 2 -14 24 -20 26 58]]

27.642
50/49 64/63 65/63 99/98
17
<<8 6 6 -4 -6 -9 -13 -34 -39 -3 -30 -36 -32 -39 -6]]

29.481
50/49 78/77 99/98 875/864
18
<<0 0 0 0 22 0 0 0 35 0 0 51 0 62 76]]

29.849
50/49 55/54 64/63 99/98
19
<<1 -13 -2 -6 -9 -23 -6 -13 -18 32 31 27 -10 -18 -9]]

30.219
64/63 78/77 91/90 121/120
20
<<9 -7 26 -10 -37 -32 16 -47 -92 80 1 -60 -118 -200 -91]]

31.366
245/243 352/351 385/384 625/624
21
<<8 6 6 18 16 -9 -13 1 -4 -3 21 15 30 23 -11]]
Fleetwood
31.835
50/49 55/54 65/63 176/175
22
<<1 9 -2 -6 13 12 -6 -13 17 -30 -45 -3 -10 44 67]]

32.306
55/54 64/63 91/90 99/98
23
<<18 -14 30 -20 -52 -64 -3 -94 -149 109 2 -69 -160 -257 -106]]

33.038
351/350 364/363 540/539 4096/4095
24
<<16 -10 34 -8 -56 -53 9 -68 -148 107 16 -93 -140 -283 -164]]

33.800
352/351 385/384 625/624 4459/4455
25
<<19 -5 28 -4 -39 -52 -9 -72 -132 79 8 -72 -108 -213 -120]]

34.251
225/224 351/350 385/384 10648/10647
26
<<10 2 2 6 -2 -20 -25 -25 -40 -1 7 -12 10 -13 -29]]

34.376
50/49 65/64 78/77 121/120
27
<<3 5 16 4 17 1 17 -4 16 23 -8 21 -44 -11 44]]

35.176
55/54 65/63 100/99 225/224
28
<<9 -7 4 -10 -15 -32 -19 -47 -57 29 1 -9 -42 -57 -15]]

35.261
78/77 99/98 176/175 507/500
29
<<4 -8 -8 -2 -14 -22 -24 -17 -37 4 23 -3 22 -10 -41]]

35.651
50/49 64/63 78/77 121/120
30
<<1 9 -2 16 35 12 -6 22 52 -30 6 48 52 106 62]]

35.982
64/63 100/99 245/243 275/273
31
<<11 -11 22 -22 -55 -43 4 -73 -128 82 -13 -87 -138 -236 -109]]

36.112
352/351 364/363 540/539 625/624
32
<<1 9 -2 -6 -9 12 -6 -13 -18 -30 -45 -54 -10 -18 -9]]

36.336
55/54 64/63 65/63 364/363
33
<<6 10 10 8 -10 2 -1 -8 -38 -5 -16 -60 -12 -65 -64]]

36.358
50/49 55/54 99/98 975/968
34
<<10 2 24 6 -2 -20 10 -25 -40 50 7 -12 -66 -94 -29]]

36.588
65/64 91/90 121/120 245/243
35
<<5 1 12 14 21 -10 5 5 15 25 29 45 -2 15 21]]

37.533
55/54 65/63 99/98 176/175
36
<<12 -2 20 -6 -42 -31 -2 -51 -111 52 -7 -90 -86 -192 -123]]

37.965
225/224 275/273 385/384 4000/3993
37
<<13 7 18 10 -7 -19 -8 -29 -59 22 -1 -42 -34 -86 -61]]

38.144
65/64 99/98 121/120 275/273
38
<<13 -15 18 -12 -51 -54 -8 -64 -129 84 24 -63 -96 -210 -132]]

39.456
176/175 351/350 540/539 33275/33124
39
<<5 1 -10 -8 -1 -10 -30 -30 -20 -26 -22 -6 12 34 26]]

39.703
64/63 65/63 100/99 169/165
40
<<1 -13 -2 -6 -31 -23 -6 -13 -53 32 31 -24 -10 -80 -85]]

39.876
64/63 99/98 121/120 275/273