List of 31et rank two temperaments by badness
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- The original revision id was 323763128.
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Original Wikitext content:
Below are listed rank-two temperaments supported by the [[31edo]] [[patent val]], below the indicated cutoff in TE badness. =5-limit temperaments with badness below 0.1= Listed is the wedgie and the TE badness times 1000 for four temperaments with [[Tenney-Euclidean metrics#Logflat%20TE%20badness|badness]] less than 0.1. || 1 || <<1 4 4]] || Meantone || 7.381 || 81/80 || || 2 || <<15 -2 -38]] || Luna || 20.576 || 274877906944/274658203125 || || 3 || <<8 1 -17]] || Würschmidt || 40.603 || 393216/390625 || || 4 || <<7 -3 -21]] || Orson || 40.807 || 2109375/2097152 || =7-limit temperaments with badness below 0.06= Listed is the wedgie and the TE badness times 1000 for 19 temperaments with badness less than 0.06. || Rank || Wedgie || Name || Badness || Commas || || 1 || <<22 -5 3 -59 -57 21]] || Tertiaseptal || 12.995 || 2401/2400 65625/65536 || || 2 || <<1 4 10 4 13 12]] || Meantone || 13.707 || 81/80 126/125 || || 3 || <<6 -7 -2 -25 -20 15]] || Miracle || 16.742 || 225/224 1029/1024 || || 4 || <<16 2 5 -34 -37 6]] || Hemiwürschmidt || 20.307 || 2401/2400 3136/3125 || || 5 || <<7 -3 8 -21 -7 27]] || Orwell || 20.735 || 225/224 1728/1715 || || 6 || <<10 9 7 -9 -17 -9]] || Myna || 27.044 || 126/125 1728/1715 || || 7 || <<9 5 -3 -13 -30 -21]] || Valentine || 31.056 || 126/125 1029/1024 || || 8 || <<38 -3 8 -93 -94 27]] || Quasiorwell || 35.832 || 2401/2400 29360128/29296875 || || 9 || <<3 12 -1 12 -10 -36]] || Mothra/Cynder || 37.146 || 81/80 1029/1024 || || 10 || <<15 -2 -5 -38 -50 -6]] || Hemithirds || 44.284 || 1029/1024 3136/3125 || || 11 || <<60 -8 11 -152 -151 48]] || Subneutral || 45.792 || 2401/2400 274877906944/274658203125 || || 12 || <<4 16 9 16 3 -24]] || Squares || 45.993 || 81/80 2401/2400 || || 13 || <<5 -11 -12 -29 -33 3]] || Tritonic || 47.578 || 225/224 50421/50000 || || 14 || <<11 13 17 -5 -4 3]] || Nusecond || 50.389 || 126/125 2430/2401 || || 15 || <<17 6 15 -30 -24 18]] || Semisept || 50.472 || 1728/1715 3136/3125 || || 16 || <<8 1 18 -17 6 39]] || Würschmidt || 50.776 || 225/224 8748/8575 || || 17 || <<23 -1 13 -55 -44 33]] || Grendel || 51.834 || 6144/6125 16875/16807 || || 18 || <<2 8 -11 8 -23 -48]] || Mohajira || 55.714 || 81/80 6144/6125 || || 19 || <<13 -10 6 -46 -27 42]] || Slender || 56.934 || 225/224 589824/588245 || =11-limit temperaments with badness below 0.05= Listed is the wedgie and the TE badness times 1000 for 68 temperaments with badness less than 0.05. || Rank || Wedgie || Name || Badness || Commas || || 1 || <<6 -7 -2 15 -25 -20 3 15 59 49]] || Miracle || 10.684 || 225/224 243/242 441/440 || || 2 || <<7 -3 8 2 -21 -7 -21 27 15 -22]] || Orwell || 15.231 || 99/98 121/120 176/175 || || 3 || <<44 -10 6 79 -118 -114 -27 42 218 201]] || Hemitert || 15.633 || 2401/2400 3025/3024 65625/65536 || || 4 || <<9 5 -3 7 -13 -30 -20 -21 -1 30]] || Valentine || 16.687 || 121/120 126/125 176/175 || || 5 || <<10 9 7 25 -9 -17 5 -9 27 46]] || Myna || 16.842 || 126/125 176/175 243/242 || || 6 || <<1 4 10 18 4 13 25 12 28 16]] || Meantone || 17.027 || 81/80 99/98 126/125 || || 7 || <<38 -3 8 64 -93 -94 -30 27 159 152]] || Quasiorwell || 17.540 || 2401/2400 3025/3024 5632/5625 || || 8 || <<15 -2 -5 22 -38 -50 -17 -6 58 79]] || Hemithirds || 19.003 || 385/384 441/440 3136/3125 || || 9 || <<23 -1 13 42 -55 -44 -13 33 101 73]] || Grendel || 19.845 || 540/539 1375/1372 5632/5625 || || 10 || <<16 2 5 40 -34 -37 8 6 86 95]] || Hemiwürschmidt || 21.069 || 243/242 441/440 3136/3125 || || 11 || <<1 4 10 -13 4 13 -24 12 -44 -71]] || Meanpop || 21.543 || 81/80 126/125 540/539 || || 12 || <<4 16 9 10 16 3 2 -24 -32 -3]] || Squares || 21.636 || 81/80 99/98 121/120 || || 13 || <<17 6 15 27 -30 -24 -16 18 42 24]] || Semisept || 22.476 || 176/175 540/539 1331/1323 || || 14 || <<5 -11 -12 -3 -29 -33 -22 3 31 33]] || Tritonic || 23.659 || 121/120 225/224 441/440 || || 15 || <<8 1 18 20 -17 6 4 39 43 -6]] || Würschmidt || 24.413 || 99/98 176/175 243/242 || || 16 || <<13 -10 6 17 -46 -27 -18 42 74 27]] || Slender || 25.342 || 225/224 385/384 1331/1323 || || 17 || <<2 8 20 5 8 26 1 24 -16 -55]] || Migration || 25.516 || 81/80 121/120 126/125 || || 18 || <<11 13 17 12 -5 -4 -19 3 -17 -25]] || Nusecond || 25.621 || 99/98 121/120 126/125 || || 19 || <<3 12 -1 -8 12 -10 -23 -36 -60 -19]] || Mothra || 25.642 || 81/80 99/98 385/384 || || 20 || <<2 8 -11 5 8 -23 1 -48 -16 52]] || Mohajira || 26.064 || 81/80 121/120 176/175 || || 21 || <<29 -8 11 57 -80 -64 -10 48 160 122]] || Eris || 27.621 || 540/539 1375/1372 65625/65536 || || 22 || <<16 2 5 9 -34 -37 -41 6 14 8]] || Hemiwur || 29.270 || 121/120 176/175 1375/1372 || || 23 || <<21 -9 -7 37 -63 -70 -14 9 117 128]] || Triwell || 29.807 || 385/384 441/440 456533/455625 || || 24 || <<22 -5 3 24 -59 -57 -38 21 73 57]] || Tertia || 30.171 || 385/384 1331/1323 1375/1372 || || 25 || <<82 -13 14 143 -211 -208 -57 69 377 353]] || || 30.609 || 2401/2400 3025/3024 369140625/369098752 || || 26 || <<3 12 -1 23 12 -10 26 -36 12 68]] || || 31.334 || 81/80 540/539 1029/1024 || || 27 || <<7 -3 8 33 -21 -7 28 27 87 65]] || || 31.438 || 225/224 441/440 1728/1715 || || 28 || <<67 -11 19 121 -173 -158 -40 75 319 274]] || || 32.121 || 3025/3024 180224/180075 703125/702464 || || 29 || <<6 -7 -2 -16 -25 -20 -46 15 -13 -38]] || || 32.946 || 99/98 176/175 1029/1024 || || 30 || <<10 9 7 -6 -9 -17 -44 -9 -45 -41]] || || 33.434 || 99/98 126/125 385/384 || || 31 || <<8 1 -13 20 -17 -43 4 -33 43 101]] || || 33.436 || 126/125 243/242 385/384 || || 32 || <<32 4 10 49 -68 -74 -33 12 100 103]] || || 34.814 || 2401/2400 3025/3024 3136/3125 || || 33 || <<22 -5 3 55 -59 -57 11 21 145 144]] || || 35.576 || 243/242 441/440 703125/702464 || || 34 || <<28 -12 1 39 -84 -77 -35 36 132 106]] || || 