editing disabled

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

Number
Wedgie
Name
Complexity
Commas
1
<<1 -8 -15]]
Helmholtz
3.103
32805/32768
2
<<2 25 35]]
Hemififths
8.326
858993459200/847288609443
3
<<3 17 20]]
Rodan
5.377
131072000/129140163
4
<<4 9 5]]
Tetracot
2.783
20000/19683
5
<<5 1 -10]]
Magic
2.417
3125/3072
6
<<6 -7 -25]]
Ampersand
4.815
34171875/33554432
7
<<7 -15 -40]]
Merman
7.733
1121008359375/1099511627776
8
<<8 -23 -55]]

10.754
36774679229296875/36028797018963968
9
<<9 10 -5]]
Shibboleth
4.189
1953125/1889568
10
<<31 39 -10]]

14.967
4656612873077392578125/4149816476691431697408
11
<<11 -6 -35]]
Septimin
6.959
35595703125/34359738368
12
<<29 14 -45]]

13.174
186264514923095703125/168285760985348702208
13
<<13 19 0]]
Bohpier
6.689
1220703125/1162261467
14
<<14 11 -15]]
Quasitemp
6.247
6103515625/5804752896
15
<<26 -3 -65]]

13.937
40233135223388671875/36893488147419103232
16
<<16 -5 -45]]
Alphorn
9.239
37078857421875/35184372088832
17
<<17 28 5]]
Slendi
9.351
24414062500000/22876792454961
18
<<23 21 -20]]

10.359
11920928955078125/10968475320188928
19
<<19 12 -25]]
Barbad
8.496
19073486328125/17832200896512
20
<<21 -4 -55]]

11.574
38623809814453125/36028797018963968

7-limit temperaments

Number
Wedgie
Name
Complexity
Commas
1
<<1 -8 -14 -15 -25 -10]]
Garibaldi
3.823
225/224 3125/3087
2
<<2 25 13 35 15 -40]]
Hemififths
6.812
2401/2400 5120/5103
3
<<3 17 -1 20 -10 -50]]
Rodan
5.012
245/243 1029/1024
4
<<4 9 26 5 30 35]]
Bunya
5.527
225/224 15625/15309
5
<<5 1 12 -10 5 25]]
Magic
2.937
225/224 245/243
6
<<6 -7 -2 -25 -20 15]]
Miracle
3.991
225/224 1029/1024
7
<<7 26 25 25 20 -15]]
Pluto
7.022
4000/3969 10976/10935
8
<<8 18 11 10 -5 -25]]
Octacot
4.551
245/243 2401/2400
9
<<9 10 -3 -5 -30 -35]]
Superkleismic
4.620
875/864 1029/1024
10
<<10 2 -17 -20 -55 -45]]
Hocum
7.155
3125/3072 4000/3969
11
<<11 -6 10 -35 -15 40]]
Septimin
5.874
225/224 84035/82944
12
<<12 27 37 15 25 10]]
Duodecicot
8.334
3125/3087 10976/10935
13
<<13 19 23 0 0 0]]
Bohpier
5.793
245/243 3125/3087
14
<<14 11 9 -15 -25 -10]]
Quasitemp
5.185
875/864 2401/2400
15
<<15 3 -5 -30 -50 -20]]
Trismegistus
7.030
1029/1024 3125/3072
16
<<16 -5 22 -45 -10 65]]
Alphorn
8.386
225/224 5764801/5668704
17
<<17 28 8 5 -35 -60]]
Slendi
8.337
4000/3969 84035/82944
18
<<18 20 35 -10 5 25]]
Superthird
7.979
245/243 78125/76832
19
<<19 12 21 -25 -20 15]]
Barbad
7.048
875/864 16875/16807
20
<<20 4 7 -40 -45 5]]
Quadrimage
8.056
2401/2400 3125/3072

