List of 19et rank two temperaments by badness

Below are listed rank-two temperaments supported by the 19edo patent val, below the indicated cutoff in TE badness.

See also List of 19et rank two temperaments by complexity.

5-limit temperaments

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

#	Wedgie	Name	Badness	Comma list
1	⟨⟨ 1 4 4 ]]	Meantone	7.381	81/80
2	⟨⟨ 6 5 -6 ]]	Hanson	13.234	15625/15552
3	⟨⟨ 7 9 -2 ]]	Sensipent	35.22	78732/78125
4	⟨⟨ 5 1 -10 ]]	Magic	39.163	3125/3072
5	⟨⟨ 51 52 -36 ]]	Egads	41.819	[-36 -52 51⟩
6	⟨⟨ 13 14 -8 ]]	Parakleismic	43.279	1224440064/1220703125
7	⟨⟨ 19 19 -14 ]]	Enneadecal	47.845	19073486328125/19042491875328
8	⟨⟨ 4 -3 -14 ]]	Negri	86.856	16875/16384

7-limit temperaments

Listed is the wedgie and the TE badness times 1000 for 18 temperaments with badness less than 0.06.

#	Wedgie	Name	Badness	Commas
1	⟨⟨ 19 19 57 -14 37 79 ]]	Enneadecal	10.954	4375/4374 703125/702464
2	⟨⟨ 1 4 10 4 13 12 ]]	Meantone	13.707	81/80 126/125
3	⟨⟨ 5 1 12 -10 5 25 ]]	Magic	18.918	225/224 245/243
4	⟨⟨ 6 5 22 -6 18 37 ]]	Catakleismic	21.501	225/224 4375/4374
5	⟨⟨ 7 9 13 -2 1 5 ]]	Sensi	25.622	126/125 245/243
6	⟨⟨ 4 -3 2 -14 -8 13 ]]	Negri	26.483	49/48 225/224
7	⟨⟨ 2 8 1 8 -4 -20 ]]	Godzilla	26.747	49/48 81/80
8	⟨⟨ 6 5 3 -6 -12 -7 ]]	Keemun	27.408	49/48 126/125
9	⟨⟨ 13 14 35 -8 19 42 ]]	Parakleismic	27.431	3136/3125 4375/4374
10	⟨⟨ 1 4 -9 4 -17 -32 ]]	Flattone	38.553	81/80 525/512
11	⟨⟨ 8 13 23 2 14 17 ]]	Unicorn	40.913	126/125 10976/10935
12	⟨⟨ 3 12 11 12 9 -8 ]]	Liese	46.706	81/80 686/675
13	⟨⟨ 12 10 25 -12 6 30 ]]	Clyde	47.261	245/243 3136/3125
14	⟨⟨ 14 18 45 -4 32 54 ]]	Subpental	54.303	3136/3125 19683/19600
15	⟨⟨ 32 33 92 -22 56 121 ]]	Acrokleismic	56.184	4375/4374 2202927104/2197265625
16	⟨⟨ 5 1 -7 -10 -25 -19 ]]	Muggles	56.206	126/125 525/512
17	⟨⟨ 7 9 32 -2 31 49 ]]	Sensei	59.218	225/224 78732/78125
18	⟨⟨ 3 -7 -8 -18 -21 1 ]]	Triton	59.245	225/224 1029/1000

11-limit temperaments

Listed is the wedgie and the TE badness times 1000 for 28 temperaments with badness less than 0.05.

