Catalog of seven-limit rank two temperaments
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Below is a complete listing of all 179 7-limit rank-two temperaments with TE complexity less than 20 and TE logflat badness less than 0.06, obtained by the wedgie method. 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 are listed below the main list, which is ordered by increasing complexity.
Temperament list
Name | Complexity | Error (¢) | Badness (k) | Wedgie | Mapping | Commas |
---|---|---|---|---|---|---|
ternary | 0.770 | 58.026 | 28.673 | ⟨⟨ 0 0 3 0 5 7 ]] | [⟨3 5 7 0], ⟨0 0 0 1]] | 10/9 16/15 |
dicot | 0.818 | 35.781 | 19.935 | ⟨⟨ 2 1 3 -3 -1 4 ]] | [⟨1 1 2 2], ⟨0 2 1 3]] | 15/14 25/24 |
mother | 0.835 | 41.553 | 24.152 | ⟨⟨ 1 -1 -2 -4 -6 -2 ]] | [⟨1 0 4 6], ⟨0 1 -1 -2]] | 16/15 21/20 |
brutus | 0.859 | 86.798 | 53.389 | ⟨⟨ 1 2 4 1 4 4 ]] | [⟨1 0 -1 -4], ⟨0 1 2 4]] | 10/9 28/25 |
geryon | 0.863 | 82.117 | 51.009 | ⟨⟨ 2 1 0 -3 -6 -3 ]] | [⟨1 1 2 3], ⟨0 2 1 0]] | 8/7 25/21 |
antaeus | 0.887 | 57.236 | 37.537 | ⟨⟨ 0 2 -2 3 -3 -10 ]] | [⟨2 3 0 10], ⟨0 0 1 -1]] | 9/8 35/32 |
beep | 0.917 | 26.605 | 18.638 | ⟨⟨ 2 3 1 0 -4 -6 ]] | [⟨1 0 0 2], ⟨0 2 3 1]] | 21/20 27/25 |
father | 0.954 | 28.092 | 21.312 | ⟨⟨ 1 -1 3 -4 2 10 ]] | [⟨1 0 4 -2], ⟨0 1 -1 3]] | 16/15 28/27 |
flat | 0.969 | 32.444 | 25.381 | ⟨⟨ 2 1 -1 -3 -7 -5 ]] | [⟨1 1 2 3], ⟨0 2 1 -1]] | 21/20 25/24 |
quad | 0.979 | 57.541 | 45.991 | ⟨⟨ 0 0 4 0 6 9 ]] | [⟨4 6 9 0], ⟨0 0 0 1]] | 9/8 25/24 |
phlegyas | 0.991 | 62.667 | 51.293 | ⟨⟨ 1 2 -2 1 -6 -10 ]] | [⟨1 0 -1 6], ⟨0 1 2 -2]] | 10/9 35/32 |
malacoda | 0.997 | 44.954 | 37.207 | ⟨⟨ 2 -1 1 -6 -4 5 ]] | [⟨1 0 3 2], ⟨0 2 -1 1]] | 15/14 35/32 |
sharptone | 1.022 | 28.544 | 24.848 | ⟨⟨ 1 4 3 4 2 -4 ]] | [⟨1 0 -4 -2], ⟨0 1 4 3]] | 21/20 28/27 |
ugolino | 1.068 | 46.010 | 43.758 | ⟨⟨ 2 3 5 0 2 3 ]] | [⟨1 0 0 -1], ⟨0 2 3 5]] | 15/14 27/25 |
charon | 1.082 | 57.767 | 56.404 | ⟨⟨ 2 4 4 2 1 -2 ]] | [⟨2 0 -2 -1], ⟨0 1 2 2]] | 10/9 49/45 |
nessus | 1.133 | 55.258 | 59.070 | ⟨⟨ 2 4 1 2 -4 -9 ]] | [⟨1 0 -1 2], ⟨0 2 4 1]] | 10/9 49/48 |
