The temperaments listed are 17edo-distinct, meaning that they are all different even if tuned in 17edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the 17c val (⟨17 27 40 48 59 63]) was chosen as the representative for each class of edo-distinctness.
5-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 17, 7
|
⟨⟨ 1 4 4 ]]
|
Meantone
|
1.231
|
81/80
|
| 17, 5
|
⟨⟨ 2 -9 -19 ]]
|
Beatles
|
3.798
|
524288/492075
|
| 17, 8
|
⟨⟨ 3 -5 -15 ]]
|
Progress
|
2.877
|
32768/30375
|
| 17, 6
|
⟨⟨ 4 -1 -11 ]]
|
Smate
|
2.272
|
2048/1875
|
| 17, 2
|
⟨⟨ 5 3 -7 ]]
|
Progression
|
2.254
|
3456/3125
|
| 17, 4
|
⟨⟨ 6 7 -3 ]]
|
Subklei
|
2.833
|
17496/15625
|
| 17, 1
|
⟨⟨ 7 11 1 ]]
|
Slurpee
|
3.743
|
177147/156250
|
| 17, 3
|
⟨⟨ 9 2 -18 ]]
|
Genocchi
|
4.355
|
2359296/1953125
|
7-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 17, 7
|
⟨⟨ 1 4 -2 4 -6 -16 ]]
|
Dominant
|
1.466
|
36/35 64/63
|
| 17, 5
|
⟨⟨ 2 8 13 8 15 8 ]]
|
Mohamaq
|
2.958
|
81/80 392/375
|
| 17, 8
|
⟨⟨ 3 -5 -6 -15 -18 0 ]]
|
Progress
|
2.762
|
64/63 392/375
|
| 17, 6
|
⟨⟨ 4 -1 9 -11 3 24 ]]
|
Smate
|
2.575
|
36/35 2048/1875
|
| 17, 2
|
⟨⟨ 5 3 7 -7 -3 8 ]]
|
Progression
|
1.976
|
36/35 392/375
|
| 17, 4
|
⟨⟨ 6 7 5 -3 -9 -8 ]]
|
Subklei
|
2.340
|
36/35 1029/1000
|
| 17, 1
|
⟨⟨ 7 11 3 1 -15 -24 ]]
|
Slurpee
|
3.369
|
36/35 51200/50421
|
| 17, 3
|
⟨⟨ 8 -2 1 -22 -21 8 ]]
|
Hemismate
|
3.783
|
256/245 392/375
|
11-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 17, 7
|
⟨⟨ 1 4 -2 -6 4 -6 -13 -16 -28 -10 ]]
|
Dominant
|
1.864
|
36/35 56/55 64/63
|
| 17, 5
|
⟨⟨ 2 8 -4 5 8 -12 1 -32 -16 28 ]]
|
Neutrominant
|
2.569
|
36/35 64/63 121/120
|
| 17, 8
|
⟨⟨ 3 -5 -6 -1 -15 -18 -12 0 15 18 ]]
|
Progress
|
2.399
|
56/55 64/63 77/75
|
| 17, 6
|
⟨⟨ 4 -1 9 10 -11 3 2 24 27 -3 ]]
|
Smate
|
2.443
|
36/35 56/55 243/242
|
| 17, 2
|
⟨⟨ 5 3 7 4 -7 -3 -11 8 -1 -13 ]]
|
Progression
|
1.749
|
36/35 56/55 77/75
|
| 17, 4
|
⟨⟨ 6 7 5 15 -3 -9 3 -8 11 25 ]]
|
Subklei
|
2.459
|
36/35 77/75 352/343
|
| 17, 1
|
⟨⟨ 7 11 3 9 1 -15 -10 -24 -17 15 ]]
|
Slurpee
|
2.916
|
36/35 121/120 352/343
|
| 17, 3
|
⟨⟨ 8 -2 1 3 -22 -21 -23 8 14 5 ]]
|
Hemismate
|
3.279
|
56/55 77/75 256/245
|
13-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 17, 7
|
⟨⟨ 1 4 -2 11 8 4 -6 14 9 -16 12 4 38 30 -13 ]]
|
Domination
|
2.061
|
26/25 36/35 64/63 66/65
|
| 17, 5
|
⟨⟨ 2 8 -4 5 -1 8 -12 1 -9 -32 -16 -32 28 12 -22 ]]
|
Neutrominant
|
2.402
|
36/35 64/63 66/65 121/120
|
| 17, 8
|
⟨⟨ 3 -5 -6 -1 -10 -15 -18 -12 -27 0 15 -5 18 -6 -31 ]]
|
Progressive
|
2.485
|
26/25 56/55 64/63 77/75
|
| 17, 6
|
⟨⟨ 4 -1 9 10 -2 -11 3 2 -18 24 27 -1 -3 -39 -44 ]]
|
Smate
|
2.520
|
26/25 36/35 56/55 243/242
|
| 17, 2
|
⟨⟨ 5 3 7 4 6 -7 -3 -11 -9 8 -1 3 -13 -9 6 ]]
|
Progression
|
1.563
|
26/25 36/35 56/55 66/65
|
| 17, 4
|
⟨⟨ 6 7 5 15 14 -3 -9 3 0 -8 11 7 25 21 -7 ]]
|
Subklei
|
2.307
|
26/25 36/35 66/65 352/343
|
| 17, 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
|
| 17, 3
|
⟨⟨ 8 -2 1 3 -4 -22 -21 -23 -36 8 14 -2 5 -15 -25 ]]
|
Hemismate
|
3.187
|
26/25 56/55 77/75 256/245
|