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 | Comma list |
---|---|---|---|---|
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 | Comma list |
---|---|---|---|---|
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 | Comma list |
---|---|---|---|---|
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 |