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

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

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

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

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

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

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

List of 27edo rank two temperaments by badness

Contents