Catalog of thirteen-limit rank two temperaments

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Below is a complete listing of all 239 13-limit rank-two temperaments with generator complexity less than 40 and TE logflat badness less than 0.025. The TE error is multiplied by 1200 so that it can be thought of as cents, and the badness is multiplied by 1000. Some "junk" temperaments of very low complexity and high error are listed below the main list, which is ordered by increasing generator complexity, with ties broken by TE complexity.

Temperament list

Name Complexity Error (¢) Badness (×1k) Mapping Commas
Dicot extension 1.6214 27.3134 18.9555 [<1 1 2 2 2 2], <0 2 1 3 5 6]] 15/14 22/21 25/24 52/49
Father extension 1.6967 21.9084 20.1335 [<1 0 4 -2 -3 7], <0 1 -1 3 4 -2]] 16/15 22/21 26/25 28/27
Dicot extension 1.7156 27.3628 22.7796 [<1 1 2 2 2 4], <0 2 1 3 5 -1]] 15/14 22/21 25/24 40/39
Sharptone extension 1.7344 27.8260 21.2719 [<1 0 -4 -2 -6 -1], <0 1 4 3 6 3]] 14/13 21/20 27/26 45/44
Plutus extension 1.7810 27.5776 24.7359 [<1 0 -4 -5 -6 -1], <0 1 4 5 6 3]] 15/14 22/21 27/26 40/39
Mother extension 1.7872 36.0627 24.9964 [<1 0 4 6 10 7], <0 1 -1 -2 -4 -2]] 14/13 16/15 26/25 35/33
Flat 1.8400 30.6716 23.4200 [<1 1 2 3 4 4], <0 2 1 -1 -2 -1]] 14/13 21/20 25/24 33/32
Eudicot 1.8400 26.9815 23.8284 [<1 1 2 2 4 4], <0 2 1 3 -2 -1]] 15/14 25/24 33/32 40/39
Mavila variant 1.9230 27.4422 23.2705 [<1 0 7 6 5 10], <0 1 -3 -2 -1 -4]] 15/14 22/21 40/39 52/49
Meanertone extension 2.0118 27.4831 23.7844 [<1 0 -4 -2 5 -1], <0 1 4 3 -1 3]] 14/13 21/20 27/26 33/32
Beep extension 2.0235 19.3072 18.0832 [<1 0 0 2 -2 -1], <0 2 3 1 7 6]] 21/20 26/25 27/25 45/44
Father extension 2.0521 22.3720 21.6827 [<1 0 4 -2 -3 -6], <0 1 -1 3 4 6]] 16/15 22/21 28/27 52/49
Pentoid variant 2.1027 19.4190 22.7850 [<1 0 0 2 5 6], <0 2 3 1 -2 -3]] 21/20 27/25 66/65 99/98
Augustus 2.1372 14.5611 22.2357 [<3 0 7 -1 1 11], <0 1 0 2 2 0]] 26/25 36/35 45/44 56/55
Hystrix extension 2.1534 17.2113 19.8014 [<1 2 3 3 4 4], <0 -3 -5 -1 -4 -2]] 22/21 36/35 40/39 52/49
Blacksmith variant 2.1534 17.4180 22.5573 [<5 8 0 14 6 7], <0 0 1 0 1 1]] 28/27 35/33 40/39 49/48
Pentoid 2.1996 18.8797 21.1593 [<1 0 0 2 5 -1], <0 2 3 1 -2 6]] 21/20 26/25 27/25 33/32
Father extension 2.2249 19.9728 21.1254 [<1 0 4 -2 10 7], <0 1 -1 3 -4 -2]] 16/15 26/25 28/27 77/75
Pelogic extension 2.2355 17.0065 21.5281 [<1 0 7 9 5 -1], <0 1 -3 -4 -1 3]] 21/20 27/26 33/32 65/64
Pelogic extension 2.2524 18.4570 22.2116 [<1 0 7 9 5 13], <0 1 -3 -4 -1 -6]] 21/20 26/25 33/32 45/44
Sharp extension 2.4075 17.3437 21.8080 [<1 1 2 1 2 4], <0 2 1 6 5 -1]] 25/24 28/27 35/33 40/39
Pater extension 2.4120 22.2679 24.9369 [<1 0 4 11 10 7], <0 1 -1 -5 -4 -2]] 16/15 22/21 26/25 100/99
Sharp extension 2.4321 17.9441 23.0236 [<1 1 2 1 2 1], <0 2 1 6 5 9]] 25/24 28/27 35/33 65/63
