List of 27edo rank two temperaments by badness

From TD Xenharmonic Wiki
Jump to navigation Jump to search

Below are listed rank-two 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 badness.

5-limit temperaments with badness below 0.1[edit]

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

Rank Wedgie Name Badness Commas
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 with badness below 0.06[edit]

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

Rank Wedgie Name Badness Commas
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 with badness below 0.05[edit]

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 Commas
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 with badness below 0.05[edit]

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

Rank Wedgie Name Badness Commas
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 with badness below 0.04[edit]

Listed is the wedgie and the TE badness times 1000 for 19 27edo patent val temperaments with badness less than 0.05.

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 with badness below 0.04[edit]

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

Rank Wedgie Name Badness Commas
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
Retrieved from "https://tdxen.replit.app/index.php?title=List_of_27edo_rank_two_temperaments_by_badness&oldid=21077"