penta | 1.163 | 41.597 | 46.882 | ⟨⟨ 3 2 4 -4 -2 4 ]] | [⟨1 1 2 2], ⟨0 3 2 4]] | 28/25 36/35 |
medusa | 1.182 | 36.664 | 42.712 | ⟨⟨ 1 -3 -2 -7 -6 4 ]] | [⟨1 0 7 6], ⟨0 1 -3 -2]] | 15/14 64/63 |
plutus | 1.224 | 36.293 | 45.275 | ⟨⟨ 1 4 5 4 5 0 ]] | [⟨1 0 -4 -5], ⟨0 1 4 5]] | 15/14 81/80 |
sodium | 1.241 | 43.494 | 55.814 | ⟨⟨ 2 5 3 3 -1 -7 ]] | [⟨1 1 1 2], ⟨0 2 5 3]] | 21/20 54/49 |
mite | 1.257 | 41.576 | 54.770 | ⟨⟨ 2 3 6 0 4 6 ]] | [⟨1 0 0 -2], ⟨0 2 3 6]] | 27/25 28/25 |
baba | 1.258 | 33.587 | 44.321 | ⟨⟨ 2 -2 1 -8 -4 8 ]] | [⟨1 0 4 2], ⟨0 2 -2 1]] | 16/15 49/45 |
quint | 1.278 | 35.517 | 48.312 | ⟨⟨ 0 0 5 0 8 12 ]] | [⟨5 8 12 0], ⟨0 0 0 1]] | 16/15 27/25 |
sharp | 1.333 | 19.537 | 28.942 | ⟨⟨ 2 1 6 -3 4 11 ]] | [⟨1 1 2 1], ⟨0 2 1 6]] | 25/24 28/27 |
walid | 1.395 | 30.187 | 48.978 | ⟨⟨ 2 -2 -2 -8 -9 1 ]] | [⟨2 0 8 9], ⟨0 1 -1 -1]] | 16/15 50/49 |
pelogic | 1.404 | 23.529 | 38.661 | ⟨⟨ 1 -3 -4 -7 -9 -1 ]] | [⟨1 0 7 9], ⟨0 1 -3 -4]] | 21/20 135/128 |
oxygen | 1.412 | 36.009 | 59.866 | ⟨⟨ 3 5 2 1 -5 -9 ]] | [⟨1 2 3 3], ⟨0 -3 -5 -2]] | 21/20 175/162 |
wallaby | 1.433 | 34.157 | 58.468 | ⟨⟨ 1 -3 3 -7 2 15 ]] | [⟨1 0 7 -2], ⟨0 1 -3 3]] | 28/27 35/32 |
dominant | 1.466 | 11.550 | 20.690 | ⟨⟨ 1 4 -2 4 -6 -16 ]] | [⟨1 0 -4 6], ⟨0 1 4 -2]] | 36/35 64/63 |
pater | 1.469 | 29.457 | 53.001 | ⟨⟨ 1 -1 -5 -4 -11 -9 ]] | [⟨1 0 4 11], ⟨0 1 -1 -5]] | 16/15 126/125 |
diminished | 1.494 | 12.047 | 22.401 | ⟨⟨ 4 4 4 -3 -5 -2 ]] | [⟨4 0 3 5], ⟨0 1 1 1]] | 36/35 50/49 |
decimal | 1.502 | 15.075 | 28.334 | ⟨⟨ 4 2 2 -6 -8 -1 ]] | [⟨2 0 3 4], ⟨0 2 1 1]] | 25/24 49/48 |
blacksmith | 1.526 | 13.210 | 25.640 | ⟨⟨ 0 5 0 8 0 -14 ]] | [⟨5 8 0 14], ⟨0 0 1 0]] | 28/27 49/48 |
hystrix | 1.543 | 22.654 | 44.944 | ⟨⟨ 3 5 1 1 -7 -12 ]] | [⟨1 2 3 3], ⟨0 -3 -5 -1]] | 36/35 160/147 |
dichotic | 1.588 | 17.871 | 37.565 | ⟨⟨ 2 1 -4 -3 -12 -12 ]] | [⟨1 1 2 4], ⟨0 2 1 -4]] | 25/24 64/63 |
octokaidecal | 1.618 | 16.849 | 36.747 | ⟨⟨ 2 6 6 5 4 -3 ]] | [⟨2 0 -5 -4], ⟨0 1 3 3]] | 28/27 50/49 |
fluorine | 1.618 | 25.482 | 55.623 | ⟨⟨ 1 6 5 7 5 -5 ]] | [⟨1 0 -7 -5], ⟨0 1 6 5]] | 21/20 243/224 |
august | 1.655 | 11.594 | 26.459 | ⟨⟨ 3 0 6 -7 1 14 ]] | [⟨3 0 7 -1], ⟨0 1 0 2]] | 36/35 128/125 |
