List of edo-distinct 53et rank two temperaments

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The temperaments listed are 53edo-distinct, meaning that they are all different even if tuned in 53edo. 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 37 54]] Monzismic 12.528 |54 -37 2>
3 <<3 29 39]] Tricot 9.520 68719476736000/68630377364883
4 <<4 21 24]] Vulture 6.600 10485760000/10460353203
5 <<5 13 9]] Amity 3.970 1600000/1594323
6 <<6 5 -6]] Hanson 2.685 15625/15552
7 <<7 -3 -21]] Orson 4.232 2109375/2097152
8 <<8 -11 -36]] Submajor 6.919 69198046875/68719476736
9 <<9 -19 -51]] Untriton 9.853 2270041927734375/2251799813685248
10 <<10 -27 -66]] 12.867 74468725439326171875/73786976294838206464
11 <<11 18 3]] Quartonic 6.026 390625000/387420489
12 <<41 43 -27]] 18.85 |-27 -43 41>
13 <<13 2 -27]] Ditonic 6.373 1220703125/1207959552
14 <<14 47 42]] 14.353 |42 -47 14>
15 <<15 -14 -57]] Misneb 11.043 145964630126953125/144115188075855872
16 <<16 31 12]] 9.845 625000000000000/617673396283947
17 <<17 23 -3]] Maja 8.443 762939453125/753145430616
18 <<35 38 -21]] 16.207 |-21 -38 35>
19 <<19 7 -33]] Semaja 8.817 19073486328125/18786186952704
20 <<20 -1 -48]] 10.481 286102294921875/281474976710656
21 <<21 44 21]] 13.75 1000000000000000000000/984770902183611232881
22 <<31 17 -45]] 13.972 4656612873077392578125/4543715546604414959616
23 <<23 28 -9]] 10.985 11920928955078125/11712917736940032
24 <<29 33 -15]] 13.582 186264514923095703125/182159296644891377664
25 <<25 12 -39]] 11.37 298023223876953125/292162779488452608
26 <<27 -4 -69]] 14.659 603497028350830078125/590295810358705651712

7-limit temperaments

Number Wedgie Name Complexity Commas
1 <<1 -8 -14 -15 -25 -10]] Garibaldi 3.823 225/224 3125/3087
2 <<2 -16 25 -30 34 103]] Hemischis 9.155 6144/6125 19683/19600
3 <<3 29 11 39 9 -56]] Tricot 7.801 2430/2401 5120/5103
4 <<4 21 -3 24 -16 -66]] Buzzard 6.420 1728/1715 5120/5103
5 <<5 13 -17 9 -41 -76]] Amity 7.127 4375/4374 5120/5103
6 <<6 5 22 -6 18 37]] Catakleismic 4.684 225/224 4375/4374
7 <<7 -3 8 -21 -7 27]] Orwell 3.685 225/224 1728/1715
8 <<8 -11 -6 -36 -32 17]] Submajor 5.869 225/224 51200/50421
9 <<9 -19 -20 -51 -57 7]] Untriton 9.195 225/224 125000000/121060821
10 <<10 26 19 18 2 -29]] Hamity 6.518 2430/2401 4000/3969
11 <<11 18 5 3 -23 -39]] Quartonic 5.395 1728/1715 4000/3969
12 <<12 10 -9 -12 -48 -49]] Hemikleismic 6.704 4000/3969 6144/6125
13 <<13 2 30 -27 11 64]] Coditone 7.512 225/224 2125764/2100875
14 <<14 47 16 42 -14 -95]] 12.061 19683/19600 51200/50421
15 <<15 -14 2 -57 -39 44]] Misneb 9.025 225/224 4194304/4117715
16 <<16 31 41 12 20 8]] 9.361 3125/3087 19683/19600
17 <<17 23 27 -3 -5 -2]] Maja 7.161 2430/2401 3125/3087
18 <<18 15 13 -18 -30 -12]] Kleiboh 6.645 1728/1715 3125/3087
19 <<19 7 -1 -33 -55 -22]] Semaja 8.139 3125/3087 6144/6125
20 <<20 -1 -15 -48 -80 -32]] 10.843 3125/3087 65536/64827
21 <<21 44 24 21 -21 -68]] 11.339 4000/3969 839808/823543
22 <<31 17 43 -45 -19 52]] 12.262 2430/2401 390625/387072
23 <<23 28 49 -9 13 35]] 10.832 4375/4374 78125/76832
24 <<24 20 35 -24 -12 25]] 9.340 2430/2401 15625/15552
25 <<25 12 21 -39 -37 15]] 9.293 1728/1715 78125/76832
26 <<26 4 7 -54 -62 5]] 10.711 6144/6125 78125/76832

