The temperaments listed are 27edo-distinct, meaning that they are all different even if tuned in 27edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the 27e val (⟨27 43 63 76 94 100]) was chosen as the representative for each class of edo-distinctness.
5-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 27, 11
|
⟨⟨ 1 9 12 ]]
|
Superpyth
|
2.947
|
20480/19683
|
| 27, 8
|
⟨⟨ 2 -9 -19 ]]
|
Beatles
|
3.798
|
524288/492075
|
| 9, 2
|
⟨⟨ 3 0 -7 ]]
|
Augmented
|
1.549
|
128/125
|
| 27, 4
|
⟨⟨ 4 9 5 ]]
|
Tetracot
|
2.783
|
20000/19683
|
| 27, 13
|
⟨⟨ 5 -9 -26 ]]
|
Fervor
|
4.996
|
67108864/61509375
|
| 9, 1
|
⟨⟨ 21 -27 -92 ]]
|
|
17.661
|
[92 -27 -21⟩
|
| 27, 10
|
⟨⟨ 7 9 -2 ]]
|
Sensipent
|
3.407
|
78732/78125
|
| 27, 2
|
⟨⟨ 8 -9 -33 ]]
|
|
6.348
|
8589934592/7688671875
|
| 3, 1
|
⟨⟨ 9 -27 -64 ]]
|
|
12.515
|
[64 -27 -9⟩
|
| 27, 7
|
⟨⟨ 10 9 -9 ]]
|
Myna
|
4.502
|
10077696/9765625
|
| 27, 1
|
⟨⟨ 11 18 3 ]]
|
Quartonic
|
6.026
|
390625000/387420489
|
| 9, 4
|
⟨⟨ 12 -27 -71 ]]
|
|
13.72
|
[71 -27 -12⟩
|
| 27, 5
|
⟨⟨ 13 9 -16 ]]
|
Kumonga
|
5.808
|
1289945088/1220703125
|
7-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 27, 11
|
⟨⟨ 1 9 -2 12 -6 -30 ]]
|
Superpyth
|
2.874
|
64/63 245/243
|
| 27, 8
|
⟨⟨ 2 -9 -4 -19 -12 16 ]]
|
Beatles
|
3.125
|
64/63 686/675
|
| 9, 2
|
⟨⟨ 3 0 -6 -7 -18 -14 ]]
|
Augene
|
2.336
|
64/63 126/125
|
| 27, 4
|
⟨⟨ 4 9 19 5 19 19 ]]
|
Wollemia
|
3.995
|
126/125 2240/2187
|
| 27, 13
|
⟨⟨ 5 -9 -10 -26 -30 2 ]]
|
Fervor
|
4.710
|
64/63 9604/9375
|
| 9, 1
|
⟨⟨ 6 0 15 -14 7 35 ]]
|
Semiaug
|
3.844
|
128/125 245/243
|
| 27, 10
|
⟨⟨ 7 9 13 -2 1 5 ]]
|
Sensi
|
3.080
|
126/125 245/243
|
| 27, 2
|
⟨⟨ 8 18 11 10 -5 -25 ]]
|
Octacot
|
4.551
|
245/243 2401/2400
|
| 3, 1
|
⟨⟨ 9 0 9 -21 -11 21 ]]
|
Niner
|
3.907
|
128/125 686/675
|
| 27, 7
|
⟨⟨ 10 9 7 -9 -17 -9 ]]
|
Myna
|
3.731
|
126/125 1728/1715
|
| 27, 1
|
⟨⟨ 11 18 5 3 -23 -39 ]]
|
Quartonic
|
5.395
|
1728/1715 4000/3969
|
| 9, 4
|
⟨⟨ 12 0 3 -28 -29 7 ]]
|
Oodako
|
5.164
|
128/125 2401/2400
|
| 27, 5
|
⟨⟨ 13 9 1 -16 -35 -23 ]]
|
Kumonga
|
5.411
|
126/125 12288/12005
|
11-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 27, 11
|
⟨⟨ 1 9 -2 16 12 -6 22 -30 6 52 ]]
|
Superpyth
|
3.410
|
64/63 100/99 245/243
|
| 27, 8
|
⟨⟨ 2 -9 -4 5 -19 -12 1 16 43 28 ]]
|
Ringo
|
3.126
|
56/55 64/63 540/539
|
| 9, 2
|
⟨⟨ 3 0 -6 -6 -7 -18 -20 -14 -14 4 ]]
|
Augene
|
2.286
|
56/55 64/63 100/99
|
| 27, 4
|
