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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 complexity for six temperaments with badness less than 0.1.
Rank
Wedgie
Name
Complexity
Commas
1
<<3 5 1]]
Porcupine
1.663
250/243
2
<<2 -4 -11]]
Srutal
2.121
2048/2025
3
<<5 1 -10]]
Magic
2.417
3125/3072
4
<<7 -3 -21]]
Orson
4.232
2109375/2097152
5
<<9 -7 -32]]
Escapade
6.243
4294967296/4271484375
6
<<16 -10 -53]]
Kwazy
10.454
9010162353515625/9007199254740992

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE complexity for 14 temperaments with badness less than 0.06.
Rank
Wedgie
Name
Complexity
Commas
1
<<2 -4 -4 -11 -12 2]]
Pajara
1.953
50/49 64/63
2
<<6 10 10 2 -1 -5]]
Hedgehog
2.784
50/49 245/243
3
<<3 5 -6 1 -18 -28]]
Porcupine
2.819
64/63 250/243
4
<<1 9 -2 12 -6 -30]]
Superpyth
2.874
64/63 245/243
5
<<8 6 6 -9 -13 -3]]
Doublewide
2.928
50/49 875/864
6
<<5 1 12 -10 5 25]]
Magic
2.937
225/224 245/243
7
<<3 5 16 1 17 23]]
Porky
3.362
225/224 250/243
8
<<7 -3 8 -21 -7 27]]
Orwell
3.685
225/224 1728/1715
9
<<4 -8 14 -22 11 55]]
Shrutar
5.101
245/243 2048/2025
10
<<6 -12 10 -33 -1 57]]
Echidna
5.925
1728/1715 2048/2025
11
<<12 -2 20 -31 -2 52]]
Wizard
6.372
225/224 118098/117649
12
<<11 -11 22 -43 4 82]]
Hendecatonic
8.442
6144/6125 10976/10935
13
<<18 -14 30 -64 -3 109]]
Septisuperfourth
11.986
6144/6125 118098/117649
14
<<23 -13 42 -74 2 134]]
Fifthplus
14.679
65625/65536 420175/419904

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE complexity for 38 temperaments with badness less than 0.05.
Rank
Wedgie
Name
Complexity
Commas
1
<<6 10 10 8 2 -1 -8 -5 -16 -12]]
Hedgehog
2.439
50/49 55/54 99/98
2
<<3 5 -6 4 1 -18 -4 -28 -8 32]]
Porcupine
2.478
55/54 64/63 100/99
3
<<2 -4 -4 -12 -11 -12 -26 2 -14 -20]]
Pajara
2.543
50/49 64/63 99/98
4
<<2 -4 -4 10 -11 -12 9 2 37 42]]
Pajarous
2.718
50/49 55/54 64/63
5
<<5 1 12 14 -10 5 5 25 29 -2]]
Telepathy
2.864
55/54 99/98 176/175
6
<<1 9 -2 -6 12 -6 -13 -30 -45 -10]]
Suprapyth
3.011
55/54 64/63 99/98
7
<<3 5 16 4 1 17 -4 23 -8 -44]]
Porky
3.020
55/54 100/99 225/224
8
<<8 6 6 18 -9 -13 1 -3 21 30]]
Fleetwood
3.081
50/49 55/54 176/175
9
<<7 -3 8 2 -21 -7 -21 27 15 -22]]
Orwell
3.242
99/98 121/120 176/175
10
<<4 -8 -8 -2 -22 -24 -17 4 23 22]]
Hemipaj
3.389
50/49 64/63 121/120
11
<<8 6 6 -4 -9 -13 -34 -3 -30 -32]]
Doublewide
3.407
50/49 99/98 875/864
12
<<1 9 -2 16 12 -6 22 -30 6 52]]
Superpyth
3.410
64/63 100/99 245/243
13
<<1 -13 -2 -6 -23 -6 -13 32 31 -10]]
Quasisupra
3.490
64/63 99/98 121/120
14
<<10 2 2 6 -20 -25 -25 -1 7 10]]
Astrology
3.575
50/49 121/120 176/175
15
<<4 14 14 20 13 11 18 -7 -2 8]]

3.637
50/49 99/98 2662/2625
16
<<5 1 -10 -8 -10 -30 -30 -26 -22 12]]

3.686
64/63 100/99 605/588
17
<<5 1 12 -8 -10 5 -30 25 -22 -64]]
Magic
3.715
100/99 225/224 245/243
18
<<0 0 0 22 0 0 35 0 51 62]]

