List of edo-distinct 41et rank two temperaments

The temperaments listed are 41edo-distinct, meaning that they are all different even if tuned in 41edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

#	Wedgie	Name	Complexity	Comma list
1	⟨⟨1 -8 -15]]	Helmholtz	3.103	32805/32768
2	⟨⟨2 25 35]]	Hemififths	8.326	858993459200/847288609443
3	⟨⟨3 17 20]]	Rodan	5.377	131072000/129140163
4	⟨⟨4 9 5]]	Tetracot	2.783	20000/19683
5	⟨⟨5 1 -10]]	Magic	2.417	3125/3072
6	⟨⟨6 -7 -25]]	Ampersand	4.815	34171875/33554432
7	⟨⟨7 -15 -40]]	Merman	7.733	1121008359375/1099511627776
8	⟨⟨8 -23 -55]]	Quadla-quadbiyo	10.754	36774679229296875/36028797018963968
9	⟨⟨9 10 -5]]	Shibboleth	4.189	1953125/1889568
10	⟨⟨31 39 -10]]	Sathiweyo	14.967	4656612873077392578125/4149816476691431697408
11	⟨⟨11 -6 -35]]	Septimin	6.959	35595703125/34359738368
12	⟨⟨29 14 -45]]	Lala-tweneyo	13.174	186264514923095703125/168285760985348702208
13	⟨⟨13 19 0]]	Bohpier	6.689	1220703125/1162261467
14	⟨⟨14 11 -15]]	Quasitemp	6.247	6103515625/5804752896
15	⟨⟨26 -3 -65]]	Quadla-thebiyo	13.937	40233135223388671875/36893488147419103232
16	⟨⟨16 -5 -45]]	Alphorn	9.239	37078857421875/35184372088832
17	⟨⟨17 28 5]]	Slendi	9.351	24414062500000/22876792454961
18	⟨⟨23 21 -20]]	Twetheyo	10.359	11920928955078125/10968475320188928
19	⟨⟨19 12 -25]]	Barbad	8.496	19073486328125/17832200896512
20	⟨⟨21 -4 -55]]	Quadla-septriyo	11.574	38623809814453125/36028797018963968

7-limit temperaments

#	Wedgie	Name	Complexity	Comma list
1	⟨⟨1 -8 -14 -15 -25 -10]]	Garibaldi	3.823	225/224 3125/3087
2	⟨⟨2 25 13 35 15 -40]]	Hemififths	6.812	2401/2400 5120/5103
3	⟨⟨3 17 -1 20 -10 -50]]	Rodan	5.012	245/243 1029/1024
4	⟨⟨4 9 26 5 30 35]]	Bunya	5.527	225/224 15625/15309
5	⟨⟨5 1 12 -10 5 25]]	Magic	2.937	225/224 245/243
6	⟨⟨6 -7 -2 -25 -20 15]]	Miracle	3.991	225/224 1029/1024
7	⟨⟨7 26 25 25 20 -15]]	Pluto	7.022	4000/3969 10976/10935
8	⟨⟨8 18 11 10 -5 -25]]	Octacot	4.551	245/243 2401/2400
9	⟨⟨9 10 -3 -5 -30 -35]]	Superkleismic	4.620	875/864 1029/1024
10	⟨⟨10 2 -17 -20 -55 -45]]	Hocum	7.155	3125/3072 4000/3969
11	⟨⟨11 -6 10 -35 -15 40]]	Septimin	5.874	225/224 84035/82944
12	⟨⟨12 27 37 15 25 10]]	Dodecacot	8.334	3125/3087 10976/10935
13	⟨⟨13 19 23 0 0 0]]	Bohpier	5.793	245/243 3125/3087
14	⟨⟨14 11 9 -15 -25 -10]]	Quasitemp	5.185	875/864 2401/2400
15	⟨⟨15 3 -5 -30 -50 -20]]	Trismegistus	7.030	1029/1024 3125/3072
16	⟨⟨16 -5 22 -45 -10 65]]	Alphorn	8.386	225/224 5764801/5668704
17	⟨⟨17 28 8 5 -35 -60]]	Slendi	8.337	4000/3969 84035/82944
18	⟨⟨18 20 35 -10 5 25]]	Superthird	7.979	245/243 78125/76832
19	⟨⟨19 12 21 -25 -20 15]]	Barbad	7.048	875/864 16875/16807
20	⟨⟨20 4 7 -40 -45 5]]	Quadrimage	8.056	2401/2400 3125/3072

