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
|