List of 22et rank two temperaments by badness

Below are listed rank-2 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 badness times 1000 for six temperaments with badness less than 0.1.

#	Wedgie	Name	Badness	Comma list
1	⟨⟨ 16 -10 -53 ]]	Kwazy	14.091	9010162353515625/9007199254740992
2	⟨⟨ 2 -4 -11 ]]	Srutal	19.915	2048/2025
3	⟨⟨ 3 5 1 ]]	Porcupine	30.778	250/243
4	⟨⟨ 5 1 -10 ]]	Magic	39.163	3125/3072
5	⟨⟨ 7 -3 -21 ]]	Orson	40.807	2109375/2097152
6	⟨⟨ 9 -7 -32 ]]	Escapade	83.778	4294967296/4271484375

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE badness times 1000 for 14 temperaments with badness less than 0.06.

#	Wedgie	Name	Badness	Comma list
1	⟨⟨ 5 1 12 -10 5 25 ]]	Magic	18.918	225/224 245/243
2	⟨⟨ 2 -4 -4 -11 -12 2 ]]	Pajara	20.033	50/49 64/63
3	⟨⟨ 7 -3 8 -21 -7 27 ]]	Orwell	20.735	225/224 1728/1715
4	⟨⟨ 23 -13 42 -74 2 134 ]]	Fifthplus	25.840	65625/65536 420175/419904
5	⟨⟨ 1 9 -2 12 -6 -30 ]]	Superpyth	32.318	64/63 245/243
6	⟨⟨ 12 -2 20 -31 -2 52 ]]	Wizard	40.846	225/224 118098/117649
7	⟨⟨ 3 5 -6 1 -18 -28 ]]	Porcupine	41.057	64/63 250/243
8	⟨⟨ 11 -11 22 -43 4 82 ]]	Hendecatonic	41.081	6144/6125 10976/10935
9	⟨⟨ 8 6 6 -9 -13 -3 ]]	Doublewide	43.462	50/49 875/864
10	⟨⟨ 6 10 10 2 -1 -5 ]]	Hedgehog	43.983	50/49 245/243
11	⟨⟨ 4 -8 14 -22 11 55 ]]	Shrutar	47.377	245/243 2048/2025
12	⟨⟨ 3 5 16 1 17 23 ]]	Porky	54.389	225/224 250/243
13	⟨⟨ 6 -12 10 -33 -1 57 ]]	Echidna	58.033	1728/1715 2048/2025
14	⟨⟨ 18 -14 30 -64 -3 109 ]]	Septisuperfourth	59.241	6144/6125 118098/117649

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 38 temperaments with badness less than 0.05.