deflated | 1.734 | 23.590 | 59.079 | ⟨⟨ 3 0 -3 -7 -13 -7 ]] | [⟨3 0 7 13], ⟨0 1 0 -1]] | 21/20 128/125 |
jamesbond | 1.749 | 16.364 | 41.714 | ⟨⟨ 0 0 7 0 11 16 ]] | [⟨7 11 16 0], ⟨0 0 0 1]] | 25/24 81/80 |
armodue | 1.804 | 18.075 | 49.038 | ⟨⟨ 1 -3 5 -7 5 20 ]] | [⟨1 0 7 -5], ⟨0 1 -3 5]] | 36/35 135/128 |
opossum | 1.895 | 13.586 | 40.650 | ⟨⟨ 3 5 9 1 6 7 ]] | [⟨1 2 3 4], ⟨0 -3 -5 -9]] | 28/27 126/125 |
pajara | 1.953 | 6.301 | 20.033 | ⟨⟨ 2 -4 -4 -11 -12 2 ]] | [⟨2 0 11 12], ⟨0 1 -2 -2]] | 50/49 64/63 |
progression | 1.976 | 14.868 | 48.356 | ⟨⟨ 5 3 7 -7 -3 8 ]] | [⟨1 1 2 2], ⟨0 5 3 7]] | 36/35 392/375 |
sidi | 2.074 | 15.794 | 56.586 | ⟨⟨ 4 2 9 -6 3 15 ]] | [⟨1 3 3 6], ⟨0 -4 -2 -9]] | 25/24 245/243 |
godzilla | 2.181 | 6.748 | 26.747 | ⟨⟨ 2 8 1 8 -4 -20 ]] | [⟨1 0 -4 2], ⟨0 2 8 1]] | 49/48 81/80 |
meantone | 2.205 | 3.384 | 13.707 | ⟨⟨ 1 4 10 4 13 12 ]] | [⟨1 0 -4 -13], ⟨0 1 4 10]] | 81/80 126/125 |
injera | 2.205 | 7.686 | 31.130 | ⟨⟨ 2 8 8 8 7 -4 ]] | [⟨2 0 -8 -7], ⟨0 1 4 4]] | 50/49 81/80 |
inflated | 2.224 | 13.279 | 54.729 | ⟨⟨ 3 0 9 -7 6 21 ]] | [⟨3 0 7 -6], ⟨0 1 0 3]] | 28/27 128/125 |
negri | 2.245 | 6.308 | 26.483 | ⟨⟨ 4 -3 2 -14 -8 13 ]] | [⟨1 2 2 3], ⟨0 -4 3 -2]] | 49/48 225/224 |
keemun | 2.280 | 6.326 | 27.408 | ⟨⟨ 6 5 3 -6 -12 -7 ]] | [⟨1 0 1 2], ⟨0 6 5 3]] | 49/48 126/125 |
superpelog | 2.316 | 13.029 | 58.216 | ⟨⟨ 2 -6 1 -14 -4 19 ]] | [⟨1 0 7 2], ⟨0 2 -6 1]] | 49/48 135/128 |
augene | 2.336 | 5.456 | 24.816 | ⟨⟨ 3 0 -6 -7 -18 -14 ]] | [⟨3 0 7 18], ⟨0 1 0 -2]] | 64/63 126/125 |
ripple | 2.454 | 11.901 | 59.735 | ⟨⟨ 5 8 2 1 -11 -18 ]] | [⟨1 2 3 3], ⟨0 -5 -8 -2]] | 36/35 2560/2401 |
triforce | 2.529 | 10.318 | 54.988 | ⟨⟨ 6 0 3 -14 -12 7 ]] | [⟨3 0 7 6], ⟨0 2 0 1]] | 49/48 128/125 |
schism | 2.544 | 10.503 | 56.648 | ⟨⟨ 1 -8 -2 -15 -6 18 ]] | [⟨1 0 15 6], ⟨0 1 -8 -2]] | 64/63 360/343 |
hexe | 2.689 | 9.578 | 57.730 | ⟨⟨ 6 0 0 -14 -17 0 ]] | [⟨6 0 14 17], ⟨0 1 0 0]] | 50/49 128/125 |
hedgehog | 2.784 | 6.810 | 43.983 | ⟨⟨ 6 10 10 2 -1 -5 ]] | [⟨2 1 1 2], ⟨0 3 5 5]] | 50/49 245/243 |
