List of edo-distinct 53et rank two temperaments

The temperaments listed are 53edo-distinct, meaning that they are all different even if tuned in 53edo. 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	Commas
1	⟨⟨ 1 -8 -15 ]]	Helmholtz	3.103	32805/32768
2	⟨⟨ 2 37 54 ]]	Monzismic	12.528	[54 -37 2⟩
3	⟨⟨ 3 29 39 ]]	Tricot	9.520	68719476736000/68630377364883
4	⟨⟨ 4 21 24 ]]	Vulture	6.600	10485760000/10460353203
5	⟨⟨ 5 13 9 ]]	Amity	3.970	1600000/1594323
6	⟨⟨ 6 5 -6 ]]	Hanson	2.685	15625/15552
7	⟨⟨ 7 -3 -21 ]]	Orson	4.232	2109375/2097152
8	⟨⟨ 8 -11 -36 ]]	Submajor	6.919	69198046875/68719476736
9	⟨⟨ 9 -19 -51 ]]	Untriton	9.853	2270041927734375/2251799813685248
10	⟨⟨ 10 -27 -66 ]]		12.867	74468725439326171875/73786976294838206464
11	⟨⟨ 11 18 3 ]]	Quartonic	6.026	390625000/387420489
12	⟨⟨ 41 43 -27 ]]		18.85	[-27 -43 41⟩
13	⟨⟨ 13 2 -27 ]]	Ditonic	6.373	1220703125/1207959552
14	⟨⟨ 14 47 42 ]]		14.353	[42 -47 14⟩
15	⟨⟨ 15 -14 -57 ]]	Misneb	11.043	145964630126953125/144115188075855872
16	⟨⟨ 16 31 12 ]]		9.845	625000000000000/617673396283947
17	⟨⟨ 17 23 -3 ]]	Maja	8.443	762939453125/753145430616
18	⟨⟨ 35 38 -21 ]]		16.207	[-21 -38 35⟩
19	⟨⟨ 19 7 -33 ]]	Semaja	8.817	19073486328125/18786186952704
20	⟨⟨ 20 -1 -48 ]]		10.481	286102294921875/281474976710656
21	⟨⟨ 21 44 21 ]]		13.75	1000000000000000000000/984770902183611232881
22	⟨⟨ 31 17 -45 ]]		13.972	4656612873077392578125/4543715546604414959616
23	⟨⟨ 23 28 -9 ]]		10.985	11920928955078125/11712917736940032
24	⟨⟨ 29 33 -15 ]]		13.582	186264514923095703125/182159296644891377664
25	⟨⟨ 25 12 -39 ]]		11.37	298023223876953125/292162779488452608
26	⟨⟨ 27 -4 -69 ]]		14.659	603497028350830078125/590295810358705651712

7-limit temperaments

#	Wedgie	Name	Complexity	Commas
1	⟨⟨ 1 -8 -14 -15 -25 -10 ]]	Garibaldi	3.823	225/224 3125/3087
2	⟨⟨ 2 -16 25 -30 34 103 ]]	Hemischis	9.155	6144/6125 19683/19600
3	⟨⟨ 3 29 11 39 9 -56 ]]	Tricot	7.801	2430/2401 5120/5103
4	⟨⟨ 4 21 -3 24 -16 -66 ]]	Buzzard	6.420	1728/1715 5120/5103
5	⟨⟨ 5 13 -17 9 -41 -76 ]]	Amity	7.127	4375/4374 5120/5103
6	⟨⟨ 6 5 22 -6 18 37 ]]	Catakleismic	4.684	225/224 4375/4374
7	⟨⟨ 7 -3 8 -21 -7 27 ]]	Orwell	3.685	225/224 1728/1715
8	⟨⟨ 8 -11 -6 -36 -32 17 ]]	Submajor	5.869	225/224 51200/50421
9	⟨⟨ 9 -19 -20 -51 -57 7 ]]	Untriton	9.195	225/224 125000000/121060821
10	⟨⟨ 10 26 19 18 2 -29 ]]	Hamity	6.518	2430/2401 4000/3969
11	⟨⟨ 11 18 5 3 -23 -39 ]]	Quartonic	5.395	1728/1715 4000/3969
12	⟨⟨ 12 10 -9 -12 -48 -49 ]]	Hemikleismic	6.704	4000/3969 6144/6125
13	⟨⟨ 13 2 30 -27 11 64 ]]	Coditone	7.512	225/224 2125764/2100875
14	⟨⟨ 14 47 16 42 -14 -95 ]]		12.061	19683/19600 51200/50421
15	⟨⟨ 15 -14 2 -57 -39 44 ]]	Misneb	9.025	225/224 4194304/4117715
16	⟨⟨ 16 31 41 12 20 8 ]]		9.361	3125/3087 19683/19600
17	⟨⟨ 17 23 27 -3 -5 -2 ]]	Maja	7.161	2430/2401 3125/3087
18	⟨⟨ 18 15 13 -18 -30 -12 ]]	Kleiboh	6.645	1728/1715 3125/3087
19	⟨⟨ 19 7 -1 -33 -55 -22 ]]	Semaja	8.139	3125/3087 6144/6125
20	⟨⟨ 20 -1 -15 -48 -80 -32 ]]		10.843	3125/3087 65536/64827
21	⟨⟨ 21 44 24 21 -21 -68 ]]		11.339	4000/3969 839808/823543
22	⟨⟨ 31 17 43 -45 -19 52 ]]		12.262	2430/2401 390625/387072
23	⟨⟨ 23 28 49 -9 13 35 ]]		10.832	4375/4374 78125/76832
24	⟨⟨ 24 20 35 -24 -12 25 ]]		9.340	2430/2401 15625/15552
25	⟨⟨ 25 12 21 -39 -37 15 ]]		9.293	1728/1715 78125/76832
26	⟨⟨ 26 4 7 -54 -62 5 ]]		10.711	6144/6125 78125/76832