#	Wedgie	Name	Badness	Comma list
1	⟨⟨ 7 -3 8 2 -21 -7 -21 27 15 -22 ]]	Orwell	15.231	99/98 121/120 176/175
2	⟨⟨ 12 -2 20 -6 -31 -2 -51 52 -7 -86 ]]	Wizard	18.539	225/224 385/384 4000/3993
3	⟨⟨ 2 -4 -4 -12 -11 -12 -26 2 -14 -20 ]]	Pajara	20.343	50/49 64/63 99/98
4	⟨⟨ 5 1 12 -8 -10 5 -30 25 -22 -64 ]]	Magic	20.352	100/99 225/224 245/243
5	⟨⟨ 3 5 -6 4 1 -18 -4 -28 -8 32 ]]	Porcupine	21.562	55/54 64/63 100/99
6	⟨⟨ 6 10 10 8 2 -1 -8 -5 -16 -12 ]]	Hedgehog	23.095	50/49 55/54 99/98
7	⟨⟨ 18 -14 30 -20 -64 -3 -94 109 2 -160 ]]	Septisuperfourth	24.619	540/539 4000/3993 5632/5625
8	⟨⟨ 1 9 -2 16 12 -6 22 -30 6 52 ]]	Superpyth	24.976	64/63 100/99 245/243
9	⟨⟨ 6 -12 10 -14 -33 -1 -43 57 9 -74 ]]	Echidna	25.987	176/175 540/539 896/891
10	⟨⟨ 4 -8 14 -2 -22 11 -17 55 23 -54 ]]	Shrutar	26.489	121/120 176/175 245/243
11	⟨⟨ 5 1 12 14 -10 5 5 25 29 -2 ]]	Telepathy	27.109	55/54 99/98 176/175
12	⟨⟨ 3 5 16 4 1 17 -4 23 -8 -44 ]]	Porky	27.268	55/54 100/99 225/224
13	⟨⟨ 46 -26 84 -34 -148 4 -213 268 11 -386 ]]		27.785	9801/9800 41503/41472 65625/65536
14	⟨⟨ 2 -4 -4 10 -11 -12 9 2 37 42 ]]	Pajarous	28.349	50/49 55/54 64/63
15	⟨⟨ 34 -24 64 -28 -117 6 -162 216 18 -300 ]]		28.943	5632/5625 9801/9800 41503/41472
16	⟨⟨ 8 6 6 -4 -9 -13 -34 -3 -30 -32 ]]	Doublewide	32.058	50/49 99/98 875/864
17	⟨⟨ 16 -10 34 -8 -53 9 -68 107 16 -140 ]]	Bisupermajor	32.080	385/384 3388/3375 9801/9800
18	⟨⟨ 1 -13 -2 -6 -23 -6 -13 32 31 -10 ]]	Quasisupra	32.203	64/63 99/98 121/120
19	⟨⟨ 1 9 -2 -6 12 -6 -13 -30 -45 -10 ]]	Suprapyth	32.768	55/54 64/63 99/98
20	⟨⟨ 8 6 6 18 -9 -13 1 -3 21 30 ]]	Fleetwood	35.202	50/49 55/54 176/175
21	⟨⟨ 9 -7 26 -10 -32 16 -47 80 1 -118 ]]	Sensa	35.844	245/243 385/384 4000/3993
22	⟨⟨ 10 2 24 6 -20 10 -25 50 7 -66 ]]	Divination	35.864	121/120 225/224 245/243
23	⟨⟨ 9 -7 4 -10 -32 -19 -47 29 1 -42 ]]		36.700	99/98 176/175 2560/2541
24	⟨⟨ 11 -11 22 -22 -43 4 -73 82 -13 -138 ]]		38.042	540/539 896/891 4375/4356
25	⟨⟨ 4 -8 -8 -2 -22 -24 -17 4 23 22 ]]	Hemipaj	38.890	50/49 64/63 121/120
26	⟨⟨ 10 2 2 6 -20 -25 -25 -1 7 10 ]]	Astrology	39.151	50/49 121/120 176/175
27	⟨⟨ 19 -5 28 -4 -52 -9 -72 79 8 -108 ]]		40.603	225/224 385/384 43923/43750
28	⟨⟨ 13 7 18 10 -19 -8 -29 22 -1 -34 ]]		41.282	99/98 121/120 625/616
29	⟨⟨ 30 -16 50 -26 -95 -5 -145 161 -5 -246 ]]		42.972	540/539 4000/3993 65625/65536
30	⟨⟨ 13 -15 18 -12 -54 -8 -64 84 24 -96 ]]		43.309	176/175 540/539 16384/16335
31	⟨⟨ 4 14 14 20 13 11 18 -7 -2 8 ]]		45.052	50/49 99/98 2662/2625
32	⟨⟨ 2 -4 18 -12 -11 23 -26 53 -14 -96 ]]		45.270	100/99 385/384 1232/1215
33	⟨⟨ 7 -3 8 -20 -21 -7 -56 27 -36 -84 ]]		45.950	100/99 225/224 1728/1715
34	⟨⟨ 11 -11 22 0 -43 4 -38 82 38 -76 ]]		46.088	121/120 176/175 10976/10935
35	⟨⟨ 5 1 -10 -8 -10 -30 -30 -26 -22 12 ]]		47.379	64/63 100/99 605/588
36	⟨⟨ 28 -12 54 -14 -84 7 -119 159 9 -226 ]]		47.776	385/384 9801/9800 456533/455625
37	⟨⟨ 0 0 0 22 0 0 35 0 51 62 ]]		48.372	50/49 64/63 245/243
38	⟨⟨ 25 -17 38 -18 -85 -10 -115 136 17 -182 ]]		49.466	540/539 5632/5625 35937/35840

