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Below are listed rank-two temperaments supported by the 26edo 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 three temperaments with badness less than 0.1.
Rank
Wedgie
Name
Badness
Commas
1
<<1 4 4]]
Meantone
7.381
81/80
2
<<35 62 17]]
Senior
21.22
|-17 62 -35>
3
<<12 22 7]]
Unidec
82.423
31381059609/31250000000

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE badness times 1000 for ten temperaments with badness less than 0.06.
Rank
Wedgie
Name
Badness
Commas
1
<<2 8 8 8 7 -4]]
Injera
31.130
50/49 81/80
2
<<3 12 -1 12 -10 -36]]
Mothra/Cynder
37.146
81/80 1029/1024
3
<<23 40 1 10 -63 -110]]
Gamera
37.648
4375/4374 589824/588245
4
<<12 22 -4 7 -40 -71]]
Unidec
38.393
1029/1024 4375/4374
5
<<1 4 -9 4 -17 -32]]
Flattone
38.553
81/80 525/512
6
<<58 102 -2 27 -166 -291]]
Orga
40.236
4375/4374 54975581388800/54936068900769
7
<<11 18 5 3 -23 -39]]
Quartonic
42.632
1728/1715 4000/3969
8
<<8 6 6 -9 -13 -3]]
Doublewide
43.462
50/49 875/864
9
<<35 62 -3 17 -103 -181]]
Seniority
44.877
4375/4374 201768035/201326592
10
<<9 10 -3 -5 -30 -35]]
Superkleismic
47.932
875/864 1029/1024

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 18 temperaments with badness less than 0.05.
Rank
Wedgie
Name
Badness
Commas
1
<<12 22 -4 -6 7 -40 -51 -71 -90 -3]]
Unidec
15.479
385/384 441/440 4375/4374
2
<<58 102 -2 -16 27 -166 -226 -291 -390 -38]]
Orga
16.188
3025/3024 4375/4374 5767168/5764801
3
<<2 8 8 12 8 7 12 -4 0 6]]
Injera
23.124
45/44 50/49 99/98
4
<<3 12 -1 -8 12 -10 -23 -36 -60 -19]]
Mothra
25.642
81/80 99/98 385/384
5
<<9 10 -3 2 -5 -30 -28 -35 -30 16]]
Superkleismic
25.659
100/99 245/242 385/384
6
<<8 6 6 -4 -9 -13 -34 -3 -30 -32]]
Doublewide
32.058
50/49 99/98 875/864
7
<<1 4 -9 6 4 -17 6 -32 0 48]]
Flattone
33.839
45/44 81/80 385/384
8
<<10 14 14 8 -1 -6 -22 -7 -30 -26]]
Crepuscular
40.758
50/49 99/98 1944/1925
9
<<46 80 2 -10 20 -126 -175 -220 -300 -35]]
Hemigamera
40.955
3025/3024 4375/4374 202397184/201768035
10
<<6 -2 -2 10 -17 -20 -5 1 30 35]]
Lemba
41.563
45/44 50/49 385/384
11
<<11 18 5 14 3 -23 -16 -39 -30 22]]
Quarto
41.786
100/99 245/242 864/847
12
<<5 -6 7 4 -21 -3 -11 33 30 -13]]
Secund
42.562
45/44 99/98 385/384
13
<<70 124 -6 -22 34 -206 -277 -362 -480 -41]]

45.479
3025/3024 4375/4374 23737807549715/23706377367552
14
<<1 4 17 6 4 24 6 28 0 -42]]

46.139
45/44 81/80 1375/1344
15
<<1 4 -9 -20 4 -17 -35 -32 -60 -25]]

46.294
81/80 99/98 525/512
16
<<14 30 4 6 15 -33 -39 -75 -90 3]]

46.373
441/440 1344/1331 1728/1715
17
<<5 20 7 4 20 -3 -11 -40 -60 -13]]

47.915
81/80 99/98 864/847
18
<<7 2 15 16 -13 4 1 29 30 -7]]

49.066
45/44 99/98 875/864

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
<<12 22 -4 -6 4 7 -40 -51 -38 -71 -90 -72 -3 26 36]]
Hendec
17.707
169/168 325/324 364/363 1716/1715
2
<<46 80 2 -10 50 20 -126 -175 -91 -220 -300 -180 -35 133 210]]
Hemigamera
20.416
1716/1715 2080/2079 2200/2197 3025/3024
3
<<9 10 -3 2 16 -5 -30 -28 -8 -35 -30 0 16 56 48]]
Superkleismic
21.478
100/99 105/104 245/242 1188/1183
4
<<2 8 8 12 18 8 7 12 21 -4 0 12 6 21 18]]
Injera
21.565
45/44 50/49 78/77 99/98
5
<<1 4 -9 6 -4 4 -17 6 -10 -32 0 -24 48 22 -36]]
Flattone
22.260
45/44 65/64 78/77 81/80
6
<<3 12 -1 -8 14 12 -10 -23 11 -36 -60 -12 -19 43 78]]
Mothra
23.954
81/80 99/98 105/104 144/143
7
<<10 14 14 8 12 -1 -6 -22 -18 -7 -30 -24 -26 -18 12]]
Crepuscular
24.368
50/49 78/77 99/98 144/143
8
<<14 30 4 6 22 15 -33 -39 -17 -75 -90 -60 3 47 54]]
Secant
25.035
144/143 351/350 364/363 441/440
9
<<6 -2 -2 10 2 -17 -20 -5 -19 1 30 12 35 13 -30]]
Lemba
25.477
45/44 50/49 65/64 78/77
10
<<5 -6 7 4 6 -21 -3 -11 -9 33 30 36 -13 -9 6]]