August 2.4321 11.6244 18.4482 [<3 0 7 -1 1 -3], <0 1 0 2 2 3]] 27/26 36/35 45/44 56/55
Arnold 2.4351 20.2444 23.3005 [<1 0 -4 6 5 -1], <0 1 4 -2 -1 3]] 22/21 27/26 33/32 40/39
Dominatrix 2.4468 13.7371 18.2887 [<1 0 -4 6 -6 -1], <0 1 4 -2 6 3]] 27/26 36/35 45/44 64/63
Jamesbond 2.4935 16.1224 23.0035 [<7 11 16 0 24 26], <0 0 0 1 0 0]] 25/24 27/26 33/32 45/44
Septimal 2.4935 13.2598 22.5694 [<7 11 16 0 24 6], <0 0 0 1 0 1]] 25/24 33/32 45/44 65/63
Diminished variant 2.5237 17.3415 21.6035 [<4 0 3 5 1 2], <0 1 1 1 2 2]] 22/21 26/25 36/35 50/49
Diminished variant 2.5237 15.0507 23.8852 [<4 0 3 5 14 2], <0 1 1 1 0 2]] 26/25 36/35 50/49 56/55
Diminished 2.5237 11.9675 19.5087 [<4 0 3 5 14 15], <0 1 1 1 0 0]] 36/35 40/39 50/49 66/65
Octokaidecal extension 2.5841 16.7342 22.5814 [<2 0 -5 -4 -6 1], <0 1 3 3 4 2]] 22/21 28/27 40/39 50/49
Octokaidecal extension 2.5841 13.2207 20.6424 [<2 0 -5 -4 7 1], <0 1 3 3 0 2]] 28/27 40/39 50/49 55/54
Dichotic extension 2.6867 18.7092 22.7413 [<1 1 2 4 4 4], <0 2 1 -4 -2 -1]] 22/21 25/24 33/32 40/39
Dichotic extension 2.8702 14.1529 21.6740 [<1 1 2 4 2 4], <0 2 1 -4 5 -1]] 25/24 40/39 45/44 65/63
Decimal extension 2.8906 12.3389 21.3256 [<2 0 3 4 -1 1], <0 2 1 1 5 4]] 25/24 45/44 49/48 78/77
Blacksmith variant 2.8906 11.1408 22.3247 [<5 8 0 14 -6 7], <0 0 1 0 2 1]] 28/27 40/39 49/48 66/65
Pajaric 2.9846 11.0657 20.4605 [<2 0 11 12 7 17], <0 1 -2 -2 0 -3]] 40/39 45/44 50/49 56/55
Armodue 3.0731 12.8903 19.3512 [<1 0 7 -5 5 -1], <0 1 -3 5 -1 3]] 27/26 33/32 36/35 45/44
Progression 3.1546 11.1466 18.1575 [<1 1 2 2 3 3], <0 5 3 7 4 6]] 26/25 36/35 56/55 66/65
Opossum variant 3.2059 14.1496 24.4605 [<1 2 3 4 4 5], <0 -3 -5 -9 -4 -10]] 26/25 28/27 55/54 65/63
Opossum 3.2059 10.9238 19.3894 [<1 2 3 4 4 4], <0 -3 -5 -9 -4 -2]] 28/27 40/39 55/54 66/65
12 & 12f 3.2429 11.5467 24.8352 [<12 19 28 34 42 0], <0 0 0 0 0 1]] 36/35 45/44 50/49 56/55
Demolished extension 3.4688 11.0754 22.8374 [<4 0 3 5 -5 -4], <0 1 1 1 3 3]] 27/26 36/35 45/44 50/49
Godzilla 3.4688 8.1712 22.5029 [<1 0 -4 2 -6 -5], <0 2 8 1 12 11]] 45/44 49/48 78/77 81/80
Meanundec 3.5621 12.3475 24.2428 [<1 0 -4 -13 -6 -1], <0 1 4 10 6 3]] 27/26 40/39 45/44 56/55
Blacksmith 3.5987 10.3814 20.4976 [<5 8 0 14 29 7], <0 0 1 0 -1 1]] 28/27 40/39 49/48 55/54
Triforce 3.7856 7.9575 20.2480 [<3 0 7 6 8 4], <0 2 0 1 1 3]] 49/48 56/55 66/65 77/75
Darjeeling 3.7856 7.3788 21.4453 [<1 0 1 2 0 0], <0 6 5 3 13 14]] 49/48 55/54 66/65 77/75
Negri 3.8157 8.6891 17.8329 [<1 2 2 3 4 4], <0 -4 3 -2 -5 -3]] 45/44 49/48 56/55 78/77
Negric 3.8157 8.5618 20.2047 [<1 2 2 3 3 4], <0 -4 3 -2 4 -3]] 33/32 49/48 65/64 91/90
Superpelog extension 3.8459 10.9415 22.4731 [<1 0 7 2 5 6], <0 2 -6 1 -2 -3]] 33/32 45/44 49/48 78/77
Semafour extension 4.0235 8.0673 23.5937 [<1 0 -4 2 5 -5], <0 2 8 1 -2 11]] 33/32 49/48 55/54 91/90
