List of edo-distinct 31et rank two temperaments

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The temperaments listed are 31edo-distinct, meaning that they are all different even if tuned in 31edo. 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

Period,

generator

Wedgie Name Complexity Commas
31, 13 <<1 4 4]] Meantone 1.231 81/80
31, 9 <<2 -23 -41]] Quasimoha 8.638 2353579470675/2199023255552
31, 6 <<3 -19 -37]] Oncle 7.564 145282683375/137438953472
31, 11 <<4 -15 -33]] Sentinel 6.545 8968066875/8589934592
31, 15 <<5 -11 -29]] Tritonic 5.612 553584375/536870912
31, 3 <<6 -7 -25]] Ampersand 4.815 34171875/33554432
31, 7 <<7 -3 -21]] Orson 4.232 2109375/2097152
31, 10 <<8 1 -17]] Würschmidt 3.958 393216/390625
31, 2 <<9 5 -13]] Valentine 4.056 1990656/1953125
31, 8 <<10 9 -9]] Mynic 4.502 10077696/9765625
31, 4 <<11 13 -5]] Nusecond 5.208 51018336/48828125
31, 14 <<12 17 -1]] Cypress 6.083 258280326/244140625
31, 1 <<13 21 3]] Diesic 7.065 10460353203/9765625000
31, 12 <<17 6 -30]] Semisept 7.920 782757789696/762939453125
31, 5 <<15 -2 -38]] Luna 8.102 274877906944/274658203125

7-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
31, 13 <<1 4 10 4 13 12]] Meantone 2.205 81/80 126/125
31, 9 <<2 8 -11 8 -23 -48]] Mohajira 4.368 81/80 6144/6125
31, 6 <<3 12 -1 12 -10 -36]] Mothra 3.573 81/80 1029/1024
31, 11 <<4 16 9 16 3 -24]] Squares 4.022 81/80 2401/2400
31, 15 <<5 -11 -12 -29 -33 3]] Tritonic 5.291 225/224 50421/50000
31, 3 <<6 -7 -2 -25 -20 15]] Miracle 3.991 225/224 1029/1024
31, 7 <<7 -3 8 -21 -7 27]] Orwell 3.685 225/224 1728/1715
31, 10 <<8 1 18 -17 6 39]] Würschmidt 4.578 225/224 8748/8575
31, 2 <<9 5 -3 -13 -30 -21]] Valentine 4.210 126/125 1029/1024
31, 8 <<10 9 7 -9 -17 -9]] Myna 3.731 126/125 1728/1715
31, 4 <<11 13 17 -5 -4 3]] Nusecond 4.454 126/125 2430/2401
31, 14 <<12 17 27 -1 9 15]] Cypress 5.957 126/125 19683/19208
31, 1 <<13 21 6 3 -27 -45]] Diesic 6.308 1728/1715 5103/5000
31, 12 <<17 6 15 -30 -24 18]] Semisept 6.499 1728/1715 3136/3125
31, 5 <<16 2 5 -34 -37 6]] Hemiwürschmidt 6.598 2401/2400 3136/3125

