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
|
Commas
|
| 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]]
|
|
5.984
|
134217728/129140163
|
7-limit temperaments
| Period generator
|
Wedgie
|
Name
|
Complexity
|
Commas
|
| 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
|
50/49 1605632/1594323
|
| 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
|
Commas
|
| 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
|
Commas
|
| 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 (Diaschismic)
|
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
|