Augene 4.0300 8.4291 20.7855 [<3 0 7 18 20 16], <0 1 0 -2 -2 -1]] 40/39 56/55 64/63 66/65
Meanenneadecal 4.0536 7.5265 21.1818 [<1 0 -4 -13 -6 -20], <0 1 4 10 6 15]] 45/44 56/55 78/77 81/80
Dominant 4.1548 9.0031 24.1076 [<1 0 -4 6 13 18], <0 1 4 -2 -6 -9]] 36/35 56/55 64/63 66/65
Porcupine 4.2906 7.7242 21.2764 [<1 2 3 2 4 4], <0 -3 -5 6 -4 -2]] 40/39 55/54 64/63 66/65
Hedgehog 4.3068 7.9361 21.5156 [<2 1 1 2 4 3], <0 3 5 5 4 6]] 50/49 55/54 65/63 99/98
Kema 4.3637 6.3766 22.7494 [<1 0 1 2 4 0], <0 6 5 3 -2 14]] 49/48 56/55 91/90 625/624
Sensa 4.6307 7.4628 23.2580 [<1 6 8 11 11 10], <0 -7 -9 -13 -12 -10]] 55/54 66/65 77/75 143/140
Sensis 4.6307 5.5229 20.0172 [<1 6 8 11 6 10], <0 -7 -9 -13 -4 -10]] 56/55 78/77 91/90 100/99
Vincenzo 4.6430 8.6347 24.7630 [<1 0 -4 -13 -6 10], <0 1 4 10 6 -4]] 45/44 56/55 65/64 81/80
Pajara variant 4.7306 7.8062 22.6765 [<2 0 11 12 26 17], <0 1 -2 -2 -6 -3]] 40/39 50/49 64/63 99/98
Injera 4.8643 6.7024 21.5655 [<2 0 -8 -7 -12 -21], <0 1 4 4 6 9]] 45/44 50/49 78/77 99/98
Flattone variant 4.9286 8.2456 24.9444 [<1 0 -4 17 5 10], <0 1 4 -9 -1 -4]] 33/32 55/54 65/64 105/104
Flattone 4.9403 6.1445 22.2597 [<1 0 -4 17 -6 10], <0 1 4 -9 6 -4]] 45/44 65/64 78/77 81/80
Nautilus 5.1345 5.6901 22.2846 [<1 2 3 3 4 5], <0 -6 -10 -3 -8 -19]] 49/48 55/54 91/90 100/99
Meantone 5.2032 4.3643 18.0484 [<1 0 -4 -13 -25 -20], <0 1 4 10 18 15]] 66/65 81/80 99/98 105/104
Ringo 5.3214 5.7998 22.6194 [<1 1 5 4 2 4], <0 2 -9 -4 5 -1]] 56/55 64/63 78/77 91/90
Superpyth 5.3375 5.1055 24.6725 [<1 0 -12 6 -22 -17], <0 1 9 -2 16 13]] 64/63 78/77 91/90 100/99
Ogene 5.3801 5.4596 22.8903 [<3 0 7 18 20 -8], <0 1 0 -2 -2 4]] 56/55 64/63 91/90 100/99
Undevigintone 5.4922 4.8990 22.9331 [<19 30 44 53 0 70], <0 0 0 0 1 0]] 49/48 65/64 81/80 91/90
Negroni 5.6280 5.5412 21.5588 [<1 2 2 3 5 4], <0 -4 3 -2 -15 -3]] 49/48 55/54 65/64 91/90
Niner 5.6784 5.4793 24.1428 [<9 0 21 11 17 19], <0 1 0 1 1 1]] 56/55 78/77 91/90 128/125
Blair 5.7085 5.5776 23.0863 [<1 0 3 1 3 3], <0 7 -3 8 2 3]] 65/64 78/77 91/90 99/98
Winston 5.7085 4.3658 19.9306 [<1 0 3 1 3 1], <0 7 -3 8 2 12]] 66/65 99/98 105/104 121/120
Agene 5.9464 5.4878 23.1130 [<3 0 7 18 20 35], <0 1 0 -2 -2 -5]] 56/55 64/63 78/77 100/99
Pajara variant 6.1261 4.7671 22.3268 [<2 0 11 12 26 36], <0 1 -2 -2 -6 -9]] 50/49 64/63 99/98 975/968
Andromeda 6.3059 3.2191 20.7493 [<1 0 15 25 32 37], <0 1 -8 -14 -18 -21]] 100/99 105/104 196/195 245/242
Crepuscular 6.3093 4.5686 24.3679 [<2 2 3 4 6 6], <0 5 7 7 4 6]] 50/49 78/77 99/98 144/143
Negril 6.5706 5.1756 24.3832 [<1 2 2 3 2 4], <0 -4 3 -2 14 -3]] 49/48 65/64 91/90 875/858
Modus 6.7257 4.1699 23.8059 [<1 1 1 4 2 4], <0 4 9 -8 10 -2]] 64/63 78/77 100/99 144/143
Lupercalia 6.7470 4.1905 21.3278 [<1 1 2 3 3 3], <0 9 5 -3 7 11]] 66/65 105/104 121/120 126/125
