List of 22et rank two temperaments by complexity

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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