porcupine | 2.819 | 6.200 | 41.057 | ⟨⟨ 3 5 -6 1 -18 -28 ]] | [⟨1 2 3 2], ⟨0 -3 -5 6]] | 64/63 250/243 |
superpyth | 2.874 | 4.695 | 32.318 | ⟨⟨ 1 9 -2 12 -6 -30 ]] | [⟨1 0 -12 6], ⟨0 1 9 -2]] | 64/63 245/243 |
doublewide | 2.928 | 6.082 | 43.462 | ⟨⟨ 8 6 6 -9 -13 -3 ]] | [⟨2 1 3 4], ⟨0 4 3 3]] | 50/49 875/864 |
magic | 2.937 | 2.631 | 18.918 | ⟨⟨ 5 1 12 -10 5 25 ]] | [⟨1 0 2 -1], ⟨0 5 1 12]] | 225/224 245/243 |
nautilus | 2.943 | 7.955 | 57.420 | ⟨⟨ 6 10 3 2 -12 -21 ]] | [⟨1 2 3 3], ⟨0 -6 -10 -3]] | 49/48 250/243 |
flattone | 2.987 | 5.186 | 38.553 | ⟨⟨ 1 4 -9 4 -17 -32 ]] | [⟨1 0 -4 17], ⟨0 1 4 -9]] | 81/80 525/512 |
catler | 3.026 | 6.590 | 50.297 | ⟨⟨ 0 0 12 0 19 28 ]] | [⟨12 19 28 0], ⟨0 0 0 1]] | 81/80 128/125 |
sensi | 3.080 | 3.242 | 25.622 | ⟨⟨ 7 9 13 -2 1 5 ]] | [⟨1 6 8 11], ⟨0 -7 -9 -13]] | 126/125 245/243 |
beatles | 3.125 | 5.636 | 45.872 | ⟨⟨ 2 -9 -4 -19 -12 16 ]] | [⟨1 1 5 4], ⟨0 2 -9 -4]] | 64/63 686/675 |
liese | 3.211 | 5.435 | 46.706 | ⟨⟨ 3 12 11 12 9 -8 ]] | [⟨1 0 -4 -3], ⟨0 3 12 11]] | 81/80 686/675 |
muggles | 3.261 | 6.343 | 56.206 | ⟨⟨ 5 1 -7 -10 -25 -19 ]] | [⟨1 0 2 5], ⟨0 5 1 -7]] | 126/125 525/512 |
triton | 3.342 | 6.365 | 59.245 | ⟨⟨ 3 -7 -8 -18 -21 1 ]] | [⟨1 0 6 7], ⟨0 3 -7 -8]] | 225/224 1029/1000 |
porky | 3.362 | 5.774 | 54.389 | ⟨⟨ 3 5 16 1 17 23 ]] | [⟨1 2 3 5], ⟨0 -3 -5 -16]] | 225/224 250/243 |
mothra | 3.573 | 3.491 | 37.146 | ⟨⟨ 3 12 -1 12 -10 -36 ]] | [⟨1 1 0 3], ⟨0 3 12 -1]] | 81/80 1029/1024 |
orwell | 3.685 | 1.832 | 20.735 | ⟨⟨ 7 -3 8 -21 -7 27 ]] | [⟨1 0 3 1], ⟨0 7 -3 8]] | 225/224 1728/1715 |
myna | 3.731 | 2.331 | 27.044 | ⟨⟨ 10 9 7 -9 -17 -9 ]] | [⟨1 9 9 8], ⟨0 -10 -9 -7]] | 126/125 1728/1715 |
garibaldi | 3.823 | 1.778 | 21.644 | ⟨⟨ 1 -8 -14 -15 -25 -10 ]] | [⟨1 0 15 25], ⟨0 1 -8 -14]] | 225/224 3125/3087 |
miracle | 3.991 | 1.261 | 16.742 | ⟨⟨ 6 -7 -2 -25 -20 15 ]] | [⟨1 1 3 3], ⟨0 6 -7 -2]] | 225/224 1029/1024 |
squares | 4.022 | 3.412 | 45.993 | ⟨⟨ 4 16 9 16 3 -24 ]] | [⟨1 3 8 6], ⟨0 -4 -16 -9]] | 81/80 2401/2400 |
valentine | 4.210 | 2.103 | 31.056 | ⟨⟨ 9 5 -3 -13 -30 -21 ]] | [⟨1 1 2 3], ⟨0 9 5 -3]] | 126/125 1029/1024 |