Superkleismic 6.7470 3.2749 21.4777 [<1 4 5 2 4 8], <0 -9 -10 3 -2 -16]] 100/99 105/104 245/242 1188/1183
Nusecond 6.9402 4.0097 23.3231 [<1 3 4 5 5 5], <0 -11 -13 -17 -12 -10]] 66/65 99/98 121/120 126/125
Magic 7.1768 3.2665 21.5095 [<1 0 2 -1 6 -2], <0 5 1 12 -8 18]] 100/99 105/104 144/143 196/195
Miraculous 7.3507 2.7371 18.6685 [<1 1 3 3 2 4], <0 6 -7 -2 15 -3]] 105/104 144/143 196/195 275/273
Mohajira 7.3637 4.3193 23.3878 [<1 1 0 6 2 4], <0 2 8 -11 5 -1]] 66/65 105/104 121/120 512/507
Mothra 7.4806 3.6713 23.9543 [<1 1 0 3 5 1], <0 3 12 -1 -8 14]] 81/80 99/98 105/104 144/143
Würschmidt 7.4927 2.7652 23.5928 [<1 7 3 15 17 1], <0 -8 -1 -18 -20 4]] 99/98 144/143 176/175 275/273
Meanpop 7.8114 3.1263 20.8828 [<1 0 -4 -13 24 -20], <0 1 4 10 -13 15]] 81/80 105/104 144/143 196/195
Agora 7.8369 3.4913 24.5215 [<1 3 8 6 7 14], <0 -4 -16 -9 -10 -29]] 81/80 99/98 105/104 121/120
Tritonic 8.0189 2.8102 22.9934 [<1 4 -3 -3 2 -5], <0 -5 11 12 3 18]] 105/104 121/120 196/195 275/273
Dwynwen 8.0948 2.9858 23.4609 [<1 1 2 3 3 2], <0 9 5 -3 7 26]] 91/90 121/120 126/125 176/175
Bohpier 8.2021 2.7870 24.8637 [<1 0 0 0 2 2], <0 13 19 23 12 14]] 100/99 144/143 245/243 275/273
Myna 8.5778 1.9478 17.1255 [<1 9 9 8 22 0], <0 -10 -9 -7 -25 5]] 126/125 144/143 176/175 196/195
Octacot 8.8331 2.6029 23.2762 [<1 1 1 2 2 4], <0 8 18 11 20 -4]] 100/99 144/143 243/242 245/242
Sensus 8.9610 2.9616 20.7887 [<1 6 8 11 23 10], <0 -7 -9 -13 -31 -10]] 91/90 126/125 169/168 352/351
Leapday 9.0442 2.8672 24.7316 [<1 0 -31 -21 -14 -9], <0 1 21 15 11 8]] 91/90 121/120 169/168 441/440
Cataclysmic 9.2501 2.4818 22.5549 [<1 0 1 -3 -5 0], <0 6 5 22 32 14]] 99/98 169/168 176/175 275/273
Diaschismic 9.3690 1.7525 18.9259 [<2 0 11 31 45 55], <0 1 -2 -8 -12 -15]] 126/125 176/175 196/195 364/363
Septimin 9.5243 2.7176 23.1168 [<1 4 1 5 5 7], <0 -11 6 -10 -7 -15]] 105/104 144/143 196/195 245/242
Witchcraft 9.5391 2.5946 23.5472 [<1 0 2 -1 -7 -2], <0 5 1 12 33 18]] 105/104 196/195 245/243 1188/1183
Orwell 9.5510 2.3097 19.7181 [<1 0 3 1 3 8], <0 7 -3 8 2 -19]] 99/98 121/120 176/175 275/273
Bunya 9.8019 2.6925 24.8861 [<1 1 1 -1 2 4], <0 4 9 26 10 -2]] 100/99 144/143 243/242 275/273
Thuja 10.7770 1.9835 22.8384 [<1 8 5 -2 4 16], <0 -12 -5 9 -1 -23]] 126/125 144/143 176/175 364/363
Alicorn 10.7943 1.9579 23.6666 [<1 2 3 4 3 5], <0 -8 -13 -23 9 -25]] 126/125 144/143 196/195 676/675
Hemififths 11.0372 1.5814 19.0896 [<1 1 -5 -1 2 4], <0 2 25 13 5 -1]] 144/143 196/195 243/242 364/363
Valentino 11.0831 2.0505 20.6653 [<1 1 2 3 3 5], <0 9 5 -3 7 -20]] 121/120 126/125 176/175 196/195
Hendec 11.2093 1.1966 17.7067 [<2 5 8 5 6 8], <0 -6 -11 2 3 -2]] 169/168 325/324 364/363 1716/1715
Bisemidim 11.3567 1.8575 23.8769 [<2 1 2 2 5 5], <0 9 11 15 8 10]] 126/125 144/143 196/195 364/363