⟨⟨ 4 9 19 10 5 19 2 19 -8 -38 ]]
|
Wollemia
|
3.472
|
56/55 100/99 243/242
|
| 27, 13
|
⟨⟨ 5 -9 -10 -1 -26 -30 -19 2 29 32 ]]
|
Fervor
|
4.112
|
56/55 64/63 1350/1331
|
| 9, 1
|
⟨⟨ 6 0 15 15 -14 7 3 35 35 -10 ]]
|
Hemiaug
|
3.575
|
56/55 128/125 245/243
|
| 27, 10
|
⟨⟨ 7 9 13 4 -2 1 -18 5 -22 -34 ]]
|
Sensis
|
2.980
|
56/55 100/99 245/243
|
| 27, 2
|
⟨⟨ 8 18 11 20 10 -5 4 -25 -16 18 ]]
|
Octacot
|
4.070
|
100/99 243/242 245/242
|
| 3, 1
|
⟨⟨ 9 0 9 9 -21 -11 -17 21 21 -6 ]]
|
Niner
|
3.394
|
56/55 128/125 540/539
|
| 27, 7
|
⟨⟨ 10 9 7 -2 -9 -17 -38 -9 -36 -30 ]]
|
Coleto
|
4.019
|
56/55 100/99 1728/1715
|
| 27, 1
|
⟨⟨ 11 18 5 14 3 -23 -16 -39 -30 22 ]]
|
Quarto
|
4.675
|
100/99 245/242 864/847
|
| 9, 4
|
⟨⟨ 12 0 3 3 -28 -29 -37 7 7 -2 ]]
|
Oodako
|
4.551
|
56/55 128/125 3773/3750
|
| 27, 5
|
⟨⟨ 13 9 1 19 -16 -35 -15 -23 13 50 ]]
|
Kumonga
|
4.924
|
126/125 176/175 864/847
|
13-limit temperaments
Period,
generator
|
Wedgie
|
Name
|
Complexity
|
Comma list
|
| 27, 11
|
⟨⟨ 1 9 -2 16 13 12 -6 22 17 -30 6 -3 52 44 -14 ]]
|
Superpyth
|
3.228
|
64/63 78/77 91/90 100/99
|
| 27, 8
|
⟨⟨ 2 -9 -4 5 -1 -19 -12 1 -9 16 43 31 28 12 -22 ]]
|
Ringo
|
2.798
|
56/55 64/63 78/77 91/90
|
| 9, 2
|
⟨⟨ 3 0 -6 -6 12 -7 -18 -20 8 -14 -14 28 4 56 64 ]]
|
Ogene
|
2.936
|
56/55 64/63 91/90 100/99
|
| 27, 4
|
⟨⟨ 4 9 -8 10 -2 5 -24 2 -18 -44 -8 -38 56 24 -44 ]]
|
Modus
|
3.607
|
64/63 78/77 100/99 144/143
|
| 27, 13
|
⟨⟨ 5 -9 -10 -1 -16 -26 -30 -19 -44 2 29 -4 32 -8 -52 ]]
|
Fervor
|
4.175
|
56/55 64/63 78/77 507/500
|
| 9, 1
|
⟨⟨ 6 0 15 15 -3 -14 7 3 -27 35 35 -7 -10 -64 -66 ]]
|
Hemiaug
|
3.785
|
56/55 91/90 128/125 245/243
|
| 27, 10
|
⟨⟨ 7 9 13 4 10 -2 1 -18 -10 5 -22 -10 -34 -20 20 ]]
|
Sensis
|
2.664
|
56/55 78/77 91/90 100/99
|
| 27, 2
|
⟨⟨ 8 18 11 20 23 10 -5 4 7 -25 -16 -13 18 24 6 ]]
|
Octocat
|
3.773
|
78/77 91/90 100/99 245/242
|
| 3, 1
|
⟨⟨ 9 0 9 9 9 -21 -11 -17 -19 21 21 21 -6 -8 -2 ]]
|
Niner
|
3.035
|
56/55 78/77 91/90 128/125
|
| 27, 7
|
⟨⟨ 10 9 7 25 22 -9 -17 5 -2 -9 27 18 46 36 -16 ]]
|
Minah
|
3.862
|
78/77 91/90 126/125 176/175
|
| 27, 1
|
⟨⟨ 11 18 5 14 8 3 -23 -16 -28 -39 -30 -48 22 4 -24 ]]
|
Quarto
|
4.328
|
78/77 100/99 144/143 245/242
|
| 9, 3
|
⟨⟨ 12 0 3 3 -6 -28 -29 -37 -54 7 7 -14 -2 -28 -32 ]]
|
Oodako
|
4.551
|
56/55 78/77 128/125 507/500
|
| 27, 5
|
⟨⟨ 13 9 1 19 7 -16 -35 -15 -37 -23 13 -17 50 16 -46 ]]
|
Kumonga
|
4.509
|
78/77 126/125 144/143 176/175
|