11-limit temperaments

Number Wedgie Name Complexity Commas
1 <<1 -8 -14 -30 -15 -25 -51 -10 -42 -36]] Helenus 5.390 99/98 176/175 3125/3087
2 <<2 -16 -28 -7 -30 -50 -18 -20 39 77]] Hemigari 6.723 121/120 225/224 3125/3087
3 <<3 29 11 16 39 9 15 -56 -63 7]] Tricot 6.753 99/98 121/120 5120/5103
4 <<4 21 -3 -14 24 -16 -36 -66 -105 -29]] Buteo 6.975 99/98 385/384 2200/2187
5 <<5 13 -17 9 9 -41 -3 -76 -24 84]] Hitchcock 6.290 121/120 176/175 2200/2187
6 <<6 5 22 32 -6 18 30 37 57 14]] Cataclysmic 5.473 99/98 176/175 2200/2187
7 <<7 -3 8 2 -21 -7 -21 27 15 -22]] Orwell 3.242 99/98 121/120 176/175
8 <<8 -11 -6 -28 -36 -32 -72 17 -27 -58]] Interpental 7.011 99/98 176/175 51200/50421
9 <<9 -19 -20 -5 -51 -57 -39 7 54 55]] Untriton 7.983 121/120 225/224 22000/21609
10 <<10 26 19 18 18 2 -6 -29 -48 -15]] Hamity 5.668 99/98 121/120 4000/3969
11 <<11 18 5 -12 3 -23 -57 -39 -90 -51]] Quartz 6.692 99/98 385/384 4000/3969
12 <<12 10 -9 11 -12 -48 -24 -49 -9 62]] Hemikleismic 5.839 121/120 176/175 4000/3969
13 <<13 2 30 34 -27 11 9 64 72 -8]] Coditone 7.203 99/98 176/175 6655/6561
14 <<14 -6 -37 4 -42 -98 -42 -69 30 139]] 11.245 121/120 4000/3969 4125/4096
15 <<15 -14 2 27 -57 -39 -9 44 111 69]] Musneb 8.909 225/224 385/384 66550/64827
16 <<16 31 41 50 12 20 24 8 9 -1]] 8.690 99/98 2662/2625 3125/3087
17 <<17 23 27 20 -3 -5 -27 -2 -33 -37]] Maja 6.299 99/98 121/120 3125/3087
18 <<18 15 13 43 -18 -30 6 -12 48 76]] Kleiboh 7.194 176/175 540/539 3125/3087
19 <<19 7 -1 13 -33 -55 -45 -22 6 40]] Semaja 7.046 121/120 176/175 3125/3087
20 <<20 -1 38 36 -48 4 -12 91 87 -30]] 9.738 99/98 176/175 161051/157464
21 <<21 44 24 6 21 -21 -63 -68 -138 -66]] 11.170 99/98 4000/3969 9317/9216
22 <<22 36 10 29 6 -46 -30 -78 -57 47]] 9.340 121/120 1728/1715 4000/3969
23 <<23 28 49 52 -9 13 3 35 24 -23]] 9.720 99/98 2662/2625 4375/4374
24 <<24 20 35 22 -24 -12 -48 25 -18 -59]] 8.261 99/98 121/120 78125/76832
25 <<25 12 21 45 -39 -37 -15 15 63 54]] 8.873 176/175 540/539 66550/64827
26 <<26 4 7 15 -54 -62 -66 5 21 18]] 9.286 121/120 176/175 34375/33614

