List of 26et rank two temperaments by badness

From Xenharmonic Wiki
Jump to: navigation, search

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