36.493 || 385/384 1375/1372 14641/14580 || || 35 || <<14 -6 16 35 -42 -14 7 54 102 43]] || || 38.377 || 225/224 243/242 2420/2401 || || 36 || <<25 7 2 47 -47 -67 -12 -15 85 125]] || || 39.162 || 441/440 3388/3375 6144/6125 || || 37 || <<4 -15 9 10 -33 3 2 63 75 -3]] || || 39.595 || 99/98 243/242 385/384 || || 38 || <<31 0 0 62 -72 -87 -9 0 144 174]] || || 39.9210 || 441/440 3136/3125 41503/41472 || || 39 || <<3 -19 -1 -8 -37 -10 -23 51 47 -19]] || || 40.217 || 99/98 121/120 1029/1024 || || 40 || <<19 14 4 32 -22 -47 -15 -30 26 76]] || || 40.539 || 126/125 176/175 14641/14580 || || 41 || <<54 -1 13 104 -127 -131 -22 33 245 247]] || || 41.496 || 2401/2400 5632/5625 46656/46585 || || 42 || <<8 1 -13 -11 -17 -43 -45 -33 -29 14]] || || 41.680 || 126/125 176/175 14641/14406 || || 43 || <<9 5 -3 38 -13 -30 29 -21 71 117]] || || 42.204 || 126/125 540/539 1029/1024 || || 44 || <<12 -14 -4 -1 -50 -40 -43 30 46 11]] || || 42.687 || 121/120 225/224 1029/1024 || || 45 || <<12 17 27 30 -1 9 6 15 11 -9]] || || 42.719 || 99/98 126/125 243/242 || || 46 || <<5 20 19 28 20 16 27 -12 -4 13]] || || 42.869 || 81/80 99/98 2541/2500 || || 47 || <<0 0 0 31 0 0 49 0 72 87]] || || 42.959 || 81/80 126/125 1029/1024 || || 48 || <<11 -18 -14 12 -54 -53 -19 18 90 82]] || || 44.005 || 225/224 441/440 9317/9216 || || 49 || <<11 13 17 43 -5 -4 30 3 55 62]] || || 44.041 || 126/125 176/175 2430/2401 || || 50 || <<13 21 6 17 3 -27 -18 -45 -33 27]] || || 44.186 || 121/120 441/440 891/875 || || 51 || <<26 11 12 34 -43 -54 -36 -3 41 54]] || || 44.660 || 176/175 1331/1323 2401/2400 || || 52 || <<61 -4 21 106 -148 -138 -43 60 260 225]] || || 44.729 || 3025/3024 5632/5625 825000/823543 || || 53 || <<60 -8 11 119 -152 -151 -19 48 304 296]] || || 44.888 || 2401/2400 46656/46585 172032/171875 || || 54 || <<19 -17 4 32 -71 -47 -15 57 133 76]] || || 45.168 || 225/224 385/384 585640/583443 || || 55 || <<5 -11 -12 28 -29 -33 27 3 103 120]] || || 45.456 || 225/224 385/384 27783/27500 || || 56 || <<5 20 19 -3 20 16 -22 -12 -76 -74]] || || 45.466 || 81/80 540/539 1375/1372 || || 57 || <<1 4 -21 -13 4 -36 -24 -60 -44 36]] || || 45.509 || 81/80 176/175 1331/1323 || || 58 || <<18 10 25 45 -26 -11 9 30 70 40]] || || 45.7950 || 176/175 243/242 1375/1372 || || 59 || <<39 1 18 82 -89 -81 -5 39 187 168]] || || 45.928 || 540/539 5632/5625 151263/151250 || || 60 || <<2 -23 -11 5 -41 -23 1 39 91 52]] || || 46.181 || 243/242 441/440 1815/1792 || || 61 || <<4 -15 -22 10 -33 -46 2 -9 75 104]] || || 46.462 || 225/224 243/242 1617/1600 || || 62 || <<9 5 28 7 -13 19 -20 51 -1 -77]] || || 47.885 || 121/120 225/224 891/875 || || 63 || <<33 8 20 67 -64 -61 -8 24 128 119]] || || 48.088 || 540/539 3136/3125 15488/15435 || || 64 || <<14 -6 -15 4 -42 -63 -42 -18 30 63]] || || 48.150 || 121/120 441/440 3136/3125 || || 65 || <<8 1 18 -11 -17 6 -45 39 -29 -93]] || || 48.186 || 225/224 385/384 891/875 || || 66 || <<50 -17 4 94 -143 -134 -24 57 277 250]] || || 48.798 || 2401/2400 3025/3024 1265625/1261568 || || 67 || <<7 -3 -23 2 -21 -56 -21 -45 15 85]] || || 49.572 || 121/120 126/125 2079/2048 || || 68 || <<20 18 14 19 -18 -34 -39 -18 -18 5]] || || 49.917 || 121/120 126/125 1728/1715 || =13-limit temperaments with badness below 0.04= Listed is the wedgie and the TE badness times 1000 for 64 temperaments with badness less than 0.04. || Rank || Wedgie || Name || Badness || Commas || || 1 || <<6 -7 -2 15 -34 -25 -20 3 -76 15 59 -53 49 -88 -173]] || Benediction || 15.715 || 225/224 243/242 351/350 441/440 || || 2 || <<10 9 7 25 -5 -9 -17 5 -45 -9 27 -45 46 -40 -110]] || Myna || 17.125 || 126/125 144/143 176/175 196/195 || || 3 || <<1 4 10 18 15 4 13 25 20 12 28 20 16 5 -15]] || Meantone || 18.048 || 66/65 81/80 99/98 105/104 || || 4 || <<6 -7 -2 15 -3 -25 -20 3 -27 15 59 19 49 -1 -66]] || Miraculous || 18.669 || 105/104 144/143 196/195 275/273 || || 5 || <<7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73]] || Orwell || 19.718 || 99/98 121/120 176/175 275/273 || || 6 || <<7 -3 8 2 12 -21 -7 -21 -7 27 15 39 -22 4 34]] || Winston || 19.931 || 66/65 99/98 105/104 121/120 || || 7 || <<9 5 -3 7 -20 -13 -30 -20 -65 -21 -1 -65 30 -45 -95]] || Valentino || 20.665 || 121/120 126/125 176/175 196/195 || || 8 || <<1 4 10 -13 15 4 13 -24 20 12 -44 20 -71 5 100]] || Meanpop || 20.883 || 81/80 105/104 144/143 196/195 || || 9 || <<9 5 -3 7 11 -13 -30 -20 -16 -21 -1 7 30 42 12]] || Lupercalia || 21.328 || 66/65 105/104 121/120 126/125 || || 10 || <<15 -2 -5 22 -23 -38 -50 -17 -92 -6 58 -46 79 -46 -161]] || Hemithirds || 21.738 || 196/195 352/351 1001/1000 1029/1024 || || 11 || <<5 -11 -12 -3 -18 -29 -33 -22 -47 3 31 -1 33 -6 -51]] || Tritonic || 22.993 || 105/104 121/120 196/195 275/273 || || 12 || <<16 2 5 40 -39 -34 -37 8 -121 6 86 -98 95 -128 -283]] || Hemiwürschmidt || 23.074 || 243/242 351/350 441/440 3584/3575 || || 13 || <<11 13 17 12 10 -5 -4 -19 -25 3 -17 -25 -25 -35 -10]] || Nusecond || 23.323 || 66/65 99/98 121/120 126/125 || || 14 || <<2 8 -11 5 -1 8 -23 1 -9 -48 -16 -32 52 38 -22]] || Mohajira || 23.388 || 66/65 105/104 121/120 512/507 || || 15 || <<8 1 18 20 -4 -17 6 4 -36 39 43 -13 -6 -78 -88]] || Würschmidt || 23.593 || 99/98 144/143 176/175 275/273 || || 16 || <<3 12 -1 -8 14 12 -10 -23 11 -36 -60 -12 -19 43 78]] || Mothra || 23.954 || 81/80 99/98 105/104 144/143 || || 17 || <<4 16 9 10 29 16 3 2 31 -24 -32 8 -3 48 63]] || Agora || 24.522 || 81/80 99/98 105/104 121/120 || || 18 || <<23 -1 13 42 -27 -55 -44 -13 -128 33 101 -59 73 -124 -249]] || Grendel || 24.839 || 352/351 540/539 625/624 1375/1372 || || 19 || <<17 6 15 27 -24 -30 -24 -16 -101 18 42 -78 24 -123 -183]] || || 25.204 || 176/175 351/350 540/539 1375/1372 || || 20 || <<0 0 0 0 31 0 0 0 49 0 0 72 0 87 107]] || Gallium || 25.484 || 81/80 99/98 121/120 126/125 || || 21 || <<4 16 9 10 -2 16 3 2 -18 -24 -32 -64 -3 -39 -44]] || Squares || 25.514 || 66/65 81/80 99/98 121/120 || || 22 || <<1 4 10 18 -16 4 13 25 -29 12 