Infraorwell 11.3869 1.9483 23.6834 [<1 14 0 16 12 20], <0 -16 3 -17 -11 -21]] 144/143 176/175 196/195 364/363
Garibaldi 11.6354 1.4775 20.6757 [<1 0 15 25 -33 -28], <0 1 -8 -14 23 20]] 225/224 275/273 325/324 385/384
Hitchcock 11.6543 1.9118 22.4484 [<1 3 6 -2 6 2], <0 -5 -13 17 -9 6]] 121/120 169/168 176/175 325/324
Quartonic 11.8517 1.7776 23.8747 [<1 2 3 3 5 4], <0 -11 -18 -5 -41 -8]] 169/168 176/175 325/324 540/539
Buzzard 12.3421 1.1747 18.8425 [<1 0 -6 4 -12 -7], <0 4 21 -3 39 27]] 176/175 351/350 676/675 847/845
Echidna 12.4332 1.4956 23.6786 [<2 1 9 2 12 19], <0 3 -6 5 -7 -16]] 176/175 351/350 364/363 540/539
Mystery 12.4896 1.0869 18.5912 [<29 46 0 14 33 40], <0 0 1 1 1 1]] 196/195 352/351 364/363 676/675
Sruti 12.7068 1.8820 23.7911 [<2 0 11 -15 -1 9], <0 2 -4 13 5 -1]] 144/143 176/175 351/350 676/675
Compton 12.9714 1.2359 21.8524 [<12 19 0 -22 -42 -67], <0 0 1 2 3 4]] 225/224 351/350 364/363 441/440
Lizard 12.9759 1.3242 21.7807 [<2 1 5 2 8 11], <0 6 -1 10 -3 -10]] 225/224 351/350 364/363 385/384
Ennealim 13.0079 1.3158 20.6966 [<9 1 1 12 -2 20], <0 2 3 2 5 2]] 169/168 243/242 325/324 441/440
Marvolo 13.0470 1.3528 21.4699 [<1 2 1 1 2 3], <0 -6 19 26 21 10]] 169/168 225/224 364/363 441/440
Rodan 13.2667 1.3261 18.4483 [<1 1 -1 3 6 8], <0 3 17 -1 -13 -22]] 196/195 245/243 352/351 364/363
Manna 13.2838 1.1773 17.0122 [<1 1 3 3 2 0], <0 6 -7 -2 15 38]] 225/224 243/242 325/324 385/384
Tritikleismic 13.4940 .8133 15.6523 [<3 0 3 10 8 0], <0 6 5 -2 3 14]] 325/324 364/363 441/440 625/624
Benediction 13.5241 1.0143 15.7152 [<1 1 3 3 2 7], <0 6 -7 -2 15 -34]] 225/224 243/242 351/350 441/440
Catakleismic 13.9069 1.1908 16.8832 [<1 0 1 -3 9 0], <0 6 5 22 -21 14]] 169/168 225/224 325/324 385/384
Qilin 14.1642 1.6395 22.8419 [<1 2 3 4 6 5], <0 -8 -13 -23 -49 -25]] 126/125 176/175 196/195 2200/2197
Harry 14.6430 .7511 13.0465 [<2 4 7 7 9 11], <0 -6 -17 -10 -15 -26]] 243/242 351/350 441/440 676/675
Semimiracle 14.7014 1.3334 24.6222 [<2 2 6 6 4 7], <0 6 -7 -2 15 2]] 169/168 225/224 243/242 385/384
Catalytic 14.7423 1.3244 22.3368 [<1 0 1 -3 -10 0], <0 6 5 22 51 14]] 169/168 225/224 325/324 1716/1715
Octopus 15.1423 1.1002 21.6786 [<8 1 3 3 16 14], <0 3 4 5 3 4]] 169/168 325/324 364/363 540/539
Enneaportent 15.2328 1.3133 22.3223 [<9 0 28 11 24 19], <0 2 -1 2 1 2]] 169/168 225/224 364/363 1716/1715
Bikleismic 15.6731 1.3198 21.8142 [<2 0 2 -6 -1 0], <0 6 5 22 15 14]] 169/168 225/224 243/242 325/324
Hemithirds 15.6794 1.1293 21.7376 [<1 4 2 2 7 0], <0 -15 2 5 -22 23]] 196/195 352/351 1001/1000 1029/1024
Gizzard 15.7868 .9255 20.2519 [<2 1 5 2 8 -2], <0 6 -1 10 -3 26]] 225/224 325/324 385/384 1573/1568
Coditone 16.1784 1.1526 24.3522 [<1 6 3 13 -3 2], <0 -13 -2 -30 19 5]] 225/224 351/350 385/384 847/845
Bison 17.5050 .7645 23.5039 [<2 5 7 3 3 4], <0 -7 -9 10 15 13]] 351/350 364/363 441/440 10985/10976
