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
|
Commas
|
| 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]]
|
Sensi
|
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
|
Commas
|
| 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
|
Commas
|
| 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
|
Commas
|
| 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
|