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.

#	Wedgie	Name	Badness	Comma list
1	⟨⟨ 7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73 ]]	Orwell	19.718	99/98 121/120 176/175 275/273
2	⟨⟨ 6 10 10 8 12 2 -1 -8 -3 -5 -16 -9 -12 -3 12 ]]	Hedgehog	21.516	50/49 55/54 65/63 99/98
3	⟨⟨ 12 -2 20 -6 -20 -31 -2 -51 -76 52 -7 -39 -86 -130 -47 ]]	Lizard	21.781	225/224 351/350 364/363 385/384
4	⟨⟨ 2 -4 -4 -12 -18 -11 -12 -26 -36 2 -14 -27 -20 -36 -18 ]]	Pajara	22.327	50/49 64/63 99/98 975/968
5	⟨⟨ 7 -3 8 2 3 -21 -7 -21 -21 27 15 18 -22 -21 3 ]]	Blair	23.086	65/64 78/77 91/90 99/98
6	⟨⟨ 6 -12 10 -14 -32 -33 -1 -43 -73 57 9 -30 -74 -127 -59 ]]	Echidna	23.679	176/175 351/350 364/363 540/539
7	⟨⟨ 1 9 -2 16 13 12 -6 22 17 -30 6 -3 52 44 -14 ]]	Superpyth	24.673	64/63 78/77 91/90 100/99
8	⟨⟨ 2 -4 -4 10 4 -11 -12 9 -1 2 37 24 42 26 -23 ]]	Pajarous	25.176	50/49 55/54 64/63 65/63
9	⟨⟨ 5 1 12 -8 -23 -10 5 -30 -55 25 -22 -57 -64 -109 -50 ]]	Necromancy	25.275	100/99 225/224 245/243 275/273
10	⟨⟨ 3 5 -6 4 17 1 -18 -4 16 -28 -8 21 32 70 44 ]]	Porcupinefish	25.314	55/54 64/63 91/90 100/99
11	⟨⟨ 5 1 12 14 -1 -10 5 5 -20 25 29 -6 -2 -47 -55 ]]	Telepathy	25.522	55/54 65/64 91/90 99/98
12	⟨⟨ 5 1 12 -8 -1 -10 5 -30 -20 25 -22 -6 -64 -47 26 ]]	Sorcery	25.829	65/64 78/77 91/90 100/99
13	⟨⟨ 3 5 -6 4 -5 1 -18 -4 -19 -28 -8 -30 32 8 -32 ]]	Porkpie	26.043	55/54 64/63 65/63 100/99
14	⟨⟨ 4 -8 14 -2 -14 -22 11 -17 -37 55 23 -3 -54 -91 -41 ]]	Srutar	26.069	91/90 121/120 176/175 245/243
15	⟨⟨ 3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32 ]]		26.543	55/54 65/64 91/90 100/99
16	⟨⟨ 2 -4 -4 -12 4 -11 -12 -26 -1 2 -14 24 -20 26 58 ]]		27.642	50/49 64/63 65/63 99/98
17	⟨⟨ 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
18	⟨⟨ 0 0 0 0 22 0 0 0 35 0 0 51 0 62 76 ]]		29.849	50/49 55/54 64/63 99/98
19	⟨⟨ 1 -13 -2 -6 -9 -23 -6 -13 -18 32 31 27 -10 -18 -9 ]]		30.219	64/63 78/77 91/90 121/120
20	⟨⟨ 9 -7 26 -10 -37 -32 16 -47 -92 80 1 -60 -118 -200 -91 ]]		31.366	245/243 352/351 385/384 625/624
