List of edo-distinct 34d rank two temperaments

The temperaments listed are 34edo-distinct, meaning that they are all different even if tuned in 34edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the 34d val, ⟨34 54 79 96 118 126], was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period, generator	Wedgie	Name	Complexity	Comma list
34, 11	⟨⟨ 8 1 -17 ]]	Würschmidt	3.958	393216/390625
17, 6	⟨⟨ 18 -2 -45 ]]		9.648	35184372088832/34332275390625
34, 15	⟨⟨ 10 -3 -28 ]]	Mabila	5.755	268435456/263671875
17, 3	⟨⟨ 2 -4 -11 ]]	Srutal	2.121	2048/2025
34, 9	⟨⟨ 6 5 -6 ]]	Hanson	2.685	15625/15552
17, 2	⟨⟨ 14 6 -23 ]]	Vishnu	6.423	6115295232/6103515625
34, 13	⟨⟨ 12 -7 -39 ]]		7.718	549755813888/533935546875
17, 7	⟨⟨ 30 8 -57 ]]		14.26	945539748965690376192/931322574615478515625
34, 5	⟨⟨ 4 9 5 ]]	Tetracot	2.783	20000/19683
17, 8	⟨⟨ 22 24 -13 ]]		10.198	2384185791015625/2313662762852352
34, 1	⟨⟨ 14 23 4 ]]		7.688	97656250000/94143178827
17, 1	⟨⟨ 6 22 21 ]]		6.749	32768000000/31381059609
34, 7	⟨⟨ 2 13 16 ]]	Immunity	4.157	1638400/1594323
17, 4	⟨⟨ 10 14 -1 ]]	Fifive	5.041	9765625/9565938
34, 3	⟨⟨ 16 19 -7 ]]		7.583	152587890625/148769467776
17, 5	⟨⟨ 26 16 -35 ]]	Quatracot	11.648	1490116119384765625/1479074071160291328
2, 1	⟨⟨ 0 17 27 ]]	Gothic	5.984	134217728/129140163

7-limit temperaments

Period, generator	Wedgie	Name	Complexity	Comma list
34, 11	⟨⟨ 8 1 18 -17 6 39 ]]	Würschmidt	4.578	225/224 8748/8575
17, 6	⟨⟨ 16 2 2 -34 -42 -1 ]]		6.802	50/49 393216/390625
34, 15	⟨⟨ 10 -3 14 -28 -6 41 ]]	Amavil	5.254	225/224 17496/16807
17, 3	⟨⟨ 2 -4 -4 -11 -12 2 ]]	Pajara	1.953	50/49 64/63
34, 9	⟨⟨ 6 5 22 -6 18 37 ]]	Catakleismic	4.684	225/224 4375/4374
17, 2	⟨⟨ 14 6 6 -23 -30 -3 ]]		5.385	50/49 110592/109375
34, 13	⟨⟨ 12 -7 10 -39 -18 43 ]]		6.472	225/224 124416/117649
17, 7	⟨⟨ 4 26 26 32 30 -13 ]]		7.556	50/49 1605632/1594323
34, 5	⟨⟨ 4 9 -8 5 -24 -44 ]]	Modus	4.203	64/63 4375/4374
17, 8	⟨⟨ 12 10 10 -12 -18 -5 ]]		4.400	50/49 15625/15552
34, 1	⟨⟨ 14 23 6 4 -30 -51 ]]		6.935	3200/3087 4375/4374
17, 1	⟨⟨ 6 22 22 21 18 -11 ]]		6.018	50/49 177147/175616
34, 7	⟨⟨ 2 13 -4 16 -12 -46 ]]	Immunized	4.300	64/63 8748/8575
17, 4	⟨⟨ 10 14 14 -1 -6 -7 ]]	Crepuscular	4.165	50/49 4375/4374
34, 3	⟨⟨ 16 19 2 -7 -42 -49 ]]		7.287	3200/3087 15625/15309
17, 5	⟨⟨ 8 18 18 10 6 -9 ]]		4.792	50/49 19683/19208
2, 1	⟨⟨ 0 17 0 27 0 -48 ]]		5.191	64/63 17496/16807