28 -52 16 -82 -122]] || Grosstone || 25.899 || 81/80 99/98 126/125 144/143 || || 23 || <<13 -10 6 17 -22 -46 -27 -18 -83 42 74 -14 27 -84 -139]] || Slender || 25.913 || 225/224 275/273 385/384 1331/1323 || || 24 || <<21 -9 -7 37 -57 -63 -70 -14 -168 9 117 -99 128 -134 -334]] || || 27.405 || 385/384 441/440 625/624 13720/13689 || || 25 || <<2 8 20 5 30 8 26 1 40 24 -16 40 -55 10 85]] || || 27.835 || 81/80 105/104 121/120 196/195 || || 26 || <<2 8 20 5 -1 8 26 1 -9 24 -16 -32 -55 -77 -22]] || Migration || 28.071 || 66/65 121/120 126/125 1215/1183 || || 27 || <<22 -5 3 24 -42 -59 -57 -38 -148 21 73 -79 57 -129 -234]] || || 28.384 || 352/351 385/384 625/624 1331/1323 || || 28 || <<17 6 15 27 7 -30 -24 -16 -52 18 42 -6 24 -36 -76]] || || 28.408 || 144/143 176/175 196/195 275/273 || || 29 || <<16 2 5 9 -8 -34 -37 -41 -72 6 14 -26 8 -41 -61]] || || 28.432 || 121/120 176/175 196/195 275/273 || || 30 || <<3 12 -1 23 14 12 -10 26 11 -36 12 -12 68 43 -37]] || || 29.207 || 66/65 81/80 105/104 1001/1000 || || 31 || <<6 -7 -2 -16 -3 -25 -20 -46 -27 15 -13 19 -38 -1 49]] || || 29.452 || 66/65 99/98 105/104 1001/1000 || || 32 || <<10 9 7 25 26 -9 -17 5 4 -9 27 27 46 47 -3]] || || 29.868 || 66/65 105/104 126/125 540/539 || || 33 || <<7 -3 8 33 -19 -21 -7 28 -56 27 87 -33 65 -83 -188]] || || 30.237 || 144/143 225/224 351/350 441/440 || || 34 || <<16 2 5 40 -8 -34 -37 8 -72 6 86 -26 95 -41 -176]] || Hemithir || 31.199 || 144/143 196/195 243/242 625/624 || || 35 || <<32 4 10 49 -47 -68 -74 -33 -193 12 100 -124 103 -169 -344]] || || 31.732 || 352/351 1001/1000 1716/1715 3025/3024 || || 36 || <<10 9 7 -6 -5 -9 -17 -44 -45 -9 -45 -45 -41 -40 5]] || || 31.850 || 66/65 99/98 126/125 385/384 || || 37 || <<15 -2 -5 22 -54 -38 -50 -17 -141 -6 58 -118 79 -133 -268]] || || 31.990 || 351/350 385/384 441/440 3146/3125 || || 38 || <<23 -1 13 42 -58 -55 -44 -13 -177 33 101 -131 73 -211 -356]] || || 32.359 || 351/350 540/539 1375/1372 5632/5625 || || 39 || <<1 4 10 -13 -16 4 13 -24 -29 12 -44 -52 -71 -82 -7]] || || 33.007 || 66/65 81/80 126/125 385/384 || || 40 || <<12 -14 -4 30 -37 -50 -40 6 -103 30 118 -34 98 -89 -239]] || || 33.451 || 225/224 243/242 441/440 1875/1859 || || 41 || <<8 1 18 20 27 -17 6 4 13 39 43 59 -6 9 19]] || || 34.382 || 66/65 99/98 105/104 243/242 || || 42 || <<8 1 -13 20 -4 -17 -43 4 -36 -33 43 -13 101 37 -88]] || || 34.458 || 105/104 126/125 144/143 243/242 || || 43 || <<3 -19 -1 -8 -17 -37 -10 -23 -38 51 47 31 -19 -44 -29]] || || 35.530 || 99/98 105/104 121/120 640/637 || || 44 || <<8 1 -13 20 -35 -17 -43 4 -85 -33 43 -85 101 -50 -195]] || || 35.585 || 126/125 196/195 385/384 1575/1573 || || 45 || <<3 12 -1 -8 -17 12 -10 -23 -38 -36 -60 -84 -19 -44 -29]] || || 36.239 || 66/65 81/80 99/98 385/384 || || 46 || <<8 1 -13 -11 -4 -17 -43 -45 -36 -33 -29 -13 14 37 27]] || || 36.331 || 66/65 105/104 126/125 512/507 || || 47 || <<5 -11 -12 -3 -49 -29 -33 -22 -96 3 31 -73 33 -93 -158]] || || 36.533 || 121/120 225/224 351/350 441/440 || || 48 || <<10 9 7 -6 26 -9 -17 -44 4 -9 -45 27 -41 47 112]] || || 36.656 || 99/98 105/104 126/125 144/143 || || 49 || <<3 12 -1 23 -17 12 -10 26 -38 -36 12 -84 68 -44 -144]] || || 36.857 || 81/80 144/143 176/175 1029/1024 || || 50 || <<22 -5 3 55 -42 -59 -57 11 -148 21 145 -79 144 -129 -349]] || || 36.876 || 243/242 441/440 625/624 3584/3575 || || 51 || <<5 20 19 28 13 20 16 27 2 -12 -4 -44 13 -34 -59]] || || 37.382 || 66/65 81/80 99/98 1001/1000 || || 52 || <<4 -15 9 10 -2 -33 3 2 -18 63 75 51 -3 -39 -44]] || || 37.408 || 99/98 105/104 144/143 243/242 || || 53 || <<13 -10 6 17 -53 -46 -27 -18 -132 42 74 -86 27 -171 -246]] || || 37.732 || 225/224 351/350 385/384 1331/1323 || || 54 || <<12 17 27 30 25 -1 9 6 -5 15 11 -5 -9 -30 -25]] || || 37.849 || 66/65 99/98 126/125 243/242 || || 55 || <<0 0 0 31 0 0 0 49 0 0 72 0 87 0 -115]] || || 37.885 || 81/80 105/104 196/195 512/507 || || 56 || <<13 21 6 17 9 3 -27 -18 -34 -45 -33 -57 27 3 -32]] || || 38.116 || 66/65 121/120 343/338 441/440 || || 57 || <<10 9 7 25 -36 -9 -17 5 -94 -9 27 -117 46 -127 -217]] || || 38.811 || 126/125 176/175 243/242 1573/1568 || || 58 || <<7 -3 8 33 12 -21 -7 28 -7 27 87 39 65 4 -81]] || || 38.812 || 105/104 196/195 275/273 648/637 || || 59 || <<9 5 -3 38 -20 -13 -30 29 -65 -21 71 -65 117 -45 -210]] || || 39.221 || 126/125 144/143 196/195 1029/1024 || || 60 || <<25 7 2 47 -28 -47 -67 -12 -137 -15 85 -91 125 -86 -271]] || || 39.271 || 196/195 352/351 1001/1000 6144/6125 || || 61 || <<14 -6 16 35 -38 -42 -14 7 -112 54 102 -66 43 -166 -261]] || || 39.531 || 225/224 243/242 351/350 2420/2401 || || 62 || <<11 13 17 12 41 -5 -4 -19 24 3 -17 47 -25 52 97]] || || 39.576 || 99/98 105/104 121/120 126/125 || || 63 || <<11 13 17 43 10 -5 -4 30 -25 3 55 -25 62 -35 -125]] || || 39.707 || 126/125 176/175 196/195 648/637 || || 64 || <<16 2 5 9 -39 -34 -37 -41 -121 6 14 -98 8 -128 -168]] || || 39.907 || 121/120 176/175 351/350 1375/1372 ||
Original HTML content:
<html><head><title>List of 31et rank two temperaments by badness</title></head><body>Below are listed rank-two temperaments supported by the <a class="wiki_link" href="/31edo">31edo</a> <a class="wiki_link" href="/patent%20val">patent val</a>, below the indicated cutoff in TE badness.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x5-limit temperaments with badness below 0.1"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit temperaments with badness below 0.1</h1>
Listed is the wedgie and the TE badness times 1000 for four temperaments with <a class="wiki_link" href="/Tenney-Euclidean%20metrics#Logflat%20TE%20badness">badness</a> less than 0.1.<br />
<table class="wiki_table">
<tr>
<td>1<br />
</td>
<td><<1 4 4]]<br />
</td>
<td>Meantone<br />
</td>
<td>7.381<br />
</td>
<td>81/80<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td><<15 -2 -38]]<br />
</td>
<td>Luna<br />
</td>
<td>20.576<br />
</td>
<td>274877906944/274658203125<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td><<8 1 -17]]<br />