Mirkat 17.8357 .6381 18.6316 [<3 2 1 2 9 1], <0 6 13 14 3 22]] 351/350 540/539 676/675 1375/1372
Subfourth 18.4588 .9671 23.7996 [<1 0 17 4 11 16], <0 4 -37 -3 -19 -31]] 352/351 364/363 540/539 676/675
Mintone 18.5191 .9414 21.8493 [<1 5 9 7 12 11], <0 -22 -43 -27 -55 -47]] 243/242 351/350 441/440 1188/1183
Hemiseven 18.5600 .8367 21.9005 [<1 4 14 2 -5 19], <0 -6 -29 2 21 -38]] 351/350 385/384 441/440 676/675
Quadritikleismic 18.6111 .6278 18.7309 [<4 0 4 7 17 0], <0 6 5 4 -3 14]] 325/324 385/384 625/624 1375/1372
Sqrtphi 18.9279 .7746 20.0402 [<1 12 11 16 17 28], <0 -30 -25 -38 -39 -70]] 325/324 364/363 625/624 1375/1372
Supers 19.8111 .7880 21.6449 [<2 1 -12 2 -9 -2], <0 3 23 5 22 13]] 352/351 540/539 729/728 1575/1573
Kwai 19.8873 .7677 24.5550 [<1 0 -50 -40 32 37], <0 1 33 27 -18 -21]] 352/351 540/539 729/728 1375/1372
Metakleismic 19.9476 .8865 24.3714 [<1 0 1 -12 -5 0], <0 6 5 56 32 14]] 325/324 352/351 364/363 625/624
Catafourth 20.2345 .6664 21.6939 [<1 13 17 13 32 9], <0 -28 -36 -25 -70 -13]] 243/242 351/350 441/440 10985/10976
Countercata 20.2925 .8135 20.1564 [<1 0 1 11 -5 0], <0 6 5 -31 32 14]] 325/324 352/351 385/384 625/624
Ketchup 20.4870 .8412 24.8236 [<2 3 4 6 7 8], <0 4 15 -9 -2 -14]] 325/324 352/351 847/845 1331/1323
Semihemi 21.5338 .5670 21.1879 [<2 0 -35 -15 -47 -37], <0 2 25 13 34 28]] 352/351 676/675 847/845 1716/1715
Grendel 21.8078 .7473 24.8390 [<1 9 2 7 17 -5], <0 -23 1 -13 -42 27]] 352/351 540/539 625/624 1375/1372
Hemiwürschmidt 22.1019 .7291 23.0740 [<1 15 4 7 37 -29], <0 -16 -2 -5 -40 39]] 243/242 351/350 441/440 3584/3575
Ekadash 22.2725 .5694 20.3814 [<2 5 8 5 6 19], <0 -6 -11 2 3 -38]] 385/384 441/440 625/624 729/728
Arch 23.8240 .5728 19.5041 [<1 2 2 2 3 4], <0 -18 14 35 20 -13]] 364/363 441/440 676/675 3136/3125
Sesquart 24.3209 .6708 22.3961 [<1 1 7 5 2 -2], <0 4 -32 -15 10 39]] 243/242 364/363 441/440 3584/3575
Ennealimnic 24.3214 .7265 23.2502 [<9 1 1 12 -2 -33], <0 2 3 2 5 10]] 243/242 364/363 441/440 625/624
Subpental 24.7013 .6592 23.9401 [<1 6 8 17 -6 16], <0 -14 -18 -45 30 -39]] 351/350 540/539 676/675 3136/3125
Widefourth 24.7390 .6202 21.6356 [<1 16 8 -2 17 12], <0 -33 -13 11 -31 -19]] 385/384 441/440 625/624 847/845
Hemimist 25.1580 .5751 22.9233 [<3 0 26 56 8 23], <0 2 -8 -20 1 -5]] 352/351 676/675 847/845 3025/3024
Quincy 25.4024 .5479 23.8618 [<1 2 3 3 4 5], <0 -30 -49 -14 -39 -94]] 364/363 441/440 676/675 4375/4374
Decal 26.0158 .4227 23.9484 [<10 0 -56 -67 -108 37], <0 1 5 6 9 0]] 441/440 729/728 1001/1000 4225/4224
Hemischis 26.2491 .5658 20.8155 [<1 0 15 -17 51 14], <0 2 -16 25 -60 -13]] 351/350 540/539 676/675 40656/40625
Hemimaquila 26.6197 .5984 24.4449 [<1 28 -7 30 19 34], <0 -34 12 -35 -20 -39]] 364/363 540/539 676/675 3584/3575
