List of 27edo rank two temperaments by badness

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Below are listed rank-2 temperaments supported by either the 27edo patent val or the 27e val, that is, the ⟨27 43 63 76 94 100] val, below the indicated cutoff in TE logflat badness.

5-limit temperaments

Listed is the wedgie and the TE badness times 1000 for four temperaments with badness less than 0.1.

Rank Wedgie Name Badness Comma list
1 ⟨⟨ 18 27 1 ]] Ennealimmal 17.191 7629394531250/7625597484987
2 ⟨⟨ 3 0 -7 ]] Augmented 22.315 128/125
3 ⟨⟨ 7 9 -2 ]] Sensipent 35.220 78732/78125
4 ⟨⟨ 4 9 5 ]] Tetracot 48.518 20000/19683

7-limit temperaments

Listed is the wedgie and the TE badness times 1000 for eight temperaments with badness less than 0.06.

Rank Wedgie Name Badness Comma list
1 ⟨⟨ 18 27 18 1 -22 -34 ]] Ennealimmal 3.610 2401/2400 4375/4374
2 ⟨⟨ 3 0 -6 -7 -18 -14 ]] Augene 24.816 64/63 126/125
3 ⟨⟨ 7 9 13 -2 1 5 ]] Sensi 25.622 126/125 245/243
4 ⟨⟨ 10 9 7 -9 -17 -9 ]] Myna 27.044 126/125 1728/1715
5 ⟨⟨ 1 9 -2 12 -6 -30 ]] Superpyth 32.318 64/63 245/243
6 ⟨⟨ 8 18 11 10 -5 -25 ]] Octacot 33.845 245/243 2401/2400
7 ⟨⟨ 11 18 5 3 -23 -39 ]] Quartonic 42.632 1728/1715 4000/3969
8 ⟨⟨ 2 -9 -4 -19 -12 16 ]] Beatles 45.872 64/63 686/675

11-limit patent val temperaments

Listed is the wedgie and the TE badness times 1000 for ten 27edo patent val temperaments with badness less than 0.05.

Rank Wedgie Name Badness Comma list
1 ⟨⟨ 54 81 54 -108 3 -66 -358 -102 -531 -490 ]] Trinealimmal 29.812 2401/2400 4375/4374 2097152/2096325
2 ⟨⟨ 18 27 18 -27 1 -22 -105 -34 -156 -138 ]] Ennealiminal 31.123 385/384 1375/1372 4375/4374
3 ⟨⟨ 1 9 -2 -6 12 -6 -13 -30 -45 -10 ]] Suprapyth 32.768 55/54 64/63 99/98
4 ⟨⟨ 10 9 7 -6 -9 -17 -44 -9 -45 -41 ]] Myno 33.434 99/98 126/125 385/384
5 ⟨⟨ 3 0 -6 9 -7 -18 4 -14 21 46 ]] Eugene 35.554 55/54 64/63 77/75
6 ⟨⟨ 7 9 13 12 -2 1 -5 5 -3 -11 ]] Sensa 36.835 55/54 77/75 99/98
7 ⟨⟨ 7 9 13 -15 -2 1 -48 5 -66 -87 ]] Sensor 37.942 126/125 245/243 385/384
8 ⟨⟨ 8 18 11 -21 10 -5 -61 -25 -111 -97 ]] 39.643 245/243 385/384 1375/1372
9 ⟨⟨ 3 0 -6 -18 -7 -18 -39 -14 -42 -30 ]] 40.832 64/63 99/98 126/125
10 ⟨⟨ 2 -9 -4 -12 -19 -12 -26 16 3 -20 ]] 49.185 64/63 77/75 99/98

11-limit 27e temperaments

Listed is the wedgie and the TE badness times 1000 for 29 27e temperaments with badness less than 0.05.

