List of edo-distinct 72et rank two temperaments

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The temperaments listed are 72edo-distinct, meaning that they are all different even if tuned in 72edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period generator Wedgie Name Complexity Commas
72 23 <<30 1 -68]] 15.274 931322574615478515625/885443715538058477568
36 13 <<12 -2 -31]] 6.558 2197265625/2147483648
24 1 <<18 3 -37]] 8.789 3814697265625/3710851743744
18 5 <<48 4 -105]] 24.043 {{-105 -4 48>>
72 19 <<6 5 -6]] Hanson 2.685 15625/15552
12 1 <<108 6 -241]] 54.584 {{-241 -6 108>>
72 7 <<6 -7 -25]] Ampersand 4.815 34171875/33554432
9 4 <<24 8 -43]] 11.22 59604644775390625/57711166318706688
8 1 <<18 -9 -56]] 11.188 75084686279296875/72057594037927936
36 17 <<60 62 -41]] 27.509 {{-41 -62 60>>
72 11 <<30 -11 -87]] 17.697 {{-87 11 30>>
6 1 <<0 12 19]] Compton 4.218 531441/524288
72 35 <<30 13 -49]] 13.746 931322574615478515625/897524058588526411776
36 7 <<60 14 -117]] 28.753 {{-117 -14 60>>
24 5 <<54 57 -35]] 24.859 {{-35 -57 54>>
9 2 <<24 -16 -81]] 15.929 2565784513950347900390625/2417851639229258349412352
72 31 <<6 17 13]] Gravity 5.177 129140163/128000000
4 1 <<36 18 -55]] 16.323 14551915228366851806640625/13958294159168762755940352
72 5 <<6 -19 -44]] 8.646 18160335421875/17592186044416
18 1 <<48 52 -29]] 22.217 {{-29 -52 48>>
24 7 <<54 21 -92]] 24.95 {{-92 -21 54>>
36 11 <<12 22 7]] Unidec 7.088 31381059609/31250000000
72 1 <<30 49 8]] 16.415 239299329230617529590083/238418579101562500000000
3 1 <<72 -24 -205]] 41.926 {{-205 24 72>>
72 25 <<42 47 -23]] 19.587 {{-23 -47 42>>
36 1 <<12 -26 -69]] 13.345 620572711994384765625/590295810358705651712
8 3 <<18 27 1]] Ennealimmal 9.386 7629394531250/7625597484987
18 7 <<48 28 -67]] 21.556 {{-67 -28 48>>
72 29 <<6 29 32]] 9.054 68630377364883/67108864000000
12 5 <<36 42 -17]] 16.975 14551915228366851806640625/14341765743445587946242048
72 17 <<6 -31 -63]] 12.723 9651146816936671875/9223372036854775808
9 1 <<24 32 -5]] 11.847 59604644775390625/59296646043258912
24 11 <<18 39 20]] 12.119 4052555153018976267/400
36 5 <<60 38 -79]] 26.843 {{-79 -38 60>>
72 13 <<30 37 -11]] 14.389 931322574615478515625/922181439264762599424
2 1 <<144 36 -277]] 68.703 {{-277 -36 144>>

