The temperaments listed are 29edo -distinct, meaning that they are all different even if tuned in 29edo. The ordering is by increasing complexity of 3 . The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.
5-limit temperaments
Period generator
Wedgie
Name
Complexity
Commas
29 12
<<1 -8 -15]]
Helmholtz
3.103
32805/32768
29 6
<<2 13 16]]
Immunity
4.157
1638400/1594323
29 4
<<3 5 1]]
Porcupine
1.663
250/243
29 3
<<4 -3 -14]]
Negri
2.739
16875/16384
29 14
<<5 18 17]]
5.519
409600000/387420489
29 2
<<6 -19 -44]]
8.646
18160335421875/17592186044416
29 10
<<7 2 -13]]
3.303
78125/73728
29 13
<<8 23 18]]
7.012
102400000000/94143178827
29 11
<<9 -14 -43]]
8.269
9341736328125/8796093022208
29 7
<<10 7 -12]]
4.455
9765625/8957952
29 9
<<11 -1 -27]]
5.836
146484375/134217728
29 1
<<17 9 -25]]
7.664
762939453125/660451885056
29 8
<<13 12 -11]]
5.857
1220703125/1088391168
29 5
<<15 -4 -41]]
8.498
2471923828125/2199023255552
7-limit temperaments
Period generator
Wedgie
Name
Complexity
Commas
29 12
<<1 -8 -14 -15 -25 -10]]
Garibaldi
3.823
225/224 3125/3087
29 6
<<2 13 1 16 -4 -34]]
Immunity
3.651
49/48 2240/2187
29 4
<<3 5 16 1 17 23]]
Porky
3.362
225/224 250/243
29 3
<<4 -3 2 -14 -8 13]]
Negri
2.245
49/48 225/224
29 14
<<5 18 17 17 13 -11]]
4.821
686/675 2240/2187
29 2
<<6 10 3 2 -12 -21]]
Nautilus
2.943
49/48 250/243
29 10
<<7 2 18 -13 9 36]]
4.251
225/224 6125/5832
29 13
<<8 23 4 18 -16 -55]]
6.241
49/48 560000/531441
29 11
<<9 15 19 3 5 2]]
Ammonite
4.506
250/243 686/675
29 7
<<10 7 5 -12 -20 -8]]
3.751
49/48 3125/3024
29 9
<<11 -1 20 -27 1 49]]
5.909
225/224 84035/78732
29 1
<<17 9 23 -25 -11 28]]
6.682
686/675 21875/20736
29 8
<<13 12 21 -11 -3 15]]
5.238
686/675 3125/3024
29 5
<<14 4 7 -26 -28 5]]
5.436
49/48 78125/73728
11-limit temperaments
Period generator
Wedgie
Name
Complexity
Commas
29 12
<<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]]
Cassandra
3.897
100/99 225/224 245/242
29 6
<<2 13 1 -7 16 -4 -18 -34 -61 -23]]
Immunity
3.977
49/48 55/54 896/891
29 4
<<3 5 16 4 1 17 -4 23 -8 -44]]
Porky
3.020
55/54 100/99 225/224
29 3
<<4 -3 2 15 -14 -8 10 13 45 35]]
Negroni
3.110
49/48 55/54 225/224
29 14
<<5 -11 -12 -3 -29 -33 -22 3 31 33]]
Tritonic
4.596
121/120 225/224 441/440
29 2
<<6 10 3 8 2 -12 -8 -21 -16 12]]
Nautilus
2.548
49/48 55/54 245/242
29 10
<<7 2 18 19 -13 9 6 36 37 -9]]
4.023
55/54 225/224 245/242
29 13
<<8 -6 4 1 -28 -16 -26 26 23 -11]]
Wilsec
3.911
49/48 121/120 225/224
29 11
<<9 15 19 12 3 5 -12 2 -24 -32]]
Ammonite
3.980
55/54 100/99 686/675
29 7
<<10 7 5 23 -12 -20 2 -8 29 47]]
4.064
49/48 55/54 625/616
29 9
<<11 -1 20 5 -27 1 -30 49 15 -55]]
5.264
121/120 225/224 1225/1188
29 1
<<17 9 23 13 -25 -11 -38 28 -1 -43]]
5.913
121/120 625/616 686/675
29 8
<<13 12 21 27 -11 -3 -2 15 21 3]]
4.823
55/54 245/242 625/616
29 5
<<14 4 7 9 -26 -28 -34 5 7 1]]
4.725
49/48 121/120 625/616
13-limit temperaments
Period generator
Wedgie
Name
Complexity
Commas
29 12
<<1 -8 -14 -18 -21 -15 -25 -32 -37 -10 -14 -19 -2 -7 -6]]
Cassandra
3.911
100/99 105/104 196/195 245/242
29 6
<<2 13 1 22 16 16 -4 28 18 -34 6 -11 58 41 -26]]
Impunity
3.934
49/48 91/90 100/99 352/351
29 4
<<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]]
Porky
3.380
55/54 65/64 91/90 100/99
29 3
<<4 -3 2 15 3 -14 -8 10 -10 13 45 18 35 1 -45]]
Negroni
2.793
49/48 55/54 65/64 91/90
29 14
<<5 18 17 26 11 17 13 24 -1 -11 -2 -41 14 -32 -58]]
4.312
91/90 100/99 169/168 245/242
29 2
<<6 10 3 8 19 2 -12 -8 8 -21 -16 7 12 42 36]]
Nautilus
2.806
49/48 55/54 91/90 100/99
29 10
<<7 2 -11 -10 -2 -13 -37 -40 -29 -31 -30 -12 10 35 30]]
Roman
4.163
65/64 100/99 105/104 245/242
29 13
<<8 -6 4 1 6 -28 -16 -26 -20 26 23 36 -11 2 17]]
Wilsec
3.527
49/48 65/64 91/90 121/120
29 11
<<9 15 19 12 14 3 5 -12 -11 2 -24 -23 -32 -31 4]]
Ammonite
3.582
55/54 91/90 100/99 169/168
29 7
<<10 7 5 23 22 -12 -20 2 -2 -8 29 25 47 43 -9]]
3.888
49/48 55/54 91/90 847/845
29 9
<<11 -1 -9 5 1 -27 -45 -30 -39 -18 15 6 45 36 -15]]
4.743
65/64 121/120 169/168 275/273
29 1
<<12 20 6 16 9 4 -24 -16 -30 -42 -32 -53 24 3 -28]]
4.724
49/48 55/54 245/242 343/338
29 8
<<13 12 21 27 17 -11 -3 -2 -21 15 21 -5 3 -30 -41]]
4.362
55/54 91/90 169/168 245/242
29 5
<<14 4 7 9 25 -26 -28 -34 -12 5 7 43 1 44 53]]
4.713
49/48 91/90 121/120 625/616
Todo: link, complete table
Add links to all the temperament names in the table.