Rank Wedgie Name Badness Comma list
1 ⟨⟨ 10 9 7 25 -9 -17 5 -9 27 46 ]] Myna 16.842 126/125 176/175 243/242
2 ⟨⟨ 3 0 -6 -6 -7 -18 -20 -14 -14 4 ]] Augene 19.613 56/55 64/63 100/99
3 ⟨⟨ 18 27 18 45 1 -22 9 -34 11 64 ]] Ennealimnic 20.347 243/242 441/440 4375/4356
4 ⟨⟨ 72 108 72 207 4 -88 79 -136 107 332 ]] Quadraennealimmal 21.320 2401/2400 4375/4374 234375/234256
5 ⟨⟨ 8 18 11 20 10 -5 4 -25 -16 18 ]] Octacot 24.078 100/99 243/242 245/242
6 ⟨⟨ 1 9 -2 16 12 -6 22 -30 6 52 ]] Superpyth 24.976 64/63 100/99 245/243
7 ⟨⟨ 7 9 13 4 -2 1 -18 5 -22 -34 ]] Sensis 28.680 56/55 100/99 245/243
8 ⟨⟨ 7 9 13 31 -2 1 25 5 41 42 ]] Sensus 29.486 126/125 176/175 245/243
9 ⟨⟨ 2 -9 -4 5 -19 -12 1 16 43 28 ]] Ringo 32.863 56/55 64/63 540/539
10 ⟨⟨ 11 18 5 41 3 -23 27 -39 33 98 ]] Quartonic 34.031 176/175 540/539 2200/2187
11 ⟨⟨ 9 0 9 9 -21 -11 -17 21 21 -6 ]] Niner 34.861 56/55 128/125 540/539
12 ⟨⟨ 4 9 -8 10 5 -24 2 -44 -8 56 ]] Modus 35.149 64/63 100/99 243/242
13 ⟨⟨ 54 81 54 162 3 -66 70 -102 96 268 ]] 36.101 2401/2400 4375/4374 42592/42525
14 ⟨⟨ 28 36 25 70 -8 -39 14 -43 38 110 ]] 36.785 243/242 441/440 78408/78125
15 ⟨⟨ 4 9 19 10 5 19 2 19 -8 -38 ]] 37.551 56/55 100/99 243/242
16 ⟨⟨ 6 0 15 15 -14 7 3 35 35 -10 ]] 38.232 56/55 128/125 245/243
17 ⟨⟨ 15 27 24 51 8 -4 29 -20 25 60 ]] 38.382 245/243 441/440 3388/3375
18 ⟨⟨ 29 45 23 86 4 -45 36 -73 44 162 ]] 38.943 540/539 4375/4374 15488/15435
19 ⟨⟨ 5 18 17 26 17 13 24 -11 -2 14 ]] 40.485 100/99 245/242 686/675
20 ⟨⟨ 25 36 31 76 -1 -21 34 -29 52 106 ]] 41.568 441/440 3388/3375 4375/4374
21 ⟨⟨ 11 18 5 14 3 -23 -16 -39 -30 22 ]] 41.786 100/99 245/242 864/847
22 ⟨⟨ 1 9 -2 -11 12 -6 -21 -30 -57 -24 ]] 41.938 56/55 64/63 245/243
23 ⟨⟨ 13 9 1 19 -16 -35 -15 -23 13 50 ]] 43.336 126/125 176/175 864/847
24 ⟨⟨ 3 0 -6 21 -7 -18 23 -14 49 80 ]] 43.613 64/63 126/125 540/539
25 ⟨⟨ 2 -9 -4 -22 -19 -12 -42 16 -20 -48 ]] 45.639 64/63 100/99 686/675
26 ⟨⟨ 17 18 20 29 -11 -16 -13 -4 5 12 ]] 45.665 126/125 245/242 540/539
27 ⟨⟨ 19 36 16 61 13 -28 31 -64 17 116 ]] 45.895 540/539 2200/2187 4375/4356
28 ⟨⟨ 10 9 7 -2 -9 -17 -38 -9 -36 -30 ]] 48.687 56/55 100/99 1728/1715
29 ⟨⟨ 14 18 26 35 -4 2 7 10 19 8 ]] 48.714 126/125 243/242 245/242

13-limit patent val temperaments

Listed is the wedgie and the TE badness times 1000 for 19 27edo patent val temperaments with badness less than 0.04.