11-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
31, 13 <<1 4 10 18 4 13 25 12 28 16]] Meantone 3.031 81/80 99/98 126/125
31, 9 <<2 8 -11 5 8 -23 1 -48 -16 52]] Mohajira 3.863 81/80 121/120 176/175
31, 6 <<3 12 -1 -8 12 -10 -23 -36 -60 -19]] Mothra 3.990 81/80 99/98 385/384
31, 11 <<4 16 9 10 16 3 2 -24 -32 -3]] Squares 3.486 81/80 99/98 121/120
31, 15 <<5 -11 -12 -3 -29 -33 -22 3 31 33]] Tritonic 4.596 121/120 225/224 441/440
31, 3 <<6 -7 -2 15 -25 -20 3 15 59 49]] Miracle 4.405 225/224 243/242 441/440
31, 7 <<7 -3 8 2 -21 -7 -21 27 15 -22]] Orwell 3.242 99/98 121/120 176/175
31, 10 <<8 1 18 20 -17 6 4 39 43 -6]] Würschmidt 4.344 99/98 176/175 243/242
31, 2 <<9 5 -3 7 -13 -30 -20 -21 -1 30]] Valentine 3.651 121/120 126/125 176/175
31, 8 <<10 9 7 25 -9 -17 5 -9 27 46]] Myna 4.127 126/125 176/175 243/242
31, 4 <<11 13 17 12 -5 -4 -19 3 -17 -25]] Nusecond 3.927 99/98 121/120 126/125
31, 14 <<12 17 27 30 -1 9 6 15 11 -9]] Cypress 5.404 99/98 126/125 243/242
31, 1 <<13 21 6 17 3 -27 -18 -45 -33 27]] Diesic 5.462 121/120 441/440 891/875
31, 12 <<17 6 15 27 -30 -24 -16 18 42 24]] Semisept 5.969 176/175 540/539 1331/1323
31, 5 <<16 2 5 9 -34 -37 -41 6 14 8]] Hemiwur 5.723 121/120 176/175 1375/1372

13-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
31, 13 <<1 4 10 18 15 4 13 25 20 12 28 20 16 5 -15]] Meantone 2.909 66/65 81/80 99/98 105/104
31, 9 <<2 8 -11 5 -1 8 -23 1 -9 -48 -16 -32 52 38 -22]] Mohajira 3.482 66/65 105/104 121/120 512/507
31, 6 <<3 12 -1 -8 14 12 -10 -23 11 -36 -60 -12 -19 43 78]] Mothra 3.943 81/80 99/98 105/104 144/143
31, 11 <<4 16 9 10 -2 16 3 2 -18 -24 -32 -64 -3 -39 -44]] Squares 3.765 66/65 81/80 99/98 121/120
31, 15 <<5 -11 -12 -3 -18 -29 -33 -22 -47 3 31 -1 33 -6 -51]] Tritonic 4.585 105/104 121/120 196/195 275/273
31, 3 <<6 -7 -2 -16 -3 -25 -20 -46 -27 15 -13 19 -38 -1 49]] Revelation 4.055 66/65 99/98 105/104 1001/1000
31, 7 <<7 -3 8 2 12 -21 -7 -21 -7 27 15 39 -22 4 34]] Winston 3.108 66/65 99/98 105/104 121/120
31, 10 <<8 1 18 20 27 -17 6 4 13 39 43 59 -6 9 19]] Worseschmidt 4.450 66/65 99/98 105/104 243/242
31, 2 <<9 5 -3 7 11 -13 -30 -20 -16 -21 -1 7 30 42 12]] Lupercalia 3.341 66/65 105/104 121/120 126/125
31, 8 <<10 9 7 25 26 -9 -17 5 4 -9 27 27 46 47 -3]] Maneh 4.087 66/65 105/104 126/125 540/539
31, 4 <<11 13 17 12 10 -5 -4 -19 -25 3 -17 -25 -25 -35 -10]] Nusecond 3.652 66/65 99/98 121/120 126/125
31, 14 <<12 17 27 30 25 -1 9 6 -5 15 11 -5 -9 -30 -25]] Cypress 4.837 66/65 99/98 126/125 243/242
31, 1 <<13 21 6 17 9 3 -27 -18 -34 -45 -33 -57 27 3 -32]] Diesic 5.087 66/65 121/120 343/338 441/440
31, 12 <<17 6 15 27 7 -30 -24 -16 -52 18 42 -6 24 -36 -76]] Semishly 5.694 144/143 176/175 196/195 275/273
31, 5 <<16 2 5 9 23 -34 -37 -41 -23 6 14 46 8 46 46]] Hemiwar 5.433 66/65 105/104 121/120 1375/1372