#	Wedgie	Name	Badness	Comma list
1	⟨⟨ 5 1 12 -8 -10 5 -30 25 -22 -64 ]]	Magic	20.352	100/99 225/224 245/243
2	⟨⟨ 1 4 10 6 4 13 6 12 0 -18 ]]	Meanenneadecal	21.423	45/44 56/55 81/80
3	⟨⟨ 1 4 10 -13 4 13 -24 12 -44 -71 ]]	Meanpop	21.543	81/80 126/125 540/539
4	⟨⟨ 6 5 22 -21 -6 18 -54 37 -66 -135 ]]	Catakleismic	21.849	225/224 385/384 4375/4374
5	⟨⟨ 4 -3 2 5 -14 -8 -6 13 22 7 ]]	Negri	26.190	45/44 49/48 56/55
6	⟨⟨ 6 5 3 -2 -6 -12 -24 -7 -22 -16 ]]	Keemun	27.410	49/48 56/55 100/99
7	⟨⟨ 7 9 13 4 -2 1 -18 5 -22 -34 ]]	Sensis	28.680	56/55 100/99 245/243
8	⟨⟨ 2 8 1 12 8 -4 12 -20 0 30 ]]	Godzilla	28.947	45/44 49/48 81/80
9	⟨⟨ 1 4 -9 6 4 -17 6 -32 0 48 ]]	Flattone	33.839	45/44 81/80 385/384
10	⟨⟨ 2 8 1 -7 8 -4 -18 -20 -44 -23 ]]	Baragon	35.673	49/48 56/55 81/80
11	⟨⟨ 0 0 0 19 0 0 30 0 44 53 ]]	Undevigintone	36.387	49/48 81/80 126/125
12	⟨⟨ 32 33 92 -74 -22 56 -228 121 -286 -526 ]]	Acrokleismic	36.878	4375/4374 41503/41472 172032/171875
13	⟨⟨ 7 9 13 -15 -2 1 -48 5 -66 -87 ]]	Sensor	37.942	126/125 245/243 385/384
14	⟨⟨ 4 -3 2 -14 -14 -8 -36 13 -22 -46 ]]	Negril	38.679	49/48 100/99 225/224
15	⟨⟨ 8 13 23 -9 2 14 -42 17 -66 -105 ]]	Alicorn	39.156	126/125 540/539 896/891
16	⟨⟨ 5 1 12 11 -10 5 0 25 22 -11 ]]	Horcrux	39.282	45/44 56/55 245/243
17	⟨⟨ 38 38 114 -95 -28 74 -282 158 -352 -661 ]]		39.701	4375/4374 41503/41472 703125/702464
18	⟨⟨ 6 5 3 17 -6 -12 6 -7 22 37 ]]	Qeema	40.056	45/44 49/48 126/125
19	⟨⟨ 3 12 11 -1 12 9 -12 -8 -44 -41 ]]	Liesel	40.721	56/55 81/80 540/539
20	⟨⟨ 13 14 35 -17 -8 19 -72 42 -88 -169 ]]	Paradigmic	41.720	540/539 896/891 3136/3125
21	⟨⟨ 19 19 57 -38 -14 37 -126 79 -154 -304 ]]	Enneadecal	43.734	540/539 4375/4374 16384/16335
22	⟨⟨ 6 5 22 -2 -6 18 -24 37 -22 -82 ]]	Cataleptic	44.335	100/99 225/224 864/847
23	⟨⟨ 14 18 45 -30 -4 32 -96 54 -132 -240 ]]	Subpental	45.352	540/539 3136/3125 8019/8000
24	⟨⟨ 3 -7 -8 -1 -18 -21 -12 1 22 25 ]]	Triton	45.675	45/44 56/55 1029/1000
25	⟨⟨ 12 10 25 -23 -12 6 -78 30 -88 -151 ]]	Clyde	47.417	245/243 385/384 3136/3125
26	⟨⟨ 5 1 -7 11 -10 -25 0 -19 22 55 ]]	Muggles	48.038	45/44 126/125 385/384
27	⟨⟨ 2 8 20 -7 8 26 -18 24 -44 -89 ]]		49.303	81/80 126/125 864/847
28	⟨⟨ 13 14 35 -36 -8 19 -102 42 -132 -222 ]]	Parakleismic	49.711	385/384 3136/3125 4375/4374

13-limit temperaments

Listed is the wedgie and the TE badness times 1000 for 46 temperaments with badness less than 0.04.