Rank Wedgie Name Badness Comma list
1 ⟨⟨ 7 9 13 12 10 -2 1 -5 -10 5 -3 -10 -11 -20 -10 ]] Sensa 23.258 55/54 66/65 77/75 143/140
2 ⟨⟨ 7 9 13 -15 10 -2 1 -48 -10 5 -66 -10 -87 -20 90 ]] Sensor 25.575 91/90 126/125 169/168 385/384
3 ⟨⟨ 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
4 ⟨⟨ 3 0 -6 9 12 -7 -18 4 8 -14 21 28 46 56 8 ]] 29.922 55/54 64/63 66/65 77/75
5 ⟨⟨ 18 27 18 -27 18 1 -22 -105 -38 -34 -156 -58 -138 -16 162 ]] 30.325 169/168 325/324 385/384 1375/1372
6 ⟨⟨ 8 18 11 -21 -4 10 -5 -61 -36 -25 -111 -76 -97 -52 64 ]] 31.136 196/195 245/243 385/384 1188/1183
7 ⟨⟨ 2 -9 -4 -12 -1 -19 -12 -26 -9 16 3 31 -20 12 41 ]] 31.669 64/63 66/65 77/75 143/140
8 ⟨⟨ 10 9 7 -6 -5 -9 -17 -44 -45 -9 -45 -45 -41 -40 5 ]] 31.850 66/65 99/98 126/125 385/384
9 ⟨⟨ 3 0 -6 -18 -15 -7 -18 -39 -35 -14 -42 -35 -30 -20 15 ]] 31.895 64/63 66/65 99/98 126/125
10 ⟨⟨ 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
11 ⟨⟨ 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
12 ⟨⟨ 9 0 9 0 9 -21 -11 -31 -19 21 0 21 -31 -8 31 ]] 34.350 66/65 77/75 128/125 143/140
13 ⟨⟨ 36 54 36 -81 9 2 -44 -253 -119 -68 -375 -179 -352 -108 331 ]] 35.856 2080/2079 2200/2197 2401/2400 3584/3575
14 ⟨⟨ 10 9 7 -33 -5 -9 -17 -87 -45 -9 -108 -45 -117 -40 105 ]] 35.960 126/125 196/195 512/507 832/825
15 ⟨⟨ 1 9 -2 -6 -14 12 -6 -13 -26 -30 -45 -66 -10 -32 -26 ]] 37.028 55/54 64/63 66/65 99/98
16 ⟨⟨ 0 0 0 27 0 0 0 43 0 0 63 0 76 0 -100 ]] 37.047 64/63 91/90 126/125 169/168
17 ⟨⟨ 26 45 29 -48 14 11 -27 -166 -74 -59 -267 -134 -235 -68 226 ]] 37.168 325/324 385/384 1375/1372 2200/2197
18 ⟨⟨ 4 9 -8 3 -2 5 -24 -9 -18 -44 -24 -38 36 24 -18 ]] 39.043 55/54 64/63 66/65 143/140
19 ⟨⟨ 17 18 20 -21 5 -11 -16 -92 -55 -4 -111 -55 -128 -60 95 ]] 39.578 126/125 196/195 385/384 1188/1183

13-limit 27e temperaments

Listed is the wedgie and the TE badness times 1000 for 61 27e temperaments with badness less than 0.04.