</td>
<td>Würschmidt<br />
</td>
<td>40.603<br />
</td>
<td>393216/390625<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td><<7 -3 -21]]<br />
</td>
<td>Orson<br />
</td>
<td>40.807<br />
</td>
<td>2109375/2097152<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="x7-limit temperaments with badness below 0.06"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit temperaments with badness below 0.06</h1>
Listed is the wedgie and the TE badness times 1000 for 19 temperaments with badness less than 0.06.<br />
<table class="wiki_table">
<tr>
<td>Rank<br />
</td>
<td>Wedgie<br />
</td>
<td>Name<br />
</td>
<td>Badness<br />
</td>
<td>Commas<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td><<22 -5 3 -59 -57 21]]<br />
</td>
<td>Tertiaseptal<br />
</td>
<td>12.995<br />
</td>
<td>2401/2400 65625/65536<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td><<1 4 10 4 13 12]]<br />
</td>
<td>Meantone<br />
</td>
<td>13.707<br />
</td>
<td>81/80 126/125<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td><<6 -7 -2 -25 -20 15]]<br />
</td>
<td>Miracle<br />
</td>
<td>16.742<br />
</td>
<td>225/224 1029/1024<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td><<16 2 5 -34 -37 6]]<br />
</td>
<td>Hemiwürschmidt<br />
</td>
<td>20.307<br />
</td>
<td>2401/2400 3136/3125<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td><<7 -3 8 -21 -7 27]]<br />
</td>
<td>Orwell<br />
</td>
<td>20.735<br />
</td>
<td>225/224 1728/1715<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td><<10 9 7 -9 -17 -9]]<br />
</td>
<td>Myna<br />
</td>
<td>27.044<br />
</td>
<td>126/125 1728/1715<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td><<9 5 -3 -13 -30 -21]]<br />
</td>
<td>Valentine<br />
</td>
<td>31.056<br />
</td>
<td>126/125 1029/1024<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td><<38 -3 8 -93 -94 27]]<br />
</td>
<td>Quasiorwell<br />
</td>
<td>35.832<br />
</td>
<td>2401/2400 29360128/29296875<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td><<3 12 -1 12 -10 -36]]<br />
</td>
<td>Mothra/Cynder<br />
</td>
<td>37.146<br />
</td>
<td>81/80 1029/1024<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td><<15 -2 -5 -38 -50 -6]]<br />
</td>
<td>Hemithirds<br />
</td>
<td>44.284<br />
</td>
<td>1029/1024 3136/3125<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td><<60 -8 11 -152 -151 48]]<br />
</td>
<td>Subneutral<br />
</td>
<td>45.792<br />
</td>
<td>2401/2400 274877906944/274658203125<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td><<4 16 9 16 3 -24]]<br />
</td>
<td>Squares<br />
</td>
<td>45.993<br />
</td>
<td>81/80 2401/2400<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td><<5 -11 -12 -29 -33 3]]<br />
</td>
<td>Tritonic<br />
</td>
<td>47.578<br />
</td>
<td>225/224 50421/50000<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td><<11 13 17 -5 -4 3]]<br />
</td>
<td>Nusecond<br />
</td>
<td>50.389<br />
</td>
<td>126/125 2430/2401<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td><<17 6 15 -30 -24 18]]<br />
</td>
<td>Semisept<br />
</td>
<td>50.472<br />
</td>
<td>1728/1715 3136/3125<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td><<8 1 18 -17 6 39]]<br />
</td>
<td>Würschmidt<br />
</td>
<td>50.776<br />
</td>
<td>225/224 8748/8575<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td><<23 -1 13 -55 -44 33]]<br />
</td>
<td>Grendel<br />
</td>
<td>51.834<br />
</td>
<td>6144/6125 16875/16807<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td><<2 8 -11 8 -23 -48]]<br />
</td>
<td>Mohajira<br />
</td>
<td>55.714<br />
</td>
<td>81/80 6144/6125<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td><<13 -10 6 -46 -27 42]]<br />
</td>
<td>Slender<br />
</td>
<td>56.934<br />
</td>
<td>225/224 589824/588245<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="x11-limit temperaments with badness below 0.05"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit temperaments with badness below 0.05</h1>
Listed is the wedgie and the TE badness times 1000 for 68 temperaments with badness less than 0.05.<br />
<table class="wiki_table">
<tr>
<td>Rank<br />
</td>
<td>Wedgie<br />
</td>
<td>Name<br />
</td>
<td>Badness<br />
</td>
<td>Commas<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td><<6 -7 -2 15 -25 -20 3 15 59 49]]<br />
</td>
<td>Miracle<br />
</td>
<td>10.684<br />
</td>
<td>225/224 243/242 441/440<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td><<7 -3 8 2 -21 -7 -21 27 15 -22]]<br />
</td>
<td>Orwell<br />
</td>
<td>15.231<br />
</td>
<td>99/98 121/120 176/175<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td><<44 -10 6 79 -118 -114 -27 42 218 201]]<br />
</td>
<td>Hemitert<br />
</td>
<td>15.633<br />
</td>
<td>2401/2400 3025/3024 65625/65536<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td><<9 5 -3 7 -13 -30 -20 -21 -1 30]]<br />
</td>
<td>Valentine<br />
</td>
<td>16.687<br />
</td>
<td>121/120 126/125 176/175<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td><<10 9 7 25 -9 -17 5 -9 27 46]]<br />
</td>
<td>Myna<br />
</td>
<td>16.842<br />
</td>
<td>126/125 176/175 243/242<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td><<1 4 10 18 4 13 25 12 28 16]]<br />
</td>
<td>Meantone<br />
</td>
<td>17.027<br />
</td>
<td>81/80 99/98 126/125<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td><<38 -3 8 64 -93 -94 -30 27 159 152]]<br />
</td>
<td>Quasiorwell<br />
</td>
<td>17.540<br />
</td>
<td>2401/2400 3025/3024 5632/5625<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td><<15 -2 -5 22 -38 -50 -17 -6 58 79]]<br />
</td>
<td>Hemithirds<br />
</td>
<td>19.003<br />
</td>
<td>385/384 441/440 3136/3125<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td><<23 -1 13 42 -55 -44 -13 33 101 73]]<br />
</td>
<td>Grendel<br />
</td>
<td>19.845<br />
</td>
<td>540/539 1375/1372 5632/5625<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td><<16 2 5 40 -34 -37 8 6 86 95]]<br />