11-limit temperaments

Period, generator	Wedgie	Name	Complexity	Comma list
34, 11	⟨⟨ 8 1 18 20 -17 6 4 39 43 -6 ]]	Würschmidt	4.344	99/98 176/175 243/242
17, 6	⟨⟨ 16 2 2 6 -34 -42 -46 -1 7 10 ]]		5.940	50/49 176/175 1344/1331
34, 15	⟨⟨ 10 -3 14 8 -28 -6 -22 41 29 -26 ]]	Amavil	4.553	99/98 176/175 864/847
17, 3	⟨⟨ 2 -4 -4 -12 -11 -12 -26 2 -14 -20 ]]	Pajara	2.543	50/49 99/98 176/175
34, 9	⟨⟨ 6 5 -12 -2 -6 -36 -24 -42 -22 36 ]]	Catalan	4.331	64/63 100/99 1331/1323
17, 2	⟨⟨ 14 6 6 18 -23 -30 -20 -3 21 30 ]]		4.804	50/49 176/175 1331/1323
34, 13	⟨⟨ 12 -7 10 -4 -39 -18 -48 43 15 -46 ]]		5.960	50/49 176/175 1331/1323
17, 7	⟨⟨ 4 -8 -8 10 -22 -24 2 4 51 56 ]]		4.167	50/49 64/63 243/242
34, 5	⟨⟨ 4 9 -8 10 5 -24 2 -44 -8 56 ]]	Modus	3.857	64/63 100/99 243/242
17, 8	⟨⟨ 12 10 10 30 -12 -18 6 -5 35 50 ]]		4.879	50/49 176/175 243/242
34, 1	⟨⟨ 14 23 6 18 4 -30 -20 -51 -38 30 ]]		6.007	100/99 352/343 864/847
17, 1	⟨⟨ 6 -12 -12 -2 -33 -36 -24 6 37 36 ]]		5.104	50/49 64/63 1331/1323
34, 7	⟨⟨ 2 13 -4 -12 16 -12 -26 -46 -73 -20 ]]	Immunized	4.820	64/63 99/98 1944/1925
17, 4	⟨⟨ 10 14 14 8 -1 -6 -22 -7 -30 -26 ]]	Crepuscular	3.829	50/49 99/98 1944/1925
34, 3	⟨⟨ 16 19 2 6 -7 -42 -46 -49 -52 10 ]]		6.595	100/99 352/343 1344/1331
17, 5	⟨⟨ 8 18 18 20 10 6 4 -9 -16 -6 ]]		4.196	50/49 99/98 243/242
2, 1	⟨⟨ 0 17 0 0 27 0 0 -48 -59 0 ]]		4.643	64/63 99/98 243/242

13-limit temperaments

Period, generator	Wedgie	Name	Complexity	Comma list
34, 11	⟨⟨ 8 1 18 20 30 -17 6 4 18 39 43 66 -6 18 30 ]]		4.700	78/77 99/98 243/242 325/324
17, 6	⟨⟨ 16 2 2 6 26 -34 -42 -46 -18 -1 7 53 10 66 68 ]]		5.878	50/49 144/143 176/175 676/675
34, 15	⟨⟨ 10 -3 14 8 12 -28 -6 -22 -18 41 29 39 -26 -18 12 ]]	Amavil	4.096	78/77 99/98 144/143 176/175
17, 3	⟨⟨ 2 -4 -4 -12 -18 -11 -12 -26 -36 2 -14 -27 -20 -36 -18 ]]	Pajara	3.161	50/49 64/63 99/98 975/968
34, 9	⟨⟨ 6 5 22 -2 14 -6 18 -24 0 37 -22 14 -82 -42 56 ]]	Cataleptic	4.339	78/77 100/99 144/143 676/675
17, 2	⟨⟨ 14 6 6 18 10 -23 -30 -20 -36 -3 21 1 30 6 -32 ]]		4.338	50/49 78/77 144/143 176/175
34, 13	⟨⟨ 12 -7 10 -4 -6 -39 -18 -48 -54 43 15 12 -46 -54 -6 ]]		5.608	78/77 99/98 176/175 1875/1859
17, 7	⟨⟨ 4 -8 -8 10 -2 -22 -24 2 -18 4 51 25 56 24 -44 ]]	Hemifourths	3.732	50/49 78/77 144/143 676/675
34, 5	⟨⟨ 4 9 -8 10 -2 5 -24 2 -18 -44 -8 -38 56 24 -44 ]]	Modus	3.607	64/63 78/77 100/99 144/143
17, 8	⟨⟨ 12 10 10 30 28 -12 -18 6 0 -5 35 28 50 42 -14 ]]		4.644	50/49 78/77 176/175 243/242
34, 1	⟨⟨ 14 23 6 18 10 4 -30 -20 -36 -51 -38 -62 30 6 -32 ]]		5.565	78/77 100/99 144/143 352/343
17, 1	⟨⟨ 6 -12 -12 -2 -20 -33 -36 -24 -54 6 37 -2 36 -12 -62 ]]		5.159	50/49 64/63 78/77 1331/1323
34, 7	⟨⟨ 2 13 -4 22 16 16 -12 28 18 -46 6 -11 76 60 -26 ]]		4.520	64/63 78/77 100/99 676/675
17, 4	⟨⟨ 10 14 14 8 12 -1 -6 -22 -18 -7 -30 -24 -26 -18 12 ]]	Crepuscular	3.447	50/49 78/77 99/98 144/143
34, 3	⟨⟨ 16 19 2 6 26 -7 -42 -46 -18 -49 -52 -10 10 66 68 ]]		6.130	100/99 144/143 275/273 1248/1225
17, 5	⟨⟨ 8 18 18 20 30 10 6 4 18 -9 -16 3 -6 18 30 ]]		4.162	50/49 78/77 99/98 243/242
2, 1	⟨⟨ 0 17 0 0 0 27 0 0 0 -48 -59 -63 0 0 0 ]]		4.238	64/63 78/77 99/98 144/143