4.028
50/49 64/63 245/243
19
<<4 -8 14 -2 -22 11 -17 55 23 -54]]
Shrutar
4.530
121/120 176/175 245/243
20
<<13 7 18 10 -19 -8 -29 22 -1 -34]]

4.554
99/98 121/120 625/616
21
<<9 -7 4 -10 -32 -19 -47 29 1 -42]]

5.075
99/98 176/175 2560/2541
22
<<10 2 24 6 -20 10 -25 50 7 -66]]

5.271
121/120 225/224 245/243
23
<<2 -4 18 -12 -11 23 -26 53 -14 -96]]

5.317
100/99 385/384 1232/1215
24
<<7 -3 8 -20 -21 -7 -56 27 -36 -84]]

5.605
100/99 225/224 1728/1715
25
<<6 -12 10 -14 -33 -1 -43 57 9 -74]]
Echidna
5.898
176/175 540/539 896/891
26
<<12 -2 20 -6 -31 -2 -51 52 -7 -86]]
Wizard
6.421
225/224 385/384 4000/3993
27
<<11 -11 22 0 -43 4 -38 82 38 -76]]

7.478
121/120 176/175 10976/10935
28
<<9 -7 26 -10 -32 16 -47 80 1 -118]]

7.718
245/243 385/384 4000/3993
29
<<13 -15 18 -12 -54 -8 -64 84 24 -96]]

8.886
176/175 540/539 16384/16335
30
<<11 -11 22 -22 -43 4 -73 82 -13 -138]]

9.219
540/539 896/891 4375/4356
31
<<19 -5 28 -4 -52 -9 -72 79 8 -108]]

9.470
225/224 385/384 43923/43750
32
<<16 -10 34 -8 -53 9 -68 107 16 -140]]

10.578
385/384 3388/3375 9801/9800
33
<<18 -14 30 -20 -64 -3 -94 109 2 -160]]
Septisuperfourth
12.086
540/539 4000/3993 5632/5625
34
<<25 -17 38 -18 -85 -10 -115 136 17 -182]]

15.106
540/539 5632/5625 35937/35840
35
<<28 -12 54 -14 -84 7 -119 159 9 -226]]

16.904
385/384 9801/9800 456533/455625
36
<<30 -16 50 -26 -95 -5 -145 161 -5 -246]]

18.435
540/539 4000/3993 65625/65536
37
<<34 -24 64 -28 -117 6 -162 216 18 -300]]

22.572
5632/5625 9801/9800 41503/41472
38
<<46 -26 84 -34 -148 4 -213 268 11 -386]]

28.911
9801/9800 41503/41472 65625/65536

13-limit temperaments with badness below 0.04

Listed is the wedgie and the TE complexity for 40 temperaments with badness less than 0.04.
Rank
Wedgie
Name
Complexity
Commas
1
<<6 10 10 8 12 2 -1 -8 -3 -5 -16 -9 -12 -3 12]]
Hedgehog
2.196
50/49 55/54 65/63 99/98
2
<<2 -4 -4 10 4 -11 -12 9 -1 2 37 24 42 26 -23]]
Pajarous
2.481
50/49 55/54 64/63 65/63
3
<<3 5 -6 4 -5 1 -18 -4 -19 -28 -8 -30 32 8 -32]]
Porkpie
2.487
55/54 64/63 65/63 100/99
4
<<2 -4 -4 -12 4 -11 -12 -26 -1 2 -14 24 -20 26 58]]
Pajara
2.588
50/49 64/63 65/63 99/98
5
<<8 6 6 18 16 -9 -13 1 -4 -3 21 15 30 23 -11]]
Fleetwood
2.861
50/49 55/54 65/63 176/175
6
<<7 -3 8 2 3 -21 -7 -21 -21 27 15 18 -22 -21 3]]
Blair
2.911
65/64 78/77 91/90 99/98
7
<<5 1 12 14 -1 -10 5 5 -20 25 29 -6 -2 -47 -55]]
Telepathy
2.980
55/54 65/64 91/90 99/98
8
<<3 5 16 4 17 1 17 -4 16 23 -8 21 -44 -11 44]]

3.040
55/54 65/63 100/99 225/224
9
<<1 9 -2 -6 -9 12 -6 -13 -18 -30 -45 -54 -10 -18 -9]]

3.151
55/54 64/63 65/63 364/363
10
<<2 -4 -4 -12 -18 -11 -12 -26 -36 2 -14 -27 -20 -36 -18]]

3.161
50/49 64/63 99/98 975/968
11
<<1 -13 -2 -6 -9 -23 -6 -13 -18 32 31 27 -10 -18 -9]]