</td>
<td>Hemiwürschmidt<br />
</td>
<td>21.069<br />
</td>
<td>243/242 441/440 3136/3125<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td><<1 4 10 -13 4 13 -24 12 -44 -71]]<br />
</td>
<td>Meanpop<br />
</td>
<td>21.543<br />
</td>
<td>81/80 126/125 540/539<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td><<4 16 9 10 16 3 2 -24 -32 -3]]<br />
</td>
<td>Squares<br />
</td>
<td>21.636<br />
</td>
<td>81/80 99/98 121/120<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td><<17 6 15 27 -30 -24 -16 18 42 24]]<br />
</td>
<td>Semisept<br />
</td>
<td>22.476<br />
</td>
<td>176/175 540/539 1331/1323<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td><<5 -11 -12 -3 -29 -33 -22 3 31 33]]<br />
</td>
<td>Tritonic<br />
</td>
<td>23.659<br />
</td>
<td>121/120 225/224 441/440<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td><<8 1 18 20 -17 6 4 39 43 -6]]<br />
</td>
<td>Würschmidt<br />
</td>
<td>24.413<br />
</td>
<td>99/98 176/175 243/242<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td><<13 -10 6 17 -46 -27 -18 42 74 27]]<br />
</td>
<td>Slender<br />
</td>
<td>25.342<br />
</td>
<td>225/224 385/384 1331/1323<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td><<2 8 20 5 8 26 1 24 -16 -55]]<br />
</td>
<td>Migration<br />
</td>
<td>25.516<br />
</td>
<td>81/80 121/120 126/125<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td><<11 13 17 12 -5 -4 -19 3 -17 -25]]<br />
</td>
<td>Nusecond<br />
</td>
<td>25.621<br />
</td>
<td>99/98 121/120 126/125<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td><<3 12 -1 -8 12 -10 -23 -36 -60 -19]]<br />
</td>
<td>Mothra<br />
</td>
<td>25.642<br />
</td>
<td>81/80 99/98 385/384<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td><<2 8 -11 5 8 -23 1 -48 -16 52]]<br />
</td>
<td>Mohajira<br />
</td>
<td>26.064<br />
</td>
<td>81/80 121/120 176/175<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td><<29 -8 11 57 -80 -64 -10 48 160 122]]<br />
</td>
<td>Eris<br />
</td>
<td>27.621<br />
</td>
<td>540/539 1375/1372 65625/65536<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td><<16 2 5 9 -34 -37 -41 6 14 8]]<br />
</td>
<td>Hemiwur<br />
</td>
<td>29.270<br />
</td>
<td>121/120 176/175 1375/1372<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td><<21 -9 -7 37 -63 -70 -14 9 117 128]]<br />
</td>
<td>Triwell<br />
</td>
<td>29.807<br />
</td>
<td>385/384 441/440 456533/455625<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td><<22 -5 3 24 -59 -57 -38 21 73 57]]<br />
</td>
<td>Tertia<br />
</td>
<td>30.171<br />
</td>
<td>385/384 1331/1323 1375/1372<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td><<82 -13 14 143 -211 -208 -57 69 377 353]]<br />
</td>
<td><br />
</td>
<td>30.609<br />
</td>
<td>2401/2400 3025/3024 369140625/369098752<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td><<3 12 -1 23 12 -10 26 -36 12 68]]<br />
</td>
<td><br />
</td>
<td>31.334<br />
</td>
<td>81/80 540/539 1029/1024<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td><<7 -3 8 33 -21 -7 28 27 87 65]]<br />
</td>
<td><br />
</td>
<td>31.438<br />
</td>
<td>225/224 441/440 1728/1715<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td><<67 -11 19 121 -173 -158 -40 75 319 274]]<br />
</td>
<td><br />
</td>
<td>32.121<br />
</td>
<td>3025/3024 180224/180075 703125/702464<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td><<6 -7 -2 -16 -25 -20 -46 15 -13 -38]]<br />
</td>
<td><br />
</td>
<td>32.946<br />
</td>
<td>99/98 176/175 1029/1024<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td><<10 9 7 -6 -9 -17 -44 -9 -45 -41]]<br />
</td>
<td><br />
</td>
<td>33.434<br />
</td>
<td>99/98 126/125 385/384<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td><<8 1 -13 20 -17 -43 4 -33 43 101]]<br />
</td>
<td><br />
</td>
<td>33.436<br />
</td>
<td>126/125 243/242 385/384<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td><<32 4 10 49 -68 -74 -33 12 100 103]]<br />
</td>
<td><br />
</td>
<td>34.814<br />
</td>
<td>2401/2400 3025/3024 3136/3125<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td><<22 -5 3 55 -59 -57 11 21 145 144]]<br />
</td>
<td><br />
</td>
<td>35.576<br />
</td>
<td>243/242 441/440 703125/702464<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td><<28 -12 1 39 -84 -77 -35 36 132 106]]<br />
</td>
<td><br />
</td>
<td>36.493<br />
</td>
<td>385/384 1375/1372 14641/14580<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td><<14 -6 16 35 -42 -14 7 54 102 43]]<br />
</td>
<td><br />
</td>
<td>38.377<br />
</td>
<td>225/224 243/242 2420/2401<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td><<25 7 2 47 -47 -67 -12 -15 85 125]]<br />
</td>
<td><br />
</td>
<td>39.162<br />
</td>
<td>441/440 3388/3375 6144/6125<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td><<4 -15 9 10 -33 3 2 63 75 -3]]<br />
</td>
<td><br />
</td>
<td>39.595<br />
</td>
<td>99/98 243/242 385/384<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td><<31 0 0 62 -72 -87 -9 0 144 174]]<br />
</td>
<td><br />
</td>
<td>39.9210<br />
</td>
<td>441/440 3136/3125 41503/41472<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td><<3 -19 -1 -8 -37 -10 -23 51 47 -19]]<br />
</td>
<td><br />
</td>
<td>40.217<br />
</td>
<td>99/98 121/120 1029/1024<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td><<19 14 4 32 -22 -47 -15 -30 26 76]]<br />
</td>
<td><br />
</td>
<td>40.539<br />
</td>
<td>126/125 176/175 14641/14580<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td><<54 -1 13 104 -127 -131 -22 33 245 247]]<br />
</td>
<td><br />
</td>
<td>41.496<br />
</td>
<td>2401/2400 5632/5625 46656/46585<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td><<8 1 -13 -11 -17 -43 -45 -33 -29 14]]<br />
</td>
<td><br />
</td>
<td>41.680<br />
</td>
<td>126/125 176/175 14641/14406<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td><<9 5 -3 38 -13 -30 29 -21 71 117]]<br />