Septisuperfourth 27.1080 .4537 22.8872 [<2 4 4 7 6 11], <0 -9 7 -15 10 -39]] 540/539 729/728 4000/3993 21168/21125
Pogo 27.6987 .3280 17.5141 [<2 1 22 2 25 -2], <0 3 -24 5 -25 13]] 540/539 729/728 4000/3993 10985/10976
Octoid 28.1048 .3789 15.2738 [<8 1 3 3 16 -21], <0 3 4 5 3 13]] 540/539 625/624 1375/1372 4000/3993
Hemiennealimmal 29.1857 .2310 12.5045 [<18 0 -1 22 48 -19], <0 2 3 2 1 6]] 676/675 1001/1000 1716/1715 3025/3024
Quanharuk 33.1711 .3531 21.3919 [<1 0 15 12 -7 -15], <0 5 -40 -29 33 59]] 540/539 729/728 1375/1372 4096/4095
Hemiseptisix 33.4393 .3824 21.1266 [<1 34 17 34 53 30], <0 -53 -24 -51 -81 -43]] 540/539 625/624 1375/1372 2200/2197
Tertiathirds 33.5315 .2302 19.4943 [<1 48 5 76 107 76], <0 -52 -3 -82 -116 -81]] 676/675 1716/1715 3025/3024 4225/4224
Gaster 33.6103 .3698 24.8815 [<1 11 38 37 -1 26], <0 -19 -72 -69 9 -45]] 540/539 729/728 1375/1372 2200/2197
34.4541 .3541 20.1941 [<2 1 -5 2 -2 -2], <0 9 40 15 37 39]] 540/539 729/728 1575/1573 2200/2197
Semihemiwürschmidt 34.6430 .3993 23.3876 [<2 14 6 9 -10 25], <0 -16 -2 -5 25 -26]] 676/675 1001/1000 1716/1715 3136/3125
Abigail 35.2653 .1098 8.8558 [<2 7 13 -1 1 -2], <0 -11 -24 19 17 27]] 1716/1715 2080/2079 3025/3024 4096/4095
Decoid 35.7438 .2238 13.4746 [<10 0 47 36 98 37], <0 2 -3 -1 -8 0]] 676/675 1001/1000 1716/1715 4096/4095
Eagle 36.1768 .2313 16.2821 [<2 4 9 8 12 13], <0 -8 -42 -23 -49 -54]] 676/675 1001/1000 1716/1715 10648/10647
Terture 36.3331 .2325 18.6469 [<3 0 -18 -32 8 -21], <0 4 21 34 2 27]] 676/675 1001/1000 3025/3024 10985/10976
Hemigamera 37.3448 .2265 20.4161 [<2 12 20 6 5 17], <0 -23 -40 -1 5 -25]] 1716/1715 2080/2079 2200/2197 3025/3024
Ponta 37.8845 .3814 23.6158 [<1 0 15 -59 135 56], <0 1 -8 39 -83 -33]] 540/539 625/624 729/728 2200/2197
38.3738 .2790 22.4115 [<1 27 54 35 6 124], <0 -30 -61 -38 -3 -142]] 729/728 1001/1000 1716/1715 3025/3024
Avicenna 38.6520 .2333 15.5572 [<3 2 8 16 9 8], <0 8 -3 -22 4 9]] 676/675 1001/1000 3025/3024 4096/4095
Deca 39.1828 .1817 16.8103 [<10 4 9 2 18 37], <0 5 6 11 7 0]] 1001/1000 3025/3024 4225/4224 4375/4374
Unthirds 39.4548 .2872 20.8877 [<1 29 33 25 25 99], <0 -42 -47 -34 -33 -146]] 625/624 1575/1573 2080/2079 2401/2400

Junk temperaments

Name Complexity Error (¢) Badness (×1k) Mapping Commas
.2702 336.2129 17.8545 [<1 2 2 3 3 0], <0 0 0 0 0 1]] 4/3 5/3 7/6 11/6
.2891 283.7695 17.6578 [<1 2 2 3 0 4], <0 0 0 0 1 0]] 4/3 5/3 7/6 13/9
.2891 287.8202 24.1056 [<1 2 2 3 0 0], <0 0 0 0 1 1]] 4/3 5/3 7/6 13/11
.5405 108.8851 16.3368 [<2 3 5 6 7 0], <0 0 0 0 0 1]] 6/5 8/7 9/7 11/10
.5781 130.7392 21.2974 [<2 3 5 6 0 7], <0 0 0 0 1 0]] 6/5 8/7 9/7 13/10
.6309 149.7414 19.8124 [<1 0 1 1 2 2], <0 1 1 1 1 1]] 6/5 7/5 11/10 13/10
.6309 145.2377 21.5971 [<1 0 2 1 2 2], <0 1 0 1 1 1]] 5/4 7/6 12/11 13/11
.6309 135.7653 21.7806 [<1 0 2 1 3 2], <0 1 0 1 0 1]] 5/4 7/6 11/8 13/12