Rank Wedgie Name Badness Comma list
1 ⟨⟨ 10 9 7 25 -5 -9 -17 5 -45 -9 27 -45 46 -40 -110 ]] Myna 17.125 126/125 144/143 176/175 196/195
2 ⟨⟨ 7 9 13 4 10 -2 1 -18 -10 5 -22 -10 -34 -20 20 ]] Sensis 20.017 56/55 78/77 91/90 100/99
3 ⟨⟨ 18 27 18 45 18 1 -22 9 -38 -34 11 -58 64 -16 -104 ]] 20.697 169/168 243/242 325/324 441/440
4 ⟨⟨ 7 9 13 31 10 -2 1 25 -10 5 41 -10 42 -20 -80 ]] Sensus 20.789 91/90 126/125 169/168 352/351
5 ⟨⟨ 28 36 25 70 13 -8 -39 14 -83 -43 38 -103 110 -56 -214 ]] 21.694 243/242 351/350 441/440 10985/10976
6 ⟨⟨ 2 -9 -4 5 -1 -19 -12 1 -9 16 43 31 28 12 -22 ]] 22.619 56/55 64/63 78/77 91/90
7 ⟨⟨ 3 0 -6 -6 12 -7 -18 -20 8 -14 -14 28 4 56 64 ]] 22.890 56/55 64/63 91/90 100/99
8 ⟨⟨ 3 0 -6 -6 -15 -7 -18 -20 -35 -14 -14 -35 4 -20 -30 ]] 23.113 56/55 64/63 78/77 100/99
9 ⟨⟨ 8 18 11 20 -4 10 -5 4 -36 -25 -16 -76 18 -52 -88 ]] 23.276 100/99 144/143 243/242 245/242
10 ⟨⟨ 4 9 -8 10 -2 5 -24 2 -18 -44 -8 -38 56 24 -44 ]] 23.806 64/63 78/77 100/99 144/143
11 ⟨⟨ 11 18 5 41 8 3 -23 27 -28 -39 33 -48 98 4 -124 ]] 23.875 169/168 176/175 325/324 540/539
12 ⟨⟨ 9 0 9 9 9 -21 -11 -17 -19 21 21 21 -6 -8 -2 ]] 24.143 56/55 78/77 91/90 128/125
13 ⟨⟨ 1 9 -2 16 13 12 -6 22 17 -30 6 -3 52 44 -14 ]] 24.673 64/63 78/77 91/90 100/99
14 ⟨⟨ 15 27 24 51 6 8 -4 29 -46 -20 25 -86 60 -72 -168 ]] 25.600 196/195 245/243 352/351 1001/1000
15 ⟨⟨ 1 9 -2 16 -14 12 -6 22 -26 -30 6 -66 52 -32 -108 ]] 26.750 64/63 100/99 144/143 196/195
16 ⟨⟨ 5 18 17 26 11 17 13 24 -1 -11 -2 -41 14 -32 -58 ]] 26.929 91/90 100/99 169/168 245/242
17 ⟨⟨ 10 9 7 25 22 -9 -17 5 -2 -9 27 18 46 36 -16 ]] 27.568 78/77 91/90 126/125 176/175
18 ⟨⟨ 8 18 11 20 23 10 -5 4 7 -25 -16 -13 18 24 6 ]] 27.601 78/77 91/90 100/99 245/242
19 ⟨⟨ 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
20 ⟨⟨ 19 36 16 61 4 13 -28 31 -64 -64 17 -124 116 -48 -212 ]] 28.492 325/324 352/351 540/539 1575/1573
21 ⟨⟨ 13 9 1 19 7 -16 -35 -15 -37 -23 13 -17 50 16 -46 ]] 28.920 78/77 126/125 144/143 176/175
22 ⟨⟨ 6 0 15 15 -3 -14 7 3 -27 35 35 -7 -10 -64 -66 ]] 30.159 56/55 91/90 128/125 245/243
23 ⟨⟨ 2 -9 -4 -22 -1 -19 -12 -42 -9 16 -20 31 -48 12 78 ]] 30.161 64/63 91/90 100/99 169/168
24 ⟨⟨ 4 9 19 10 -2 5 19 2 -18 19 -8 -38 -38 -76 -44 ]] 31.219 56/55 91/90 100/99 352/351
25 ⟨⟨ 17 18 20 29 5 -11 -16 -13 -55 -4 5 -55 12 -60 -90 ]] 31.847 126/125 144/143 196/195 245/242
26 ⟨⟨ 14 18 26 35 20 -4 2 7 -20 10 19 -20 8 -40 -60 ]] 33.016 91/90 126/125 169/168 245/242