</td>
<td><br />
</td>
<td>42.204<br />
</td>
<td>126/125 540/539 1029/1024<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td><<12 -14 -4 -1 -50 -40 -43 30 46 11]]<br />
</td>
<td><br />
</td>
<td>42.687<br />
</td>
<td>121/120 225/224 1029/1024<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td><<12 17 27 30 -1 9 6 15 11 -9]]<br />
</td>
<td><br />
</td>
<td>42.719<br />
</td>
<td>99/98 126/125 243/242<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td><<5 20 19 28 20 16 27 -12 -4 13]]<br />
</td>
<td><br />
</td>
<td>42.869<br />
</td>
<td>81/80 99/98 2541/2500<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td><<0 0 0 31 0 0 49 0 72 87]]<br />
</td>
<td><br />
</td>
<td>42.959<br />
</td>
<td>81/80 126/125 1029/1024<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td><<11 -18 -14 12 -54 -53 -19 18 90 82]]<br />
</td>
<td><br />
</td>
<td>44.005<br />
</td>
<td>225/224 441/440 9317/9216<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td><<11 13 17 43 -5 -4 30 3 55 62]]<br />
</td>
<td><br />
</td>
<td>44.041<br />
</td>
<td>126/125 176/175 2430/2401<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td><<13 21 6 17 3 -27 -18 -45 -33 27]]<br />
</td>
<td><br />
</td>
<td>44.186<br />
</td>
<td>121/120 441/440 891/875<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td><<26 11 12 34 -43 -54 -36 -3 41 54]]<br />
</td>
<td><br />
</td>
<td>44.660<br />
</td>
<td>176/175 1331/1323 2401/2400<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td><<61 -4 21 106 -148 -138 -43 60 260 225]]<br />
</td>
<td><br />
</td>
<td>44.729<br />
</td>
<td>3025/3024 5632/5625 825000/823543<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td><<60 -8 11 119 -152 -151 -19 48 304 296]]<br />
</td>
<td><br />
</td>
<td>44.888<br />
</td>
<td>2401/2400 46656/46585 172032/171875<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td><<19 -17 4 32 -71 -47 -15 57 133 76]]<br />
</td>
<td><br />
</td>
<td>45.168<br />
</td>
<td>225/224 385/384 585640/583443<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td><<5 -11 -12 28 -29 -33 27 3 103 120]]<br />
</td>
<td><br />
</td>
<td>45.456<br />
</td>
<td>225/224 385/384 27783/27500<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td><<5 20 19 -3 20 16 -22 -12 -76 -74]]<br />
</td>
<td><br />
</td>
<td>45.466<br />
</td>
<td>81/80 540/539 1375/1372<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td><<1 4 -21 -13 4 -36 -24 -60 -44 36]]<br />
</td>
<td><br />
</td>
<td>45.509<br />
</td>
<td>81/80 176/175 1331/1323<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td><<18 10 25 45 -26 -11 9 30 70 40]]<br />
</td>
<td><br />
</td>
<td>45.7950<br />
</td>
<td>176/175 243/242 1375/1372<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td><<39 1 18 82 -89 -81 -5 39 187 168]]<br />
</td>
<td><br />
</td>
<td>45.928<br />
</td>
<td>540/539 5632/5625 151263/151250<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td><<2 -23 -11 5 -41 -23 1 39 91 52]]<br />
</td>
<td><br />
</td>
<td>46.181<br />
</td>
<td>243/242 441/440 1815/1792<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td><<4 -15 -22 10 -33 -46 2 -9 75 104]]<br />
</td>
<td><br />
</td>
<td>46.462<br />
</td>
<td>225/224 243/242 1617/1600<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td><<9 5 28 7 -13 19 -20 51 -1 -77]]<br />
</td>
<td><br />
</td>
<td>47.885<br />
</td>
<td>121/120 225/224 891/875<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td><<33 8 20 67 -64 -61 -8 24 128 119]]<br />
</td>
<td><br />
</td>
<td>48.088<br />
</td>
<td>540/539 3136/3125 15488/15435<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td><<14 -6 -15 4 -42 -63 -42 -18 30 63]]<br />
</td>
<td><br />
</td>
<td>48.150<br />
</td>
<td>121/120 441/440 3136/3125<br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td><<8 1 18 -11 -17 6 -45 39 -29 -93]]<br />
</td>
<td><br />
</td>
<td>48.186<br />
</td>
<td>225/224 385/384 891/875<br />
</td>
</tr>
<tr>
<td>66<br />
</td>
<td><<50 -17 4 94 -143 -134 -24 57 277 250]]<br />
</td>
<td><br />
</td>
<td>48.798<br />
</td>
<td>2401/2400 3025/3024 1265625/1261568<br />
</td>
</tr>
<tr>
<td>67<br />
</td>
<td><<7 -3 -23 2 -21 -56 -21 -45 15 85]]<br />
</td>
<td><br />
</td>
<td>49.572<br />
</td>
<td>121/120 126/125 2079/2048<br />
</td>
</tr>
<tr>
<td>68<br />
</td>
<td><<20 18 14 19 -18 -34 -39 -18 -18 5]]<br />
</td>
<td><br />
</td>
<td>49.917<br />
</td>
<td>121/120 126/125 1728/1715<br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="x13-limit temperaments with badness below 0.04"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit temperaments with badness below 0.04</h1>
Listed is the wedgie and the TE badness times 1000 for 64 temperaments with badness less than 0.04.<br />
<table class="wiki_table">
<tr>
<td>Rank<br />
</td>
<td>Wedgie<br />
</td>
<td>Name<br />
</td>
<td>Badness<br />
</td>
<td>Commas<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td><<6 -7 -2 15 -34 -25 -20 3 -76 15 59 -53 49 -88 -173]]<br />
</td>
<td>Benediction<br />
</td>
<td>15.715<br />
</td>
<td>225/224 243/242 351/350 441/440<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td><<10 9 7 25 -5 -9 -17 5 -45 -9 27 -45 46 -40 -110]]<br />
</td>
<td>Myna<br />
</td>
<td>17.125<br />
</td>
<td>126/125 144/143 176/175 196/195<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td><<1 4 10 18 15 4 13 25 20 12 28 20 16 5 -15]]<br />
</td>
<td>Meantone<br />
</td>
<td>18.048<br />
</td>
<td>66/65 81/80 99/98 105/104<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td><<6 -7 -2 15 -3 -25 -20 3 -27 15 59 19 49 -1 -66]]<br />
</td>
<td>Miraculous<br />
</td>
<td>18.669<br />
</td>
<td>105/104 144/143 196/195 275/273<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td><<7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73]]<br />
</td>
<td>Orwell<br />
</td>
<td>19.718<br />
</td>