11-limit temperaments

#	Wedgie	Name	Complexity	Commas
1	⟨⟨ 1 -8 -14 -30 -15 -25 -51 -10 -42 -36 ]]	Helenus	5.390	99/98 176/175 3125/3087
2	⟨⟨ 2 -16 -28 -7 -30 -50 -18 -20 39 77 ]]	Hemigari	6.723	121/120 225/224 3125/3087
3	⟨⟨ 3 29 11 16 39 9 15 -56 -63 7 ]]	Tricot	6.753	99/98 121/120 5120/5103
4	⟨⟨ 4 21 -3 -14 24 -16 -36 -66 -105 -29 ]]	Buteo	6.975	99/98 385/384 2200/2187
5	⟨⟨ 5 13 -17 9 9 -41 -3 -76 -24 84 ]]	Hitchcock	6.290	121/120 176/175 2200/2187
6	⟨⟨ 6 5 22 32 -6 18 30 37 57 14 ]]	Cataclysmic	5.473	99/98 176/175 2200/2187
7	⟨⟨ 7 -3 8 2 -21 -7 -21 27 15 -22 ]]	Orwell	3.242	99/98 121/120 176/175
8	⟨⟨ 8 -11 -6 -28 -36 -32 -72 17 -27 -58 ]]	Interpental	7.011	99/98 176/175 51200/50421
9	⟨⟨ 9 -19 -20 -5 -51 -57 -39 7 54 55 ]]	Untriton	7.983	121/120 225/224 22000/21609
10	⟨⟨ 10 26 19 18 18 2 -6 -29 -48 -15 ]]	Hamity	5.668	99/98 121/120 4000/3969
11	⟨⟨ 11 18 5 -12 3 -23 -57 -39 -90 -51 ]]	Quartz	6.692	99/98 385/384 4000/3969
12	⟨⟨ 12 10 -9 11 -12 -48 -24 -49 -9 62 ]]	Hemikleismic	5.839	121/120 176/175 4000/3969
13	⟨⟨ 13 2 30 34 -27 11 9 64 72 -8 ]]	Coditonic	7.203	99/98 176/175 6655/6561
14	⟨⟨ 14 -6 -37 4 -42 -98 -42 -69 30 139 ]]		11.245	121/120 4000/3969 4125/4096
15	⟨⟨ 15 -14 2 27 -57 -39 -9 44 111 69 ]]	Musneb	8.909	225/224 385/384 66550/64827
16	⟨⟨ 16 31 41 50 12 20 24 8 9 -1 ]]		8.690	99/98 2662/2625 3125/3087
17	⟨⟨ 17 23 27 20 -3 -5 -27 -2 -33 -37 ]]	Maja	6.299	99/98 121/120 3125/3087
18	⟨⟨ 18 15 13 43 -18 -30 6 -12 48 76 ]]	Kleiboh	7.194	176/175 540/539 3125/3087
19	⟨⟨ 19 7 -1 13 -33 -55 -45 -22 6 40 ]]	Semaja	7.046	121/120 176/175 3125/3087
20	⟨⟨ 20 -1 38 36 -48 4 -12 91 87 -30 ]]		9.738	99/98 176/175 161051/157464
21	⟨⟨ 21 44 24 6 21 -21 -63 -68 -138 -66 ]]		11.170	99/98 4000/3969 9317/9216
22	⟨⟨ 22 36 10 29 6 -46 -30 -78 -57 47 ]]		9.340	121/120 1728/1715 4000/3969
23	⟨⟨ 23 28 49 52 -9 13 3 35 24 -23 ]]		9.720	99/98 2662/2625 4375/4374
24	⟨⟨ 24 20 35 22 -24 -12 -48 25 -18 -59 ]]		8.261	99/98 121/120 78125/76832
25	⟨⟨ 25 12 21 45 -39 -37 -15 15 63 54 ]]		8.873	176/175 540/539 66550/64827
26	⟨⟨ 26 4 7 15 -54 -62 -66 5 21 18 ]]		9.286	121/120 176/175 34375/33614

