List of edo-distinct 31et rank two temperaments

The temperaments listed are 31edo-distinct, meaning that they are all different even if tuned in 31edo. 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

Period, Generator	Wedgie	Name	Complexity	Commas
31, 13	⟨⟨1 4 4]]	Meantone	1.231	81/80
31, 9	⟨⟨2 -23 -41]]	Quasimoha	8.638	2353579470675/2199023255552
31, 6	⟨⟨3 -19 -37]]	Oncle	7.564	145282683375/137438953472
31, 11	⟨⟨4 -15 -33]]	Sentinel	6.545	8968066875/8589934592
31, 15	⟨⟨5 -11 -29]]	Tritonic	5.612	553584375/536870912
31, 3	⟨⟨6 -7 -25]]	Ampersand	4.815	34171875/33554432
31, 7	⟨⟨7 -3 -21]]	Orson	4.232	2109375/2097152
31, 10	⟨⟨8 1 -17]]	Würschmidt	3.958	393216/390625
31, 2	⟨⟨9 5 -13]]	Valentine	4.056	1990656/1953125
31, 8	⟨⟨10 9 -9]]	Mynic	4.502	10077696/9765625
31, 4	⟨⟨11 13 -5]]	Nusecond	5.208	51018336/48828125
31, 14	⟨⟨12 17 -1]]	Cypress	6.083	258280326/244140625
31, 1	⟨⟨13 21 3]]	Diesic	7.065	10460353203/9765625000
31, 12	⟨⟨17 6 -30]]	Semisept	7.920	782757789696/762939453125
31, 5	⟨⟨15 -2 -38]]	Luna	8.102	274877906944/274658203125

7-limit temperaments

Period, Generator	Wedgie	Name	Complexity	Comma list
31, 13	⟨⟨1 4 10 4 13 12]]	Meantone	2.205	81/80 126/125
31, 9	⟨⟨2 8 -11 8 -23 -48]]	Mohajira	4.368	81/80 6144/6125
31, 6	⟨⟨3 12 -1 12 -10 -36]]	Mothra	3.573	81/80 1029/1024
31, 11	⟨⟨4 16 9 16 3 -24]]	Squares	4.022	81/80 2401/2400
31, 15	⟨⟨5 -11 -12 -29 -33 3]]	Tritonic	5.291	225/224 50421/50000
31, 3	⟨⟨6 -7 -2 -25 -20 15]]	Miracle	3.991	225/224 1029/1024
31, 7	⟨⟨7 -3 8 -21 -7 27]]	Orwell	3.685	225/224 1728/1715
31, 10	⟨⟨8 1 18 -17 6 39]]	Würschmidt	4.578	225/224 8748/8575
31, 2	⟨⟨9 5 -3 -13 -30 -21]]	Valentine	4.210	126/125 1029/1024
31, 8	⟨⟨10 9 7 -9 -17 -9]]	Myna	3.731	126/125 1728/1715
31, 4	⟨⟨11 13 17 -5 -4 3]]	Nusecond	4.454	126/125 2430/2401
31, 14	⟨⟨12 17 27 -1 9 15]]	Cypress	5.957	126/125 19683/19208
31, 1	⟨⟨13 21 6 3 -27 -45]]	Diesic	6.308	1728/1715 5103/5000
31, 12	⟨⟨17 6 15 -30 -24 18]]	Semisept	6.499	1728/1715 3136/3125
31, 5	⟨⟨16 2 5 -34 -37 6]]	Hemiwürschmidt	6.598	2401/2400 3136/3125