<td>99/98 121/120 176/175 275/273<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td><<7 -3 8 2 12 -21 -7 -21 -7 27 15 39 -22 4 34]]<br />
</td>
<td>Winston<br />
</td>
<td>19.931<br />
</td>
<td>66/65 99/98 105/104 121/120<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td><<9 5 -3 7 -20 -13 -30 -20 -65 -21 -1 -65 30 -45 -95]]<br />
</td>
<td>Valentino<br />
</td>
<td>20.665<br />
</td>
<td>121/120 126/125 176/175 196/195<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td><<1 4 10 -13 15 4 13 -24 20 12 -44 20 -71 5 100]]<br />
</td>
<td>Meanpop<br />
</td>
<td>20.883<br />
</td>
<td>81/80 105/104 144/143 196/195<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td><<9 5 -3 7 11 -13 -30 -20 -16 -21 -1 7 30 42 12]]<br />
</td>
<td>Lupercalia<br />
</td>
<td>21.328<br />
</td>
<td>66/65 105/104 121/120 126/125<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td><<15 -2 -5 22 -23 -38 -50 -17 -92 -6 58 -46 79 -46 -161]]<br />
</td>
<td>Hemithirds<br />
</td>
<td>21.738<br />
</td>
<td>196/195 352/351 1001/1000 1029/1024<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td><<5 -11 -12 -3 -18 -29 -33 -22 -47 3 31 -1 33 -6 -51]]<br />
</td>
<td>Tritonic<br />
</td>
<td>22.993<br />
</td>
<td>105/104 121/120 196/195 275/273<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td><<16 2 5 40 -39 -34 -37 8 -121 6 86 -98 95 -128 -283]]<br />
</td>
<td>Hemiwürschmidt<br />
</td>
<td>23.074<br />
</td>
<td>243/242 351/350 441/440 3584/3575<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td><<11 13 17 12 10 -5 -4 -19 -25 3 -17 -25 -25 -35 -10]]<br />
</td>
<td>Nusecond<br />
</td>
<td>23.323<br />
</td>
<td>66/65 99/98 121/120 126/125<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td><<2 8 -11 5 -1 8 -23 1 -9 -48 -16 -32 52 38 -22]]<br />
</td>
<td>Mohajira<br />
</td>
<td>23.388<br />
</td>
<td>66/65 105/104 121/120 512/507<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td><<8 1 18 20 -4 -17 6 4 -36 39 43 -13 -6 -78 -88]]<br />
</td>
<td>Würschmidt<br />
</td>
<td>23.593<br />
</td>
<td>99/98 144/143 176/175 275/273<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td><<3 12 -1 -8 14 12 -10 -23 11 -36 -60 -12 -19 43 78]]<br />
</td>
<td>Mothra<br />
</td>
<td>23.954<br />
</td>
<td>81/80 99/98 105/104 144/143<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td><<4 16 9 10 29 16 3 2 31 -24 -32 8 -3 48 63]]<br />
</td>
<td>Agora<br />
</td>
<td>24.522<br />
</td>
<td>81/80 99/98 105/104 121/120<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td><<23 -1 13 42 -27 -55 -44 -13 -128 33 101 -59 73 -124 -249]]<br />
</td>
<td>Grendel<br />
</td>
<td>24.839<br />
</td>
<td>352/351 540/539 625/624 1375/1372<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td><<17 6 15 27 -24 -30 -24 -16 -101 18 42 -78 24 -123 -183]]<br />
</td>
<td><br />
</td>
<td>25.204<br />
</td>
<td>176/175 351/350 540/539 1375/1372<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td><<0 0 0 0 31 0 0 0 49 0 0 72 0 87 107]]<br />
</td>
<td>Gallium<br />
</td>
<td>25.484<br />
</td>
<td>81/80 99/98 121/120 126/125<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td><<4 16 9 10 -2 16 3 2 -18 -24 -32 -64 -3 -39 -44]]<br />
</td>
<td>Squares<br />
</td>
<td>25.514<br />
</td>
<td>66/65 81/80 99/98 121/120<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td><<1 4 10 18 -16 4 13 25 -29 12 28 -52 16 -82 -122]]<br />
</td>
<td>Grosstone<br />
</td>
<td>25.899<br />
</td>
<td>81/80 99/98 126/125 144/143<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td><<13 -10 6 17 -22 -46 -27 -18 -83 42 74 -14 27 -84 -139]]<br />
</td>
<td>Slender<br />
</td>
<td>25.913<br />
</td>
<td>225/224 275/273 385/384 1331/1323<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td><<21 -9 -7 37 -57 -63 -70 -14 -168 9 117 -99 128 -134 -334]]<br />
</td>
<td><br />
</td>
<td>27.405<br />
</td>
<td>385/384 441/440 625/624 13720/13689<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td><<2 8 20 5 30 8 26 1 40 24 -16 40 -55 10 85]]<br />
</td>
<td><br />
</td>
<td>27.835<br />
</td>
<td>81/80 105/104 121/120 196/195<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td><<2 8 20 5 -1 8 26 1 -9 24 -16 -32 -55 -77 -22]]<br />
</td>
<td>Migration<br />
</td>
<td>28.071<br />
</td>
<td>66/65 121/120 126/125 1215/1183<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td><<22 -5 3 24 -42 -59 -57 -38 -148 21 73 -79 57 -129 -234]]<br />
</td>
<td><br />
</td>
<td>28.384<br />
</td>
<td>352/351 385/384 625/624 1331/1323<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td><<17 6 15 27 7 -30 -24 -16 -52 18 42 -6 24 -36 -76]]<br />
</td>
<td><br />
</td>
<td>28.408<br />
</td>
<td>144/143 176/175 196/195 275/273<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td><<16 2 5 9 -8 -34 -37 -41 -72 6 14 -26 8 -41 -61]]<br />
</td>
<td><br />
</td>
<td>28.432<br />
</td>
<td>121/120 176/175 196/195 275/273<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td><<3 12 -1 23 14 12 -10 26 11 -36 12 -12 68 43 -37]]<br />
</td>
<td><br />
</td>
<td>29.207<br />
</td>
<td>66/65 81/80 105/104 1001/1000<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td><<6 -7 -2 -16 -3 -25 -20 -46 -27 15 -13 19 -38 -1 49]]<br />
</td>
<td><br />
</td>
<td>29.452<br />
</td>
<td>66/65 99/98 105/104 1001/1000<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td><<10 9 7 25 26 -9 -17 5 4 -9 27 27 46 47 -3]]<br />
</td>
<td><br />
</td>
<td>29.868<br />
</td>
<td>66/65 105/104 126/125 540/539<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td><<7 -3 8 33 -19 -21 -7 28 -56 27 87 -33 65 -83 -188]]<br />
</td>
<td><br />
</td>
<td>30.237<br />
</td>
<td>144/143 225/224 351/350 441/440<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td><<16 2 5 40 -8 -34 -37 8 -72 6 86 -26 95 -41 -176]]<br />
</td>
<td>Hemithir<br />
</td>
<td>31.199<br />
</td>
<td>144/143 196/195 243/242 625/624<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td><<32 4 10 49 -47 -68 -74 -33 -193 12 100 -124 103 -169 -344]]<br />