3.168
64/63 78/77 91/90 121/120
12
<<5 1 12 14 21 -10 5 5 15 25 29 45 -2 15 21]]

3.194
55/54 65/63 99/98 176/175
13
<<3 5 -6 4 17 1 -18 -4 16 -28 -8 21 32 70 44]]

3.195
55/54 64/63 91/90 100/99
14
<<1 9 -2 16 13 12 -6 22 17 -30 6 -3 52 44 -14]]

3.228
64/63 78/77 91/90 100/99
15
<<1 9 -2 -6 13 12 -6 -13 17 -30 -45 -3 -10 44 67]]

3.234
55/54 64/63 91/90 99/98
16
<<5 1 -10 -8 -1 -10 -30 -30 -20 -26 -22 -6 12 34 26]]

3.296
64/63 65/63 100/99 169/165
17
<<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]]

3.380
55/54 65/64 91/90 100/99
18
<<5 1 12 -8 -1 -10 5 -30 -20 25 -22 -6 -64 -47 26]]

3.413
65/64 78/77 91/90 100/99
19
<<0 0 0 0 22 0 0 0 35 0 0 51 0 62 76]]

3.436
50/49 55/54 64/63 99/98
20
<<4 -8 -8 -2 -14 -22 -24 -17 -37 4 23 -3 22 -10 -41]]

3.467
50/49 64/63 78/77 121/120
21
<<10 2 2 6 -2 -20 -25 -25 -40 -1 7 -12 10 -13 -29]]

3.495
50/49 65/64 78/77 121/120
22
<<8 6 6 -4 -6 -9 -13 -34 -39 -3 -30 -36 -32 -39 -6]]

3.603
50/49 78/77 99/98 875/864
23
<<6 10 10 8 -10 2 -1 -8 -38 -5 -16 -60 -12 -65 -64]]

3.844
50/49 55/54 99/98 975/968
24
<<7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73]]

4.717
99/98 121/120 176/175 275/273
25
<<4 -8 14 -2 -14 -22 11 -17 -37 55 23 -3 -54 -91 -41]]

4.806
91/90 121/120 176/175 245/243
26
<<1 -13 -2 -6 -31 -23 -6 -13 -53 32 31 -24 -10 -80 -85]]

5.065
64/63 99/98 121/120 275/273
27
<<9 -7 4 -10 -15 -32 -19 -47 -57 29 1 -9 -42 -57 -15]]

5.170
78/77 99/98 176/175 507/500
28
<<10 2 24 6 -2 -20 10 -25 -40 50 7 -12 -66 -94 -29]]

5.251
65/64 91/90 121/120 245/243
29
<<13 7 18 10 -7 -19 -8 -29 -59 22 -1 -42 -34 -86 -61]]

5.337
65/64 99/98 121/120 275/273
30
<<5 1 12 -8 -23 -10 5 -30 -55 25 -22 -57 -64 -109 -50]]

5.378
100/99 225/224 245/243 275/273
31
<<1 9 -2 16 35 12 -6 22 52 -30 6 48 52 106 62]]

5.435
64/63 100/99 245/243 275/273
32
<<6 -12 10 -14 -32 -33 -1 -43 -73 57 9 -30 -74 -127 -59]]

7.120
176/175 351/350 364/363 540/539
33
<<12 -2 20 -6 -20 -31 -2 -51 -76 52 -7 -39 -86 -130 -47]]

7.303
225/224 351/350 364/363 385/384
34
<<9 -7 26 -10 -37 -32 16 -47 -92 80 1 -60 -118 -200 -91]]

9.701
245/243 352/351 385/384 625/624
35
<<12 -2 20 -6 -42 -31 -2 -51 -111 52 -7 -90 -86 -192 -123]]

9.808
225/224 275/273 385/384 4000/3993
36
<<13 -15 18 -12 -51 -54 -8 -64 -129 84 24 -63 -96 -210 -132]]

11.639
176/175 351/350 540/539 33275/33124
37
<<19 -5 28 -4 -39 -52 -9 -72 -132 79 8 -72 -108 -213 -120]]

11.812
225/224 351/350 385/384 10648/10647
38
<<11 -11 22 -22 -55 -43 4 -73 -128 82 -13 -87 -138 -236 -109]]

12.215
352/351 364/363 540/539 625/624
39
<<16 -10 34 -8 -56 -53 9 -68 -148 107 16 -93 -140 -283 -164]]

14.161
352/351 385/384 625/624 4459/4455
40
<<18 -14 30 -20 -52 -64 -3 -94 -149 109 2 -69 -160 -257 -106]]

14.257
351/350 364/363 540/539 4096/4095