11-limit temperaments

Period, Generator	Wedgie	Name	Complexity	Comma list
31, 13	⟨⟨1 4 10 18 4 13 25 12 28 16]]	Meantone	3.031	81/80 99/98 126/125
31, 9	⟨⟨2 8 -11 5 8 -23 1 -48 -16 52]]	Mohajira	3.863	81/80 121/120 176/175
31, 6	⟨⟨3 12 -1 -8 12 -10 -23 -36 -60 -19]]	Mothra	3.990	81/80 99/98 385/384
31, 11	⟨⟨4 16 9 10 16 3 2 -24 -32 -3]]	Squares	3.486	81/80 99/98 121/120
31, 15	⟨⟨5 -11 -12 -3 -29 -33 -22 3 31 33]]	Tritonic	4.596	121/120 225/224 441/440
31, 3	⟨⟨6 -7 -2 15 -25 -20 3 15 59 49]]	Miracle	4.405	225/224 243/242 441/440
31, 7	⟨⟨7 -3 8 2 -21 -7 -21 27 15 -22]]	Orwell	3.242	99/98 121/120 176/175
31, 10	⟨⟨8 1 18 20 -17 6 4 39 43 -6]]	Würschmidt	4.344	99/98 176/175 243/242
31, 2	⟨⟨9 5 -3 7 -13 -30 -20 -21 -1 30]]	Valentine	3.651	121/120 126/125 176/175
31, 8	⟨⟨10 9 7 25 -9 -17 5 -9 27 46]]	Myna	4.127	126/125 176/175 243/242
31, 4	⟨⟨11 13 17 12 -5 -4 -19 3 -17 -25]]	Nusecond	3.927	99/98 121/120 126/125
31, 14	⟨⟨12 17 27 30 -1 9 6 15 11 -9]]	Cypress	5.404	99/98 126/125 243/242
31, 1	⟨⟨13 21 6 17 3 -27 -18 -45 -33 27]]	Diesic	5.462	121/120 441/440 891/875
31, 12	⟨⟨17 6 15 27 -30 -24 -16 18 42 24]]	Semisept	5.969	176/175 540/539 1331/1323
31, 5	⟨⟨16 2 5 9 -34 -37 -41 6 14 8]]	Hemiwur	5.723	121/120 176/175 1375/1372

13-limit temperaments

Period, Generator	Wedgie	Name	Complexity	Comma list
31, 13	⟨⟨1 4 10 18 15 4 13 25 20 12 28 20 16 5 -15]]	Meantone	2.909	66/65 81/80 99/98 105/104
31, 9	⟨⟨2 8 -11 5 -1 8 -23 1 -9 -48 -16 -32 52 38 -22]]	Mohajira	3.482	66/65 105/104 121/120 512/507
31, 6	⟨⟨3 12 -1 -8 14 12 -10 -23 11 -36 -60 -12 -19 43 78]]	Mothra	3.943	81/80 99/98 105/104 144/143
31, 11	⟨⟨4 16 9 10 -2 16 3 2 -18 -24 -32 -64 -3 -39 -44]]	Squares	3.765	66/65 81/80 99/98 121/120
31, 15	⟨⟨5 -11 -12 -3 -18 -29 -33 -22 -47 3 31 -1 33 -6 -51]]	Tritonic	4.585	105/104 121/120 196/195 275/273
31, 3	⟨⟨6 -7 -2 -16 -3 -25 -20 -46 -27 15 -13 19 -38 -1 49]]	Revelation	4.055	66/65 99/98 105/104 1001/1000
31, 7	⟨⟨7 -3 8 2 12 -21 -7 -21 -7 27 15 39 -22 4 34]]	Winston	3.108	66/65 99/98 105/104 121/120
31, 10	⟨⟨8 1 18 20 27 -17 6 4 13 39 43 59 -6 9 19]]	Worseschmidt	4.450	66/65 99/98 105/104 243/242
31, 2	⟨⟨9 5 -3 7 11 -13 -30 -20 -16 -21 -1 7 30 42 12]]	Lupercalia	3.341	66/65 105/104 121/120 126/125
31, 8	⟨⟨10 9 7 25 26 -9 -17 5 4 -9 27 27 46 47 -3]]	Maneh	4.087	66/65 105/104 126/125 540/539
31, 4	⟨⟨11 13 17 12 10 -5 -4 -19 -25 3 -17 -25 -25 -35 -10]]	Nusecond	3.652	66/65 99/98 121/120 126/125
31, 14	⟨⟨12 17 27 30 25 -1 9 6 -5 15 11 -5 -9 -30 -25]]	Cypress	4.837	66/65 99/98 126/125 243/242
31, 1	⟨⟨13 21 6 17 9 3 -27 -18 -34 -45 -33 -57 27 3 -32]]	Diesic	5.087	66/65 121/120 343/338 441/440
31, 12	⟨⟨17 6 15 27 7 -30 -24 -16 -52 18 42 -6 24 -36 -76]]	Semishly	5.694	144/143 176/175 196/195 275/273
31, 5	⟨⟨16 2 5 9 23 -34 -37 -41 -23 6 14 46 8 46 46]]	Hemiwar	5.433	66/65 105/104 121/120 1375/1372