21	⟨⟨ 8 6 6 18 16 -9 -13 1 -4 -3 21 15 30 23 -11 ]]	Fleetwood	31.835	50/49 55/54 65/63 176/175
22	⟨⟨ 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
23	⟨⟨ 18 -14 30 -20 -52 -64 -3 -94 -149 109 2 -69 -160 -257 -106 ]]		33.038	351/350 364/363 540/539 4096/4095
24	⟨⟨ 16 -10 34 -8 -56 -53 9 -68 -148 107 16 -93 -140 -283 -164 ]]		33.800	352/351 385/384 625/624 4459/4455
25	⟨⟨ 19 -5 28 -4 -39 -52 -9 -72 -132 79 8 -72 -108 -213 -120 ]]		34.251	225/224 351/350 385/384 10648/10647
26	⟨⟨ 10 2 2 6 -2 -20 -25 -25 -40 -1 7 -12 10 -13 -29 ]]		34.376	50/49 65/64 78/77 121/120
27	⟨⟨ 3 5 16 4 17 1 17 -4 16 23 -8 21 -44 -11 44 ]]		35.176	55/54 65/63 100/99 225/224
28	⟨⟨ 9 -7 4 -10 -15 -32 -19 -47 -57 29 1 -9 -42 -57 -15 ]]		35.261	78/77 99/98 176/175 507/500
29	⟨⟨ 4 -8 -8 -2 -14 -22 -24 -17 -37 4 23 -3 22 -10 -41 ]]		35.651	50/49 64/63 78/77 121/120
30	⟨⟨ 1 9 -2 16 35 12 -6 22 52 -30 6 48 52 106 62 ]]		35.982	64/63 100/99 245/243 275/273
31	⟨⟨ 11 -11 22 -22 -55 -43 4 -73 -128 82 -13 -87 -138 -236 -109 ]]		36.112	352/351 364/363 540/539 625/624
32	⟨⟨ 1 9 -2 -6 -9 12 -6 -13 -18 -30 -45 -54 -10 -18 -9 ]]		36.336	55/54 64/63 65/63 364/363
33	⟨⟨ 6 10 10 8 -10 2 -1 -8 -38 -5 -16 -60 -12 -65 -64 ]]		36.358	50/49 55/54 99/98 975/968
34	⟨⟨ 10 2 24 6 -2 -20 10 -25 -40 50 7 -12 -66 -94 -29 ]]		36.588	65/64 91/90 121/120 245/243
35	⟨⟨ 5 1 12 14 21 -10 5 5 15 25 29 45 -2 15 21 ]]		37.533	55/54 65/63 99/98 176/175
36	⟨⟨ 12 -2 20 -6 -42 -31 -2 -51 -111 52 -7 -90 -86 -192 -123 ]]		37.965	225/224 275/273 385/384 4000/3993
37	⟨⟨ 13 7 18 10 -7 -19 -8 -29 -59 22 -1 -42 -34 -86 -61 ]]		38.144	65/64 99/98 121/120 275/273
38	⟨⟨ 13 -15 18 -12 -51 -54 -8 -64 -129 84 24 -63 -96 -210 -132 ]]		39.456	176/175 351/350 540/539 33275/33124
39	⟨⟨ 5 1 -10 -8 -1 -10 -30 -30 -20 -26 -22 -6 12 34 26 ]]		39.703	64/63 65/63 100/99 169/165
40	⟨⟨ 1 -13 -2 -6 -31 -23 -6 -13 -53 32 31 -24 -10 -80 -85 ]]		39.876	64/63 99/98 121/120 275/273