#	Wedgie	Name	Badness	Comma list
1	⟨⟨ 6 5 22 -21 14 -6 18 -54 0 37 -66 14 -135 -42 126 ]]	Catakleismic	16.883	169/168 225/224 325/324 385/384
2	⟨⟨ 4 -3 2 5 3 -14 -8 -6 -10 13 22 18 7 1 -8 ]]	Negri	17.833	45/44 49/48 56/55 78/77
3	⟨⟨ 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
4	⟨⟨ 1 4 10 -13 15 4 13 -24 20 12 -44 20 -71 5 100 ]]	Meanpop	20.883	81/80 105/104 144/143 196/195
5	⟨⟨ 1 4 10 6 15 4 13 6 20 12 0 20 -18 5 30 ]]	Meanenneadecal	21.182	45/44 56/55 78/77 81/80
6	⟨⟨ 5 1 12 -8 18 -10 5 -30 10 25 -22 38 -64 6 92 ]]	Magic	21.509	100/99 105/104 144/143 196/195
7	⟨⟨ 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
8	⟨⟨ 2 8 1 12 11 8 -4 12 10 -20 0 -4 30 27 -6 ]]	Godzilla	22.503	45/44 49/48 78/77 81/80
9	⟨⟨ 6 5 3 -2 14 -6 -12 -24 0 -7 -22 14 -16 28 56 ]]	Kema	22.749	49/48 56/55 91/90 100/99
10	⟨⟨ 0 0 0 19 0 0 0 30 0 0 44 0 53 0 -70 ]]	Undevigintone	22.933	49/48 65/64 81/80 91/90
11	⟨⟨ 8 13 23 -9 25 2 14 -42 10 17 -66 10 -105 -15 120 ]]	Alicorn	23.667	126/125 144/143 196/195 676/675
12	⟨⟨ 4 -3 2 -14 3 -14 -8 -36 -10 13 -22 18 -46 1 62 ]]	Negril	24.383	49/48 65/64 91/90 875/858
13	⟨⟨ 1 4 10 6 -4 4 13 6 -10 12 0 -24 -18 -48 -36 ]]	Vincenzo	24.763	45/44 56/55 65/64 81/80
14	⟨⟨ 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
15	⟨⟨ 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
16	⟨⟨ 2 8 1 -7 11 8 -4 -18 10 -20 -44 -4 -23 27 64 ]]		26.703	49/48 56/55 81/80 91/90
17	⟨⟨ 3 12 11 -1 7 12 9 -12 0 -8 -44 -28 -41 -21 28 ]]	Liesel	27.304	56/55 78/77 81/80 91/90
18	⟨⟨ 6 5 22 -2 14 -6 18 -24 0 37 -22 14 -82 -42 56 ]]	Cataleptic	27.343	78/77 100/99 144/143 676/675
19	⟨⟨ 1 4 10 -13 -4 4 13 -24 -10 12 -44 -24 -71 -48 34 ]]	Meanplop	27.666	65/64 81/80 126/125 169/165
20	⟨⟨ 6 5 3 17 14 -6 -12 6 0 -7 22 14 37 28 -14 ]]	Qeema	29.419	45/44 49/48 78/77 126/125
21	⟨⟨ 6 5 3 -2 -5 -6 -12 -24 -30 -7 -22 -30 -16 -25 -10 ]]	Keemun	29.749	49/48 56/55 78/77 100/99
22	⟨⟨ 5 1 -7 11 -1 -10 -25 0 -20 -19 22 -6 55 23 -44 ]]	Muggles	30.386	45/44 65/64 78/77 126/125
23	⟨⟨ 2 8 20 -7 11 8 26 -18 10 24 -44 -4 -89 -43 64 ]]		30.438	78/77 126/125 144/143 676/675