11-limit temperaments

#	Wedgie	Name	Complexity	Comma list
1	⟨⟨1 -8 -14 -18 -15 -25 -32 -10 -14 -2]]	Andromeda	3.897	100/99 225/224 245/242
2	⟨⟨2 -16 13 5 -30 15 1 75 67 -31]]	Salsa	6.022	243/242 245/242 385/384
3	⟨⟨3 17 -1 28 20 -10 34 -50 6 82]]	Varan	5.714	100/99 245/243 2835/2816
4	⟨⟨4 9 26 10 5 30 2 35 -8 -62]]	Bunya	4.833	100/99 225/224 243/242
5	⟨⟨5 1 12 -8 -10 5 -30 25 -22 -64]]	Magic	3.715	100/99 225/224 245/243
6	⟨⟨6 -7 -2 15 -25 -20 3 15 59 49]]	Miracle	4.405	225/224 243/242 441/440
7	⟨⟨7 -15 -16 -3 -40 -45 -29 5 45 47]]	Merman	6.311	225/224 441/440 1344/1331
8	⟨⟨8 18 11 20 10 -5 4 -25 -16 18]]	Octacot	4.070	100/99 243/242 245/242
9	⟨⟨9 10 -3 2 -5 -30 -28 -35 -30 16]]	Superkleismic	4.137	100/99 245/242 385/384
10	⟨⟨10 2 24 25 -20 10 5 50 51 -13]]	Hocus	5.497	225/224 243/242 245/242
11	⟨⟨11 -6 10 7 -35 -15 -27 40 37 -15]]	Septimin	5.089	225/224 245/242 385/384
12	⟨⟨12 -14 -4 -11 -50 -40 -59 30 23 -17]]	Hemimiracle	7.207	225/224 245/242 1029/1024
13	⟨⟨13 19 23 12 0 0 -26 0 -38 -46]]	Bohpier	5.298	100/99 245/243 1344/1331
14	⟨⟨14 11 9 35 -15 -25 7 -10 43 67]]	Quato	5.844	243/242 441/440 625/616
15	⟨⟨15 3 -5 17 -30 -50 -25 -20 29 65]]	Trismegistus	6.319	385/384 441/440 625/616
16	⟨⟨16 -5 22 -1 -45 -10 -57 65 15 -79]]	Alphorn	7.744	225/224 385/384 12250/11979
17	⟨⟨17 28 8 22 5 -35 -24 -60 -46 34]]	Slendi	7.223	100/99 245/242 46656/46585
18	⟨⟨18 20 35 4 -10 5 -56 25 -60 -110]]	Superthird	8.196	100/99 245/243 78125/76832
19	⟨⟨19 12 21 27 -25 -20 -23 15 21 3]]	Barbad	6.192	245/242 540/539 625/616
20	⟨⟨20 4 7 9 -40 -45 -55 5 7 1]]	Quadrimage	7.054	245/242 385/384 625/616

13-limit temperaments

#	Wedgie	Name	Complexity	Comma list
1	⟨⟨1 -8 -14 -18 -21 -15 -25 -32 -37 -10 -14 -19 -2 -7 -6]]	Andromeda	3.911	100/99 105/104 196/195 245/242
2	⟨⟨2 -16 13 5 -1 -30 15 1 -9 75 67 57 -31 -51 -22]]	Salsa	5.392	105/104 144/143 243/242 245/242
3	⟨⟨3 17 -1 28 19 20 -10 34 19 -50 6 -19 82 57 -38]]	Varan	5.210	100/99 105/104 245/243 352/351
4	⟨⟨4 9 -15 10 -2 5 -35 2 -18 -60 -8 -38 80 50 -44]]	Monkey	4.761	100/99 105/104 144/143 243/242
5	⟨⟨5 1 12 -8 18 -10 5 -30 10 25 -22 38 -64 6 92]]	Magic	3.967	100/99 105/104 144/143 196/195
6	⟨⟨6 -7 -2 15 -3 -25 -20 3 -27 15 59 19 49 -1 -66]]	Miraculous	4.061	105/104 144/143 196/195 275/273
7	⟨⟨7 26 25 38 17 25 20 36 1 -15 -2 -57 20 -45 -82]]	Plutino	6.266	100/99 196/195 245/242 729/728
8	⟨⟨8 18 11 20 37 10 -5 4 29 -25 -16 19 18 63 54]]	Octopod	4.827	100/99 105/104 243/242 245/242
9	⟨⟨9 10 -3 2 16 -5 -30 -28 -8 -35 -30 0 16 56 48]]	Superkleismic	3.957	100/99 105/104 245/242 1188/1183
10	⟨⟨10 2 24 25 36 -20 10 5 20 50 51 76 -13 12 32]]	Hocus	5.741	105/104 196/195 243/242 245/242
11	⟨⟨11 -6 10 7 15 -35 -15 -27 -17 40 37 57 -15 5 26]]	Septimin	4.706	105/104 144/143 196/195 245/242
12	⟨⟨12 -14 -4 -11 -6 -50 -40 -59 -54 30 23 38 -17 -2 20]]	Hemimiracle	6.475	105/104 196/195 245/242 512/507
13	⟨⟨13 19 23 12 14 0 0 -26 -26 0 -38 -38 -46 -46 4]]	Bohpier	4.857	100/99 144/143 245/243 275/273
14	⟨⟨14 11 9 35 34 -15 -25 7 2 -10 43 38 67 62 -12]]	Quato	5.669	105/104 243/242 275/273 325/324
15	⟨⟨15 3 -5 17 13 -30 -50 -25 -35 -20 29 19 65 55 -18]]	Trismegistus	5.670	105/104 144/143 275/273 625/616
16	⟨⟨16 36 22 40 33 20 -10 8 -7 -50 -32 -57 36 11 -34]]	Dificot	7.283	100/99 243/242 245/242 343/338
17	⟨⟨17 28 8 22 12 5 -35 -24 -44 -60 -46 -76 34 4 -40]]	Slendi	6.716	100/99 144/143 245/242 343/338
18	⟨⟨18 20 35 4 32 -10 5 -56 -16 25 -60 0 -110 -40 96]]	Superthird	7.416	100/99 144/143 196/195 1375/1352
19	⟨⟨19 12 21 27 11 -25 -20 -23 -53 15 21 -19 3 -47 -62]]	Barbad	5.903	144/143 196/195 245/242 275/273
20	⟨⟨20 4 7 9 31 -40 -45 -55 -25 5 7 57 1 61 74]]	Quadrimage	6.821	105/104 144/143 245/242 625/616