11-limit temperaments

Number
Wedgie
Name
Complexity
Commas
1
<<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]]
Cassandra
3.897
100/99 225/224 245/242
2
<<2 -16 13 5 -30 15 1 75 67 -31]]
Salsa
6.022
243/242 245/242 385/384
3
<<3 17 -1 28 20 -10 34 -50 6 82]]
Varan
5.714
100/99 245/243 2835/2816
4
<<4 9 26 10 5 30 2 35 -8 -62]]
Bunya
4.833
100/99 225/224 243/242
5
<<5 1 12 -8 -10 5 -30 25 -22 -64]]
Magic
3.715
100/99 225/224 245/243
6
<<6 -7 -2 15 -25 -20 3 15 59 49]]
Miracle
4.405
225/224 243/242 441/440
7
<<7 -15 -16 -3 -40 -45 -29 5 45 47]]
Merman
6.311
225/224 441/440 1344/1331
8
<<8 18 11 20 10 -5 4 -25 -16 18]]
Octacot
4.070
100/99 243/242 245/242
9
<<9 10 -3 2 -5 -30 -28 -35 -30 16]]
Superkleismic
4.137
100/99 245/242 385/384
10
<<10 2 24 25 -20 10 5 50 51 -13]]
Hocus
5.497
225/224 243/242 245/242
11
<<11 -6 10 7 -35 -15 -27 40 37 -15]]
Septimin
5.089
225/224 245/242 385/384
12
<<12 -14 -4 -11 -50 -40 -59 30 23 -17]]
Hemimiracle
7.207
225/224 245/242 1029/1024
13
<<13 19 23 12 0 0 -26 0 -38 -46]]
Bohpier
5.298
100/99 245/243 1344/1331
14
<<14 11 9 35 -15 -25 7 -10 43 67]]
Quato
5.844
243/242 441/440 625/616
15
<<15 3 -5 17 -30 -50 -25 -20 29 65]]
Trismegistus
6.319
385/384 441/440 625/616
16
<<16 -5 22 -1 -45 -10 -57 65 15 -79]]
Alphorn
7.744
225/224 385/384 12250/11979
17
<<17 28 8 22 5 -35 -24 -60 -46 34]]
Slendi
7.223
100/99 245/242 46656/46585
18
<<18 20 35 4 -10 5 -56 25 -60 -110]]
Superthird
8.196
100/99 245/243 78125/76832
19
<<19 12 21 27 -25 -20 -23 15 21 3]]
Barbad
6.192
245/242 540/539 625/616
20
<<20 4 7 9 -40 -45 -55 5 7 1]]
Quadrimage
7.054
245/242 385/384 625/616

13-limit temperaments

Number
Wedgie
Name
Complexity
Commas
1
<<1 -8 -14 -18 -21 -15 -25 -32 -37 -10 -14 -19 -2 -7 -6]]
Cassandra
3.911
100/99 105/104 196/195 245/242
2
<<2 -16 13 5 -1 -30 15 1 -9 75 67 57 -31 -51 -22]]
Salsa
5.392
105/104 144/143 243/242 245/242
3
<<3 17 -1 28 19 20 -10 34 19 -50 6 -19 82 57 -38]]
Varan
5.210
100/99 105/104 245/243 352/351
4
<<4 9 -15 10 -2 5 -35 2 -18 -60 -8 -38 80 50 -44]]
Monkey
4.761
100/99 105/104 144/143 243/242
5
<<5 1 12 -8 18 -10 5 -30 10 25 -22 38 -64 6 92]]
Magic
3.967
100/99 105/104 144/143 196/195
6
<<6 -7 -2 15 -3 -25 -20 3 -27 15 59 19 49 -1 -66]]
Miraculous
4.061
105/104 144/143 196/195 275/273
7
<<7 26 25 38 17 25 20 36 1 -15 -2 -57 20 -45 -82]]
Plutino
6.266
100/99 196/195 245/242 729/728
8
<<8 18 11 20 37 10 -5 4 29 -25 -16 19 18 63 54]]
Octopod
4.827
100/99 105/104 243/242 245/242
9
<<9 10 -3 2 16 -5 -30 -28 -8 -35 -30 0 16 56 48]]
Superkleismic
3.957
100/99 105/104 245/242 1188/1183
10
<<10 2 24 25 36 -20 10 5 20 50 51 76 -13 12 32]]
Hocus
5.741
105/104 196/195 243/242 245/242
11
<<11 -6 10 7 15 -35 -15 -27 -17 40 37 57 -15 5 26]]
Septimin
4.706
105/104 144/143 196/195 245/242
12
<<12 -14 -4 -11 -6 -50 -40 -59 -54 30 23 38 -17 -2 20]]
Hemimiracle
6.475
105/104 196/195 245/242 512/507
13
<<13 19 23 12 14 0 0 -26 -26 0 -38 -38 -46 -46 4]]
Bohpier
4.857
100/99 144/143 245/243 275/273
14
<<14 11 9 35 34 -15 -25 7 2 -10 43 38 67 62 -12]]
Quato
5.669
105/104 243/242 275/273 325/324
15
<<15 3 -5 17 13 -30 -50 -25 -35 -20 29 19 65 55 -18]]
Trismegistus
5.670
105/104 144/143 275/273 625/616
16
<<16 36 22 40 33 20 -10 8 -7 -50 -32 -57 36 11 -34]]
Dificot
7.283
100/99 243/242 245/242 343/338
17
<<17 28 8 22 12 5 -35 -24 -44 -60 -46 -76 34 4 -40]]
Slendi
6.716
100/99 144/143 245/242 343/338
18
<<18 20 35 4 32 -10 5 -56 -16 25 -60 0 -110 -40 96]]
Superthird
7.416
100/99 144/143 196/195 1375/1352
19
<<19 12 21 27 11 -25 -20 -23 -53 15 21 -19 3 -47 -62]]
Barbad
5.903
144/143 196/195 245/242 275/273
20
<<20 4 7 9 31 -40 -45 -55 -25 5 7 57 1 61 74]]
Quadrimage
6.821
105/104 144/143 245/242 625/616