7-limit temperaments

Period generator Wedgie Name Complexity Commas
72 23 <<30 1 -10 -68 -100 -26]] 14.338 1029/1024 9765625/9633792
36 13 <<12 -2 20 -31 -2 52]] Wizard 6.372 225/224 118098/117649
24 1 <<18 3 42 -37 16 89]] 10.447 225/224 516560652/514714375
18 5 <<24 -4 -32 -62 -118 -63]] 15.506 33075/32768 390625/388962
72 29 <<6 5 22 -6 18 37]] Catakleismic 4.684 225/224 4375/4374
12 1 <<36 6 12 -74 -82 11]] 14.649 2401/2400 9765625/9633792
72 17 <<6 -7 -2 -25 -20 15]] Miracle 3.991 225/224 1029/1024
9 4 <<24 8 -8 -43 -80 -41]] 11.17 1029/1024 390625/387072
8 1 <<18 -9 18 -56 -22 67]] 9.546 225/224 40353607/40310784
36 7 <<12 10 -28 -12 -78 -93]] 10.777 15625/15552 33075/32768
72 35 <<30 61 38 27 -24 -83]] 15.688 2401/2400 43046721/42875000
6 1 <<0 12 24 19 38 22]] Waage 5.927 225/224 250047/250000
72 11 <<30 13 14 -49 -62 -4]] 11.448 2401/2400 390625/387072
36 17 <<12 58 68 64 74 -5]] 17.548 321489/320000 3796875/3764768
24 5 <<18 15 -6 -18 -60 -56]] Tritikleismic 8.707 1029/1024 15625/15552
9 1 <<24 -16 16 -81 -42 82]] 13.172 225/224 13841287201/13759414272
72 31 <<6 17 46 13 56 59]] Marvo 9.910 225/224 78125000/78121827
4 1 <<36 18 36 -55 -44 33]] 13.461 16875/16807 390625/387072
72 5 <<6 -19 -26 -44 -58 -7]] 8.954 225/224 156250000/155649627
18 7 <<24 20 16 -24 -42 -19]] Quadritikleismic 8.908 2401/2400 15625/15552
24 7 <<18 51 66 39 54 10]] 15.417 177147/175616 250047/250000
36 1 <<12 22 -4 7 -40 -71]] Unidec 7.662 1029/1024 4375/4374
72 25 <<30 49 14 8 -62 -105]] 14.645 4375/4374 823543/819200
3 1 <<0 24 -24 38 -38 -123]] 10.92 19683/19600 33075/32768
72 1 <<30 25 38 -30 -24 18]] 11.259 15625/15552 16875/16807
36 11 <<12 46 44 45 36 -27]] 12.434 16875/16807 177147/175616
8 3 <<18 27 18 1 -22 -34]] Ennealimmal 7.714 2401/2400 4375/4374
18 1 <<24 44 64 14 34 25]] 14.117 19683/19600 390625/388962
72 19 <<6 29 -2 32 -20 -86]] Hemiseven 8.570 1029/1024 19683/19600
12 5 <<36 30 60 -36 -6 55]] 14.767 15625/15552 118098/117649
72 7 <<6 41 22 51 18 -64]] 10.742 2401/2400 177147/175616
9 2 <<24 32 40 -5 -4 3]] Octoid 10.207 4375/4374 16875/16807
24 11 <<18 39 42 20 16 -12]] Mirkat 10.652 16875/16807 19683/19600
36 5 <<12 34 20 26 -2 -49]] Harry 8.457 2401/2400 19683/19600
72 13 <<30 37 62 -11 14 40]] 13.883 4375/4374 3796875/3764768
2 1 <<0 36 0 57 0 -101]] 10.957 1029/1024 118098/117649