13-limit temperaments

Number Wedgie Name Complexity Commas
1 <<1 -8 -14 -30 -33 -15 -25 -51 -56 -10 -42 -47 -36 -41 -3]] Helenus 5.812 99/98 176/175 275/273 847/845
2 <<2 -16 -28 -7 -13 -30 -50 -18 -28 -20 39 29 77 67 -19]] Hemigari 6.013 121/120 169/168 225/224 275/273
3 <<3 29 11 16 7 39 9 15 0 -56 -63 -91 7 -21 -35]] Tricot 6.236 99/98 121/120 169/168 352/351
4 <<4 21 -3 -14 27 24 -16 -36 28 -66 -105 -15 -29 87 145]] Buteo 7.137 99/98 275/273 385/384 572/567
5 <<5 13 -17 9 -6 9 -41 -3 -28 -76 -24 -62 84 46 -54]] Hitchcock 5.834 121/120 169/168 176/175 325/324
6 <<6 5 22 32 14 -6 18 30 0 37 57 14 14 -42 -70]] Cataclysmic 4.918 99/98 169/168 176/175 275/273
7 <<7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73]] Orwell 4.717 99/98 121/120 176/175 275/273
8 <<8 -11 -6 25 1 -36 -32 12 -28 17 96 43 91 25 -89]] Submajor 6.305 169/168 225/224 275/273 385/384
9 <<9 -19 -20 -5 -32 -51 -57 -39 -84 7 54 -4 55 -16 -92]] Untriton 8.047 121/120 225/224 275/273 1040/1029
10 <<10 26 19 18 41 18 2 -6 28 -29 -48 -1 -15 45 75]] Hamity 5.887 99/98 121/120 275/273 572/567
11 <<11 18 5 -12 8 3 -23 -57 -28 -39 -90 -48 -51 4 72]] Quartz 5.990 99/98 169/168 275/273 385/384
12 <<12 10 -9 11 28 -12 -48 -24 0 -49 -9 28 62 112 56]] Hemikleismic 6.023 121/120 176/175 275/273 325/324
13 <<13 2 30 34 48 -27 11 9 28 64 72 104 -8 24 40]] Coditone 7.622 99/98 176/175 325/324 847/845
14 <<14 -6 16 4 15 -42 -14 -42 -28 54 30 57 -44 -17 37]] Doublethink 5.858 99/98 121/120 169/168 176/175
15 <<15 -14 2 -26 -18 -57 -39 -93 -84 44 -12 10 -80 -58 34]] Misneb 8.837 99/98 176/175 640/637 847/845
16 <<16 -22 -12 -3 2 -72 -64 -60 -56 34 69 86 33 50 18]] 9.127 121/120 169/168 225/224 640/637
17 <<17 23 27 20 22 -3 -5 -27 -28 -2 -33 -34 -37 -38 2]] Maja 5.680 99/98 121/120 169/168 275/273
18 <<18 15 13 43 42 -18 -30 6 0 -12 48 42 76 70 -14]] Kleiboh 6.913 176/175 275/273 325/324 540/539
19 <<19 7 -1 13 9 -33 -55 -45 -56 -22 6 -5 40 29 -17]] Semaja 6.343 121/120 169/168 176/175 275/273
20 <<20 -1 38 36 29 -48 4 -12 -28 91 87 71 -30 -59 -33]] 8.717 99/98 169/168 176/175 4235/4212
21 <<21 -9 24 6 -4 -63 -21 -63 -84 81 45 24 -66 -100 -36]] 9.168 99/98 121/120 176/175 2200/2197
22 <<22 36 10 29 16 6 -46 -30 -56 -78 -57 -96 47 8 -52]] 8.657 121/120 169/168 325/324 640/637
23 <<23 28 49 52 36 -9 13 3 -28 35 24 -20 -23 -80 -68]] 8.776 99/98 169/168 275/273 2662/2625
24 <<24 20 35 22 3 -24 -12 -48 -84 25 -18 -67 -59 -121 -71]] 8.623 99/98 121/120 275/273 4225/4224
25 <<25 12 21 45 23 -39 -37 -15 -56 15 63 9 54 -13 -87]] 8.025 169/168 176/175 275/273 540/539
26 <<26 4 7 15 43 -54 -62 -66 -28 5 21 85 18 95 93]] 9.145 121/120 176/175 676/675 1040/1029