13-limit temperaments

#	Wedgie	Name	Complexity	Commas
1	⟨⟨ 1 -8 -14 -30 -33 -15 -25 -51 -56 -10 -42 -47 -36 -41 -3 ]]	Helenus	5.812	99/98 176/175 275/273 847/845
2	⟨⟨ 2 -16 -28 -7 -13 -30 -50 -18 -28 -20 39 29 77 67 -19 ]]	Hemigari	6.013	121/120 169/168 225/224 275/273
3	⟨⟨ 3 29 11 16 7 39 9 15 0 -56 -63 -91 7 -21 -35 ]]	Tricot	6.236	99/98 121/120 169/168 352/351
4	⟨⟨ 4 21 -3 -14 27 24 -16 -36 28 -66 -105 -15 -29 87 145 ]]	Buteo	7.137	99/98 275/273 385/384 572/567
5	⟨⟨ 5 13 -17 9 -6 9 -41 -3 -28 -76 -24 -62 84 46 -54 ]]	Hitchcock	5.834	121/120 169/168 176/175 325/324
6	⟨⟨ 6 5 22 32 14 -6 18 30 0 37 57 14 14 -42 -70 ]]	Cataclysmic	4.918	99/98 169/168 176/175 275/273
7	⟨⟨ 7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73 ]]	Orwell	4.717	99/98 121/120 176/175 275/273
8	⟨⟨ 8 -11 -6 25 1 -36 -32 12 -28 17 96 43 91 25 -89 ]]	Submajor	6.305	169/168 225/224 275/273 385/384
9	⟨⟨ 9 -19 -20 -5 -32 -51 -57 -39 -84 7 54 -4 55 -16 -92 ]]	Untriton	8.047	121/120 225/224 275/273 1040/1029
10	⟨⟨ 10 26 19 18 41 18 2 -6 28 -29 -48 -1 -15 45 75 ]]	Hamity	5.887	99/98 121/120 275/273 572/567
11	⟨⟨ 11 18 5 -12 8 3 -23 -57 -28 -39 -90 -48 -51 4 72 ]]	Quartz	5.990	99/98 169/168 275/273 385/384
12	⟨⟨ 12 10 -9 11 28 -12 -48 -24 0 -49 -9 28 62 112 56 ]]	Hemikleismic	6.023	121/120 176/175 275/273 325/324
13	⟨⟨ 13 2 30 34 48 -27 11 9 28 64 72 104 -8 24 40 ]]	Coditonic	7.622	99/98 176/175 325/324 847/845
14	⟨⟨ 14 -6 16 4 15 -42 -14 -42 -28 54 30 57 -44 -17 37 ]]	Doublethink	5.858	99/98 121/120 169/168 176/175
15	⟨⟨ 15 -14 2 -26 -18 -57 -39 -93 -84 44 -12 10 -80 -58 34 ]]	Misneb	8.837	99/98 176/175 640/637 847/845
16	⟨⟨ 16 -22 -12 -3 2 -72 -64 -60 -56 34 69 86 33 50 18 ]]		9.127	121/120 169/168 225/224 640/637
17	⟨⟨ 17 23 27 20 22 -3 -5 -27 -28 -2 -33 -34 -37 -38 2 ]]	Maja	5.680	99/98 121/120 169/168 275/273
18	⟨⟨ 18 15 13 43 42 -18 -30 6 0 -12 48 42 76 70 -14 ]]	Kleiboh	6.913	176/175 275/273 325/324 540/539
19	⟨⟨ 19 7 -1 13 9 -33 -55 -45 -56 -22 6 -5 40 29 -17 ]]	Semaja	6.343	121/120 169/168 176/175 275/273
20	⟨⟨ 20 -1 38 36 29 -48 4 -12 -28 91 87 71 -30 -59 -33 ]]		8.717	99/98 169/168 176/175 4235/4212
21	⟨⟨ 21 -9 24 6 -4 -63 -21 -63 -84 81 45 24 -66 -100 -36 ]]		9.168	99/98 121/120 176/175 2200/2197
22	⟨⟨ 22 36 10 29 16 6 -46 -30 -56 -78 -57 -96 47 8 -52 ]]		8.657	121/120 169/168 325/324 640/637
23	⟨⟨ 23 28 49 52 36 -9 13 3 -28 35 24 -20 -23 -80 -68 ]]		8.776	99/98 169/168 275/273 2662/2625
24	⟨⟨ 24 20 35 22 3 -24 -12 -48 -84 25 -18 -67 -59 -121 -71 ]]		8.623	99/98 121/120 275/273 4225/4224
25	⟨⟨ 25 12 21 45 23 -39 -37 -15 -56 15 63 9 54 -13 -87 ]]		8.025	169/168 176/175 275/273 540/539
26	⟨⟨ 26 4 7 15 43 -54 -62 -66 -28 5 21 85 18 95 93 ]]		9.145	121/120 176/175 676/675 1040/1029