24	⟨⟨ 5 1 12 11 18 -10 5 0 10 25 22 38 -11 6 22 ]]	Horcrux	31.938	45/44 56/55 78/77 875/864
25	⟨⟨ 2 8 1 12 -8 8 -4 12 -20 -20 0 -48 30 -26 -72 ]]		32.878	45/44 49/48 65/64 81/80
26	⟨⟨ 12 10 25 -4 28 -12 6 -48 0 30 -44 28 -98 -14 112 ]]		32.989	100/99 144/143 196/195 2197/2187
27	⟨⟨ 5 1 12 11 -1 -10 5 0 -20 25 22 -6 -11 -47 -44 ]]	Glamour	33.317	45/44 56/55 65/64 507/500
28	⟨⟨ 3 -7 -8 -1 -12 -18 -21 -12 -30 1 22 -2 25 -4 -38 ]]		33.858	45/44 56/55 78/77 507/500
29	⟨⟨ 11 6 15 -10 13 -16 -7 -54 -20 18 -44 8 -80 -19 82 ]]	Sycamore	34.295	91/90 100/99 169/168 385/384
30	⟨⟨ 1 4 -9 25 -4 4 -17 36 -10 -32 44 -24 101 22 -106 ]]		34.640	65/64 81/80 105/104 625/616
31	⟨⟨ 2 8 1 -7 -8 8 -4 -18 -20 -20 -44 -48 -23 -26 -2 ]]		35.063	49/48 56/55 65/64 81/80
32	⟨⟨ 5 1 -7 -8 -1 -10 -25 -30 -20 -19 -22 -6 2 23 26 ]]		35.188	56/55 65/64 100/99 105/104
33	⟨⟨ 0 0 0 0 19 0 0 0 30 0 0 44 0 53 66 ]]		35.286	45/44 49/48 56/55 81/80
34	⟨⟨ 13 14 35 -17 24 -8 19 -72 -10 42 -88 4 -169 -62 146 ]]	Paradigmic	35.781	169/168 325/324 540/539 832/825
35	⟨⟨ 3 12 11 18 7 12 9 18 0 -8 0 -28 12 -21 -42 ]]	Lisa	36.144	45/44 81/80 91/88 147/143
36	⟨⟨ 11 6 15 9 13 -16 -7 -24 -20 18 0 8 -27 -19 12 ]]		37.127	56/55 78/77 91/90 125/121
37	⟨⟨ 10 2 24 -16 17 -20 10 -60 -10 50 -44 32 -128 -41 118 ]]		37.146	100/99 169/168 225/224 245/243
38	⟨⟨ 6 5 3 17 -5 -6 -12 6 -30 -7 22 -30 37 -25 -80 ]]		37.435	45/44 49/48 65/64 126/125
39	⟨⟨ 3 -7 11 -1 7 -18 9 -12 0 45 22 42 -41 -21 28 ]]		37.666	45/44 65/64 78/77 245/243
40	⟨⟨ 1 4 -9 -13 -4 4 -17 -24 -10 -32 -44 -24 -5 22 34 ]]		37.680	56/55 65/64 81/80 105/104
41	⟨⟨ 7 9 13 4 29 -2 1 -18 20 5 -22 34 -34 33 86 ]]		38.025	56/55 100/99 105/104 245/243
42	⟨⟨ 2 -11 1 -7 -8 -22 -4 -18 -20 33 22 22 -23 -26 -2 ]]		38.389	45/44 49/48 78/77 896/891
43	⟨⟨ 3 -7 -8 -1 7 -18 -21 -12 0 1 22 42 25 49 28 ]]		38.573	45/44 56/55 65/64 1323/1280
44	⟨⟨ 8 13 23 10 25 2 14 -12 10 17 -22 10 -52 -15 50 ]]		39.090	56/55 78/77 100/99 729/715
45	⟨⟨ 8 13 4 10 6 2 -16 -12 -20 -27 -22 -34 14 2 -16 ]]	Rhinoceros	39.343	49/48 78/77 100/99 126/121
46	⟨⟨ 7 9 13 23 10 -2 1 12 -10 5 22 -10 19 -20 -50 ]]		39.653	45/44 91/88 126/125 147/143