27 ⟨⟨ 43 63 49 121 19 0 -43 43 -129 -63 63 -189 170 -128 -382 ]] 33.431 441/440 1001/1000 4225/4224 4375/4374
28 ⟨⟨ 1 9 -2 -11 13 12 -6 -21 17 -30 -57 -3 -24 44 86 ]] 33.840 56/55 64/63 91/90 245/243
29 ⟨⟨ 26 45 29 92 14 11 -27 56 -74 -59 58 -134 158 -68 -292 ]] 34.147 325/324 352/351 1001/1000 1716/1715
30 ⟨⟨ 4 9 19 10 25 5 19 2 25 19 -8 25 -38 0 50 ]] 34.792 56/55 78/77 100/99 243/242
31 ⟨⟨ 21 27 12 66 3 -6 -40 32 -73 -48 60 -93 144 -36 -234 ]] 34.829 176/175 351/350 540/539 9295/9261
32 ⟨⟨ 9 27 9 36 9 22 -11 26 -19 -55 -10 -79 70 -8 -102 ]] 34.906 100/99 169/168 245/243 352/351
33 ⟨⟨ 3 0 -6 21 -15 -7 -18 23 -35 -14 49 -35 80 -20 -130 ]] 35.433 64/63 126/125 144/143 196/195
34 ⟨⟨ 17 18 20 56 5 -11 -16 30 -55 -4 68 -55 88 -60 -190 ]] 35.582 126/125 176/175 196/195 13013/12960
35 ⟨⟨ 3 0 -6 21 12 -7 -18 23 8 -14 49 28 80 56 -36 ]] 36.487 64/63 78/77 91/90 126/125
36 ⟨⟨ 29 45 23 86 -1 4 -45 36 -109 -73 44 -169 162 -88 -322 ]] 36.611 352/351 540/539 1575/1573 4375/4374
37 ⟨⟨ 6 0 15 15 24 -14 7 3 16 35 35 56 -10 12 28 ]] 37.026 56/55 78/77 128/125 325/324
38 ⟨⟨ 0 0 0 27 0 0 0 43 0 0 63 0 76 0 -100 ]] 37.047 64/63 91/90 126/125 169/168
39 ⟨⟨ 8 18 11 47 -4 10 -5 47 -36 -25 47 -76 94 -52 -188 ]] 37.112 176/175 196/195 245/243 512/507
40 ⟨⟨ 6 0 -12 15 -3 -14 -36 3 -27 -28 35 -7 84 36 -66 ]] 37.181 64/63 78/77 126/125 144/143
41 ⟨⟨ 1 9 -2 -11 -14 12 -6 -21 -26 -30 -57 -66 -24 -32 -8 ]] 37.212 56/55 64/63 78/77 245/243
42 ⟨⟨ 0 0 0 0 27 0 0 0 43 0 0 63 0 76 94 ]] 37.226 56/55 64/63 100/99 245/243
43 ⟨⟨ 10 9 7 -2 -5 -9 -17 -38 -45 -9 -36 -45 -30 -40 -10 ]] 37.726 56/55 78/77 100/99 640/637
44 ⟨⟨ 20 18 14 50 17 -18 -34 10 -47 -18 54 -27 92 -4 -126 ]] 37.854 126/125 169/168 176/175 540/539
45 ⟨⟨ 21 27 12 39 3 -6 -40 -11 -73 -48 -3 -93 68 -36 -134 ]] 38.042 144/143 351/350 441/440 975/968
46 ⟨⟨ 25 36 31 76 1 -1 -21 34 -91 -29 52 -131 106 -112 -278 ]] 38.133 196/195 352/351 1001/1000 4375/4374
47 ⟨⟨ 36 54 36 117 9 2 -44 61 -119 -68 85 -179 204 -108 -402 ]] 38.278 352/351 1001/1000 1716/1715 4375/4374
48 ⟨⟨ 14 18 -1 35 -7 -4 -41 7 -63 -53 19 -83 102 -16 -154 ]] 38.614 144/143 176/175 243/242 1040/1029
49 ⟨⟨ 18 27 18 45 -9 1 -22 9 -81 -34 11 -121 64 -92 -198 ]] 38.711 144/143 196/195 243/242 4375/4356
50 ⟨⟨ 33 54 42 96 24 9 -26 38 -84 -54 36 -144 124 -88 -272 ]] 39.392 325/324 441/440 1001/1000 10985/10976
51 ⟨⟨ 5 -9 -10 -1 -16 -26 -30 -19 -44 2 29 -4 32 -8 -52 ]] 39.705 56/55 64/63 78/77 507/500
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