11-limit temperaments

Period generator Wedgie Name Complexity Commas
72 23 <<30 1 -10 39 -68 -100 -42 -26 87 144]] 13.253 385/384 441/440 1171875/1162084
36 13 <<12 -2 20 -6 -31 -2 -51 52 -7 -86]] Wizard 6.421 225/224 385/384 4000/3993
24 1 <<18 3 42 45 -37 16 9 89 94 -19]] 9.837 225/224 243/242 12005/11979
18 5 <<24 -4 40 60 -62 -4 12 104 153 30]] 12.855 225/224 243/242 117649/117128
72 29 <<6 5 22 -21 -6 18 -54 37 -66 -135]] Catakleismic 7.254 225/224 385/384 4375/4374
12 1 <<36 6 12 18 -74 -82 -96 11 21 9]] 12.763 385/384 1375/1372 9375/9317
72 17 <<6 -7 -2 15 -25 -20 3 15 59 49]] Miracle 4.405 225/224 385/384 441/440
9 4 <<24 8 -8 24 -43 -80 -45 -41 28 95]] 9.859 385/384 441/440 9375/9317
8 1 <<18 -9 18 9 -56 -22 -48 67 52 -37]] Enneaportent 8.286 225/224 385/384 12005/11979
36 7 <<12 10 44 30 -12 36 6 74 35 -68]] Bikleismic 8.191 225/224 243/242 4375/4356
72 35 <<30 -11 38 3 -87 -24 -99 119 45 -123]] 14.155 225/224 385/384 5359375/5314683
6 1 <<0 12 24 36 19 38 57 22 42 18]] Compton 6.767 225/224 441/440 4375/4356
72 11 <<30 13 14 3 -49 -62 -99 -4 -38 -40]] 10.735 385/384 1375/1372 4000/3993
36 17 <<12 -14 -4 -42 -50 -40 -108 30 -49 -104]] 10.342 225/224 1029/1024 4375/4356
24 5 <<18 15 -6 9 -18 -60 -48 -56 -31 46]] Tritikleismic 7.587 385/384 441/440 4000/3993
9 1 <<24 -16 16 24 -81 -42 -45 82 111 12]] 11.615 225/224 385/384 324135/322102
72 31 <<6 17 46 15 13 56 3 59 -24 -117]] Marvo 8.731 225/224 243/242 4000/3993
4 1 <<36 18 36 54 -55 -44 -39 33 63 27]] 12.044 540/539 1375/1372 15625/15488
72 5 <<6 -19 -26 -21 -44 -58 -54 -7 17 31]] Marvolo 7.935 225/224 441/440 4000/3993
18 7 <<24 20 16 60 -24 -42 12 -19 70 113]] 9.965 243/242 441/440 15625/15488
24 7 <<18 -21 -6 -27 -75 -60 -105 45 10 -55]] 11.495 225/224 1029/1024 4000/3993
36 1 <<12 22 -4 -6 7 -40 -51 -71 -90 -3]] Unidec 7.532 385/384 441/440 12005/11979
72 25 <<30 49 14 39 8 -62 -42 -105 -79 61]] 12.684 441/440 4000/3993 41503/41472
3 1 <<0 24 -24 0 38 -38 0 -123 -83 83]] Hours 9.462 243/242 385/384 9801/9800
72 1 <<30 25 38 39 -30 -24 -42 18 4 -22]] Sqrtphi 9.756 540/539 1375/1372 4375/4356
36 11 <<12 -26 -28 -6 -69 -78 -51 8 76 80]] 10.906 225/224 441/440 102487/102400
8 3 <<18 27 18 45 1 -22 9 -34 11 64]] Ennealimnic 7.578 243/242 441/440 4375/4356
18 1 <<24 44 64 60 14 34 12 25 -13 -53]] 12.384 243/242 1375/1372 6250/6237
72 19 <<6 29 -2 -21 32 -20 -54 -86 -149 -52]] Hemiseven 9.733 385/384 441/440 19683/19600
12 5 <<36 42 12 54 -17 -82 -39 -90 -20 110]] 13.571 441/440 4375/4356 41503/41472
72 7 <<6 41 22 15 51 18 3 -64 -107 -34]] Neominor 9.493 243/242 441/440 35937/35840
9 2 <<24 32 40 24 -5 -4 -45 3 -55 -71]] Octoid 9.170 540/539 1375/1372 4000/3993
24 11 <<18 39 42 9 20 16 -48 -12 -114 -120]] Mirkat 10.575 540/539 1375/1372 8019/8000
36 5 <<12 34 20 30 26 -2 6 -49 -48 15]] Harry 7.373 243/242 441/440 4000/3993
72 13 <<30 37 -10 3 -11 -100 -99 -127 -121 43]] 14.463 385/384 441/440 1953125/1948617
2 1 <<0 36 0 36 57 0 57 -101 -41 101]] 10.349 540/539 1029/1024 4000/3993