The temperaments listed are 16edo-distinct, meaning that they are all different even if tuned in 16edo. 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
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 16, 7
|
⟨⟨ 1 -3 -7 ]]
|
Mavila
|
1.377
|
135/128
|
| 8, 1
|
⟨⟨ 2 10 11 ]]
|
|
3.113
|
59049/51200
|
| 16, 3
|
⟨⟨ 3 7 4 ]]
|
Laconic
|
2.149
|
2187/2000
|
| 4, 1
|
⟨⟨ 4 4 -3 ]]
|
Diminished
|
1.826
|
648/625
|
| 16, 5
|
⟨⟨ 5 1 -10 ]]
|
Magic
|
2.417
|
3125/3072
|
| 8, 3
|
⟨⟨ 6 -2 -17 ]]
|
|
3.484
|
140625/131072
|
| 16, 1
|
⟨⟨ 7 11 1 ]]
|
|
3.743
|
177147/156250
|
| 2, 1
|
⟨⟨ 8 -8 -31 ]]
|
|
6.008
|
2562890625/2147483648
|
7-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 16, 7
|
⟨⟨ 1 -3 5 -7 5 20 ]]
|
Armodue
|
1.804
|
36/35 135/128
|
| 8, 1
|
⟨⟨ 2 -6 -6 -14 -15 3 ]]
|
Bipelog
|
2.546
|
50/49 135/128
|
| 16, 3
|
⟨⟨ 3 7 -1 4 -10 -22 ]]
|
Gorgo
|
2.252
|
36/35 1029/1024
|
| 4, 1
|
⟨⟨ 4 4 4 -3 -5 -2 ]]
|
Diminished
|
1.494
|
36/35 50/49
|
| 16, 5
|
⟨⟨ 5 1 9 -10 0 18 ]]
|
|
2.430
|
36/35 1875/1792
|
| 8, 3
|
⟨⟨ 6 -2 -2 -17 -20 1 ]]
|
Lemba
|
3.086
|
50/49 525/512
|
| 16, 1
|
⟨⟨ 7 11 3 1 -15 -24 ]]
|
|
3.369
|
36/35 51200/50421
|
| 2, 1
|
⟨⟨ 8 8 -8 -6 -35 -41 ]]
|
|
4.993
|
648/625 1323/1280
|
11-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 16, 7
|
⟨⟨ 1 -3 5 -1 -7 5 -5 20 8 -20 ]]
|
Armodue
|
1.603
|
33/32 36/35 45/44
|
| 8, 1
|
⟨⟨ 2 -6 -6 -2 -14 -15 -10 3 16 15 ]]
|
Bipelog
|
2.211
|
33/32 45/44 50/49
|
| 16, 3
|
⟨⟨ 3 7 -1 -3 4 -10 -15 -22 -31 -5 ]]
|
|
2.320
|
33/32 36/35 352/343
|
| 4, 1
|
⟨⟨ 4 4 4 12 -3 -5 5 -2 14 20 ]]
|
Demolished
|
1.831
|
36/35 45/44 50/49
|
| 16, 5
|
⟨⟨ 5 1 9 11 -10 0 0 18 22 0 ]]
|
|
2.303
|
36/35 45/44 363/343
|
| 8, 3
|
⟨⟨ 6 -2 -2 -6 -17 -20 -30 1 -7 -10 ]]
|
|
3.032
|
50/49 176/175 363/343
|
| 16, 1
|
⟨⟨ 7 11 3 9 1 -15 -10 -24 -17 15 ]]
|
Slurpee
|
2.916
|
36/35 121/120 352/343
|
| 2, 1
|
⟨⟨ 8 8 8 8 -6 -10 -15 -4 -9 -5 ]]
|
|
2.606
|
36/35 50/49 363/343
|
13-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 16, 7
|
⟨⟨ 1 -3 5 -1 3 -7 5 -5 1 20 8 18 -20 -10 14 ]]
|
Armodue
|
1.481
|
27/26 33/32 36/35 45/44
|
| 8, 1
|
⟨⟨ 2 -6 -6 -2 -10 -14 -15 -10 -23 3 16 -1 15 -6 -27 ]]
|
|
2.256
|
33/32 45/44 50/49 78/77
|
| 16, 3
|
⟨⟨ 3 7 -1 -3 9 4 -10 -15 3 -22 -31 -5 -5 29 42 ]]
|
|
2.293
|
27/26 36/35 143/140 275/273
|
| 4, 1
|
⟨⟨ 4 4 4 12 12 -3 -5 5 4 -2 14 13 20 19 -3 ]]
|
|
1.829
|
27/26 36/35 45/44 50/49
|
| 16, 5
|
⟨⟨ 5 1 9 11 15 -10 0 0 5 18 22 31 0 9 11 ]]
|
|
2.376
|
27/26 36/35 78/77 605/588
|
| 8, 3
|
⟨⟨ 6 -2 -2 -6 2 -17 -20 -30 -19 1 -7 12 -10 13 29 ]]
|
|
2.725
|
33/32 50/49 66/65 105/104
|
| 16, 1
|
⟨⟨ 7 11 3 9 5 1 -15 -10 -18 -24 -17 -29 15 3 -16 ]]
|
Slurpee
|
2.700
|
36/35 66/65 143/140 352/343
|
| 2, 1
|
⟨⟨ 8 8 8 8 8 -6 -10 -15 -17 -4 -9 -11 -5 -7 -2 ]]
|
|
2.354
|
36/35 50/49 66/65 143/140
|