.6309 118.9826 21.3636 [<1 0 1 3 2 2], <0 1 1 0 1 1]] 6/5 8/7 11/10 13/10
.6309 118.2399 24.7286 [<1 0 1 3 2 1], <0 1 1 0 1 2]] 6/5 8/7 11/10 15/13
.6309 99.9329 21.2702 [<1 0 1 3 2 4], <0 1 1 0 1 0]] 6/5 8/7 11/10 14/13
.7124 120.1537 22.8145 [<1 0 1 0 2 1], <0 1 1 2 1 2]] 6/5 9/7 11/10 14/13
.7124 112.9622 24.7317 [<2 3 5 0 7 7], <0 0 0 1 0 0]] 6/5 9/8 11/10 13/10
.8107 83.1978 22.0229 [<3 5 7 8 10 0], <0 0 0 0 0 1]] 7/6 10/9 11/9 16/15
.8614 81.8009 18.7149 [<1 0 -1 1 0 2], <0 1 2 1 2 1]] 7/6 10/9 11/9 13/12
.8614 93.1286 21.7729 [<1 0 -1 1 2 2], <0 1 2 1 1 1]] 7/6 10/9 12/11 13/11
.8614 76.3571 22.8403 [<1 0 -1 3 2 2], <0 1 2 0 1 1]] 8/7 10/9 12/11 13/11
.8614 57.0733 19.3277 [<2 3 0 1 2 7], <0 0 1 1 1 0]] 9/8 11/10 13/12 15/14
.8614 61.7635 21.4961 [<2 3 0 1 7 3], <0 0 1 1 0 1]] 9/8 12/11 14/13 15/13
.8614 64.6390 22.8779 [<2 3 0 1 7 7], <0 0 1 1 0 0]] 9/8 12/11 13/11 15/14
.8672 75.4782 22.2821 [<3 5 7 8 0 11], <0 0 0 0 1 0]] 7/6 10/9 13/12 16/15
1.0616 72.2918 22.6134 [<1 0 4 3 2 2], <0 1 -1 0 1 1]] 8/7 12/11 13/11 15/14
1.0616 68.1560 21.3950 [<1 0 4 3 2 4], <0 1 -1 0 1 0]] 8/7 12/11 14/13 15/13
1.0686 48.2352 24.6210 [<3 5 7 0 2 11], <0 0 0 1 1 0]] 10/9 13/12 16/15 22/21
1.0686 46.0898 24.1511 [<3 5 7 0 2 3], <0 0 0 1 1 1]] 10/9 14/13 16/15 22/21
1.0810 54.4751 21.7669 [<4 6 9 11 14 0], <0 0 0 0 0 1]] 9/8 12/11 15/14 25/22
1.0810 53.8146 21.8059 [<2 3 0 1 2 -2], <0 0 1 1 1 2]] 9/8 11/10 15/14 26/25
1.1563 51.8815 22.1512 [<1 0 -1 -2 -3 2], <0 1 2 3 4 1]] 10/9 13/12 15/14 22/21
1.1563 55.5099 24.5510 [<4 6 9 11 0 15], <0 0 0 0 1 0]] 9/8 14/13 15/13 35/32
1.1563 41.3624 24.4943 [<4 6 9 11 0 1], <0 0 0 0 1 1]] 9/8 15/14 25/24 55/52
1.1714 53.8501 22.8620 [<1 0 4 3 2 7], <0 1 -1 0 1 -2]] 8/7 12/11 15/14 26/25
1.2619 55.5942 23.7686 [<1 1 2 2 3 3], <0 2 1 3 2 2]] 12/11 13/11 15/14 25/22
1.2619 53.0408 23.1630 [<1 1 2 2 3 3], <0 2 1 3 2 3]] 12/11 14/13 15/13 25/22
1.2920 43.2424 21.8817 [<1 0 0 2 1 2], <0 2 3 1 3 2]] 11/10 13/12 21/20 27/25
1.2920 39.0609 21.8839 [<1 0 0 2 2 3], <0 2 3 1 2 1]] 12/11 14/13 21/20 27/25
1.2920 42.8838 24.2613 [<1 0 0 2 1 3], <0 2 3 1 3 1]] 11/10 14/13 21/20 27/25
1.3433 43.8182 20.8537 [<1 0 4 6 5 7], <0 1 -1 -2 -1 -2]] 11/10 14/13 16/15 26/25
1.3433 48.6247 23.3373 [<1 0 4 6 5 2], <0 1 -1 -2 -1 1]] 11/10 13/12 16/15 21/20
1.3433 41.3652 22.5640 [<1 0 4 6 2 7], <0 1 -1 -2 1 -2]] 12/11 14/13 16/15 26/25
1.3512 38.8900 22.4912 [<5 8 12 14 17 0], <0 0 0 0 0 1]] 11/10 16/15 21/20 27/25
1.4453 33.1105 21.4624 [<5 8 12 14 0 19], <0 0 0 0 1 0]] 14/13 16/15 26/25 27/25
1.4993 37.8027 22.5820 [<1 0 4 -2 2 -1], <0 1 -1 3 1 3]] 12/11 14/13 16/15 27/26
1.6091 33.9540 24.0271 [<1 0 4 -2 2 7], <0 1 -1 3 1 -2]] 12/11 16/15 26/25 35/33
1.6181 43.6565 23.8050 [<1 1 2 3 3 3], <0 2 1 -1 1 2]] 11/10 13/12 21/20 25/24
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