The temperaments listed are 41edo-distinct, meaning that they are all different even if tuned in 41edo. 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
| #
|
Name
|
Complexity
|
Comma list
|
| 1
|
Helmholtz
|
3.103
|
32805/32768
|
| 2
|
Hemififths
|
8.326
|
858993459200/847288609443
|
| 3
|
Rodan
|
5.377
|
131072000/129140163
|
| 4
|
Tetracot
|
2.783
|
20000/19683
|
| 5
|
Magic
|
2.417
|
3125/3072
|
| 6
|
Ampersand
|
4.815
|
34171875/33554432
|
| 7
|
Merman
|
7.733
|
1121008359375/1099511627776
|
| 8
|
Quadla-quadbiyo
|
10.754
|
36774679229296875/36028797018963968
|
| 9
|
Shibboleth
|
4.189
|
1953125/1889568
|
| 10
|
Sathiweyo
|
14.967
|
4656612873077392578125/4149816476691431697408
|
| 11
|
Septimin
|
6.959
|
35595703125/34359738368
|
| 12
|
Lala-tweneyo
|
13.174
|
186264514923095703125/168285760985348702208
|
| 13
|
Bohpier
|
6.689
|
1220703125/1162261467
|
| 14
|
Quasitemp
|
6.247
|
6103515625/5804752896
|
| 15
|
Quadla-thebiyo
|
13.937
|
40233135223388671875/36893488147419103232
|
| 16
|
Alphorn
|
9.239
|
37078857421875/35184372088832
|
| 17
|
Slendi
|
9.351
|
24414062500000/22876792454961
|
| 18
|
Twetheyo
|
10.359
|
11920928955078125/10968475320188928
|
| 19
|
Barbad
|
8.496
|
19073486328125/17832200896512
|
| 20
|
Quadla-septriyo
|
11.574
|
38623809814453125/36028797018963968
|
7-limit temperaments
11-limit temperaments
| #
|
Name
|
Complexity
|
Comma list
|
| 1
|
Andromeda
|
3.897
|
100/99 225/224 245/242
|
| 2
|
Salsa
|
6.022
|
243/242 245/242 385/384
|
| 3
|
Varan
|
5.714
|
100/99 245/243 2835/2816
|
| 4
|
Bunya
|
4.833
|
100/99 225/224 243/242
|
| 5
|
Magic
|
3.715
|
100/99 225/224 245/243
|
| 6
|
Miracle
|
4.405
|
225/224 243/242 441/440
|
| 7
|
Merman
|
6.311
|
225/224 441/440 1344/1331
|
| 8
|
Octacot
|
4.070
|
100/99 243/242 245/242
|
| 9
|
Superkleismic
|
4.137
|
100/99 245/242 385/384
|
| 10
|
Hocus
|
5.497
|
225/224 243/242 245/242
|
| 11
|
Septimin
|
5.089
|
225/224 245/242 385/384
|
| 12
|
Hemimiracle
|
7.207
|
225/224 245/242 1029/1024
|
| 13
|
Bohpier
|
5.298
|
100/99 245/243 1344/1331
|
| 14
|
Quato
|
5.844
|
243/242 441/440 625/616
|
| 15
|
Trismegistus
|
6.319
|
385/384 441/440 625/616
|
| 16
|
Alphorn
|
7.744
|
225/224 385/384 12250/11979
|
| 17
|
Slendi
|
7.223
|
100/99 245/242 46656/46585
|
| 18
|
Superthird
|
8.196
|
100/99 245/243 78125/76832
|
| 19
|
Barbad
|
6.192
|
245/242 540/539 625/616
|
| 20
|
Quadrimage
|
7.054
|
245/242 385/384 625/616
|
13-limit temperaments
| #
|
Name
|
Complexity
|
Comma list
|
| 1
|
Andromeda
|
3.911
|
100/99 105/104 196/195 245/242
|
| 2
|
Salsa
|
5.392
|
105/104 144/143 243/242 245/242
|
| 3
|
Varan
|
5.210
|
100/99 105/104 245/243 352/351
|
| 4
|
Monkey
|
4.761
|
100/99 105/104 144/143 243/242
|
| 5
|
Magic
|
3.967
|
100/99 105/104 144/143 196/195
|
| 6
|
Miraculous
|
4.061
|
105/104 144/143 196/195 275/273
|
| 7
|
Plutino
|
6.266
|
100/99 196/195 245/242 729/728
|
| 8
|
Octopod
|
4.827
|
100/99 105/104 243/242 245/242
|
| 9
|
Superkleismic
|
3.957
|
100/99 105/104 245/242 1188/1183
|
| 10
|
Hocus
|
5.741
|
105/104 196/195 243/242 245/242
|
| 11
|
Septimin
|
4.706
|
105/104 144/143 196/195 245/242
|
| 12
|
Hemimiracle
|
6.475
|
105/104 196/195 245/242 512/507
|
| 13
|
Bohpier
|
4.857
|
100/99 144/143 245/243 275/273
|
| 14
|
Quato
|
5.669
|
105/104 243/242 275/273 325/324
|
| 15
|
Trismegistus
|
5.670
|
105/104 144/143 275/273 625/616
|
| 16
|
Dificot
|
7.283
|
100/99 243/242 245/242 343/338
|
| 17
|
Slendi
|
6.716
|
100/99 144/143 245/242 343/338
|
| 18
|
Superthird
|
7.416
|
100/99 144/143 196/195 1375/1352
|
| 19
|
Barbad
|
5.903
|
144/143 196/195 245/242 275/273
|
| 20
|
Quadrimage
|
6.821
|
105/104 144/143 245/242 625/616
|