26.212
45/44 65/64 78/77 99/98
11
<<1 4 -9 -20 -4 4 -17 -35 -10 -32 -60 -24 -25 22 60]]

26.566
65/64 81/80 99/98 105/104
12
<<11 18 5 14 8 3 -23 -16 -28 -39 -30 -48 22 4 -24]]

27.692
78/77 100/99 144/143 245/242
13
<<21 32 -7 -4 20 2 -70 -79 -46 -106 -120 -72 13 82 84]]

28.393
325/324 364/363 441/440 2200/2197
14
<<11 18 5 -12 8 3 -23 -57 -28 -39 -90 -48 -51 4 72]]

28.818
99/98 169/168 275/273 385/384
15
<<5 20 7 4 6 20 -3 -11 -9 -40 -60 -60 -13 -9 6]]

29.285
78/77 81/80 99/98 144/143
16
<<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
17
<<7 2 -11 -10 -2 -13 -37 -40 -29 -31 -30 -12 10 35 30]]

30.043
65/64 100/99 105/104 245/242
18
<<8 6 6 -4 20 -9 -13 -34 2 -3 -30 24 -32 34 84]]

30.921
50/49 99/98 105/104 144/143
19
<<15 34 -5 -14 18 19 -50 -74 -27 -107 -150 -84 -22 69 114]]

30.934
351/350 385/384 441/440 1188/1183
20
<<4 16 -10 -2 10 16 -27 -17 1 -68 -60 -36 29 65 42]]

31.039
81/80 105/104 144/143 245/242
21
<<2 8 8 12 -8 8 7 12 -20 -4 0 -48 6 -52 -72]]

31.589
45/44 50/49 65/64 99/98
22
<<3 12 -1 -8 -12 12 -10 -23 -30 -36 -60 -72 -19 -30 -12]]

32.520
65/64 78/77 81/80 99/98
23
<<26 52 0 0 26 22 -73 -90 -55 -146 -180 -132 0 73 90]]

32.946
351/350 364/363 441/440 15379/15360
24
<<3 12 -1 18 14 12 -10 18 11 -36 0 -12 54 43 -18]]

34.124
45/44 78/77 81/80 640/637
25
<<20 28 2 -10 24 -2 -53 -85 -36 -74 -120 -48 -35 60 120]]

34.179
275/273 325/324 385/384 1573/1568
26
<<6 -2 -2 -16 2 -17 -20 -46 -19 1 -30 12 -38 13 66]]

34.689
50/49 65/64 99/98 105/104
27
<<8 6 6 22 20 -9 -13 7 2 -3 30 24 41 34 -12]]

35.040
45/44 50/49 78/77 325/324
28
<<1 4 17 6 -4 4 24 6 -10 28 0 -24 -42 -74 -36]]

35.184
45/44 65/64 81/80 1188/1183
29
<<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
30
<<9 10 -3 2 -10 -5 -30 -28 -49 -35 -30 -60 16 -17 -42]]

36.254
65/64 78/77 100/99 245/242
31
<<32 50 -2 -16 28 5 -93 -136 -74 -145 -210 -120 -38 86 156]]

36.996
325/324 385/384 1573/1568 2200/2197
32
<<2 8 -18 -14 -8 8 -34 -29 -20 -64 -60 -48 23 44 24]]

37.031
65/64 81/80 105/104 245/242
33
<<13 26 13 0 26 11 -16 -45 -7 -43 -90 -36 -45 25 90]]

37.851
99/98 144/143 275/273 1040/1029
34
<<19 24 11 10 28 -6 -36 -50 -26 -42 -60 -24 -10 38 60]]

38.179
100/99 144/143 275/273 1040/1029
35
<<7 2 15 16 24 -13 4 1 12 29 30 48 -7 12 24]]

38.402
45/44 78/77 99/98 325/324
36
<<7 2 15 16 -2 -13 4 1 -29 29 30 -12 -7 -61 -66]]

39.063
45/44 65/64 99/98 275/273
37
<<25 48 9 -6 30 18 -56 -96 -45 -114 -180 -108 -48 51 126]]

39.183
351/350 640/637 1188/1183 1573/1568
38
<<1 4 17 6 22 4 24 6 31 28 0 36 -42 -1 54]]

39.550
45/44 78/77 81/80 1344/1331
39
<<2 8 8 -14 -8 8 7 -29 -20 -4 -60 -48 -67 -52 24]]

39.744
50/49 65/64 78/77 81/80
40
<<22 36 10 2 16 6 -46 -73 -56 -78 -120 -96 -29 8 48]]

39.891
169/168 325/324 364/363 640/637