</td>
<td><br />
</td>
<td>31.732<br />
</td>
<td>352/351 1001/1000 1716/1715 3025/3024<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td><<10 9 7 -6 -5 -9 -17 -44 -45 -9 -45 -45 -41 -40 5]]<br />
</td>
<td><br />
</td>
<td>31.850<br />
</td>
<td>66/65 99/98 126/125 385/384<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td><<15 -2 -5 22 -54 -38 -50 -17 -141 -6 58 -118 79 -133 -268]]<br />
</td>
<td><br />
</td>
<td>31.990<br />
</td>
<td>351/350 385/384 441/440 3146/3125<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td><<23 -1 13 42 -58 -55 -44 -13 -177 33 101 -131 73 -211 -356]]<br />
</td>
<td><br />
</td>
<td>32.359<br />
</td>
<td>351/350 540/539 1375/1372 5632/5625<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td><<1 4 10 -13 -16 4 13 -24 -29 12 -44 -52 -71 -82 -7]]<br />
</td>
<td><br />
</td>
<td>33.007<br />
</td>
<td>66/65 81/80 126/125 385/384<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td><<12 -14 -4 30 -37 -50 -40 6 -103 30 118 -34 98 -89 -239]]<br />
</td>
<td><br />
</td>
<td>33.451<br />
</td>
<td>225/224 243/242 441/440 1875/1859<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td><<8 1 18 20 27 -17 6 4 13 39 43 59 -6 9 19]]<br />
</td>
<td><br />
</td>
<td>34.382<br />
</td>
<td>66/65 99/98 105/104 243/242<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td><<8 1 -13 20 -4 -17 -43 4 -36 -33 43 -13 101 37 -88]]<br />
</td>
<td><br />
</td>
<td>34.458<br />
</td>
<td>105/104 126/125 144/143 243/242<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td><<3 -19 -1 -8 -17 -37 -10 -23 -38 51 47 31 -19 -44 -29]]<br />
</td>
<td><br />
</td>
<td>35.530<br />
</td>
<td>99/98 105/104 121/120 640/637<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td><<8 1 -13 20 -35 -17 -43 4 -85 -33 43 -85 101 -50 -195]]<br />
</td>
<td><br />
</td>
<td>35.585<br />
</td>
<td>126/125 196/195 385/384 1575/1573<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td><<3 12 -1 -8 -17 12 -10 -23 -38 -36 -60 -84 -19 -44 -29]]<br />
</td>
<td><br />
</td>
<td>36.239<br />
</td>
<td>66/65 81/80 99/98 385/384<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td><<8 1 -13 -11 -4 -17 -43 -45 -36 -33 -29 -13 14 37 27]]<br />
</td>
<td><br />
</td>
<td>36.331<br />
</td>
<td>66/65 105/104 126/125 512/507<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td><<5 -11 -12 -3 -49 -29 -33 -22 -96 3 31 -73 33 -93 -158]]<br />
</td>
<td><br />
</td>
<td>36.533<br />
</td>
<td>121/120 225/224 351/350 441/440<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td><<10 9 7 -6 26 -9 -17 -44 4 -9 -45 27 -41 47 112]]<br />
</td>
<td><br />
</td>
<td>36.656<br />
</td>
<td>99/98 105/104 126/125 144/143<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td><<3 12 -1 23 -17 12 -10 26 -38 -36 12 -84 68 -44 -144]]<br />
</td>
<td><br />
</td>
<td>36.857<br />
</td>
<td>81/80 144/143 176/175 1029/1024<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td><<22 -5 3 55 -42 -59 -57 11 -148 21 145 -79 144 -129 -349]]<br />
</td>
<td><br />
</td>
<td>36.876<br />
</td>
<td>243/242 441/440 625/624 3584/3575<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td><<5 20 19 28 13 20 16 27 2 -12 -4 -44 13 -34 -59]]<br />
</td>
<td><br />
</td>
<td>37.382<br />
</td>
<td>66/65 81/80 99/98 1001/1000<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td><<4 -15 9 10 -2 -33 3 2 -18 63 75 51 -3 -39 -44]]<br />
</td>
<td><br />
</td>
<td>37.408<br />
</td>
<td>99/98 105/104 144/143 243/242<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td><<13 -10 6 17 -53 -46 -27 -18 -132 42 74 -86 27 -171 -246]]<br />
</td>
<td><br />
</td>
<td>37.732<br />
</td>
<td>225/224 351/350 385/384 1331/1323<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td><<12 17 27 30 25 -1 9 6 -5 15 11 -5 -9 -30 -25]]<br />
</td>
<td><br />
</td>
<td>37.849<br />
</td>
<td>66/65 99/98 126/125 243/242<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td><<0 0 0 31 0 0 0 49 0 0 72 0 87 0 -115]]<br />
</td>
<td><br />
</td>
<td>37.885<br />
</td>
<td>81/80 105/104 196/195 512/507<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td><<13 21 6 17 9 3 -27 -18 -34 -45 -33 -57 27 3 -32]]<br />
</td>
<td><br />
</td>
<td>38.116<br />
</td>
<td>66/65 121/120 343/338 441/440<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td><<10 9 7 25 -36 -9 -17 5 -94 -9 27 -117 46 -127 -217]]<br />
</td>
<td><br />
</td>
<td>38.811<br />
</td>
<td>126/125 176/175 243/242 1573/1568<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td><<7 -3 8 33 12 -21 -7 28 -7 27 87 39 65 4 -81]]<br />
</td>
<td><br />
</td>
<td>38.812<br />
</td>
<td>105/104 196/195 275/273 648/637<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td><<9 5 -3 38 -20 -13 -30 29 -65 -21 71 -65 117 -45 -210]]<br />
</td>
<td><br />
</td>
<td>39.221<br />
</td>
<td>126/125 144/143 196/195 1029/1024<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td><<25 7 2 47 -28 -47 -67 -12 -137 -15 85 -91 125 -86 -271]]<br />
</td>
<td><br />
</td>
<td>39.271<br />
</td>
<td>196/195 352/351 1001/1000 6144/6125<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td><<14 -6 16 35 -38 -42 -14 7 -112 54 102 -66 43 -166 -261]]<br />
</td>
<td><br />
</td>
<td>39.531<br />
</td>
<td>225/224 243/242 351/350 2420/2401<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td><<11 13 17 12 41 -5 -4 -19 24 3 -17 47 -25 52 97]]<br />
</td>
<td><br />
</td>
<td>39.576<br />
</td>
<td>99/98 105/104 121/120 126/125<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td><<11 13 17 43 10 -5 -4 30 -25 3 55 -25 62 -35 -125]]<br />
</td>
<td><br />
</td>
<td>39.707<br />
</td>
<td>126/125 176/175 196/195 648/637<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td><<16 2 5 9 -39 -34 -37 -41 -121 6 14 -98 8 -128 -168]]<br />
</td>
<td><br />
</td>
<td>39.907<br />
</td>
<td>121/120 176/175 351/350 1375/1372<br />
</td>
</tr>
</table>
</body></html>