diaschismic | 4.290 | 2.472 | 37.914 | ⟨⟨ 2 -4 -16 -11 -31 -26 ]] | [⟨2 0 11 31], ⟨0 1 -2 -8]] | 126/125 2048/2025 |
mohajira | 4.368 | 3.504 | 55.714 | ⟨⟨ 2 8 -11 8 -23 -48 ]] | [⟨1 1 0 6], ⟨0 2 8 -11]] | 81/80 6144/6125 |
nusecond | 4.454 | 3.048 | 50.389 | ⟨⟨ 11 13 17 -5 -4 3 ]] | [⟨1 3 4 5], ⟨0 -11 -13 -17]] | 126/125 2430/2401 |
octacot | 4.551 | 1.961 | 33.845 | ⟨⟨ 8 18 11 10 -5 -25 ]] | [⟨1 1 1 2], ⟨0 8 18 11]] | 245/243 2401/2400 |
würschmidt | 4.578 | 2.908 | 50.776 | ⟨⟨ 8 1 18 -17 6 39 ]] | [⟨1 7 3 15], ⟨0 -8 -1 -18]] | 225/224 8748/8575 |
superkleismic | 4.620 | 2.695 | 47.932 | ⟨⟨ 9 10 -3 -5 -30 -35 ]] | [⟨1 4 5 2], ⟨0 -9 -10 3]] | 875/864 1029/1024 |
catakleismic | 4.684 | 1.176 | 21.501 | ⟨⟨ 6 5 22 -6 18 37 ]] | [⟨1 0 1 -3], ⟨0 6 5 22]] | 225/224 4375/4374 |
unicorn | 4.847 | 2.090 | 40.913 | ⟨⟨ 8 13 23 2 14 17 ]] | [⟨1 2 3 4], ⟨0 -8 -13 -23]] | 126/125 10976/10935 |
rodan | 5.012 | 1.773 | 37.112 | ⟨⟨ 3 17 -1 20 -10 -50 ]] | [⟨1 1 -1 3], ⟨0 3 17 -1]] | 245/243 1029/1024 |
shrutar | 5.101 | 2.185 | 47.377 | ⟨⟨ 4 -8 14 -22 11 55 ]] | [⟨2 1 9 -2], ⟨0 2 -4 7]] | 245/243 2048/2025 |
tritonic | 5.291 | 2.039 | 47.578 | ⟨⟨ 5 -11 -12 -29 -33 3 ]] | [⟨1 4 -3 -3], ⟨0 -5 11 12]] | 225/224 50421/50000 |
quartonic | 5.395 | 1.758 | 42.632 | ⟨⟨ 11 18 5 3 -23 -39 ]] | [⟨1 2 3 3], ⟨0 -11 -18 -5]] | 1728/1715 4000/3969 |
clyde | 5.610 | 1.802 | 47.261 | ⟨⟨ 12 10 25 -12 6 30 ]] | [⟨1 6 6 12], ⟨0 -12 -10 -25]] | 245/243 3136/3125 |
septimin | 5.874 | 1.896 | 54.502 | ⟨⟨ 11 -6 10 -35 -15 40 ]] | [⟨1 4 1 5], ⟨0 -11 6 -10]] | 225/224 84035/82944 |
echidna | 5.925 | 1.984 | 58.033 | ⟨⟨ 6 -12 10 -33 -1 57 ]] | [⟨2 1 9 2], ⟨0 3 -6 5]] | 1728/1715 2048/2025 |
compton | 5.927 | 1.219 | 35.686 | ⟨⟨ 0 12 24 19 38 22 ]] | [⟨12 19 0 -22], ⟨0 0 1 2]] | 225/224 250047/250000 |
bidia | 5.940 | 1.921 | 56.474 | ⟨⟨ 4 -8 -20 -22 -43 -24 ]] | [⟨4 0 22 43], ⟨0 1 -2 -5]] | 2048/2025 3136/3125 |
wizard | 6.372 | 1.207 | 40.846 | ⟨⟨ 12 -2 20 -31 -2 52 ]] | [⟨2 1 5 2], ⟨0 6 -1 10]] | 225/224 118098/117649 |
buzzard | 6.420 | 1.396 | 47.963 | ⟨⟨ 4 21 -3 24 -16 -66 ]] | [⟨1 0 -6 4], ⟨0 4 21 -3]] | 1728/1715 5120/5103 |
semisept | 6.499 | 1.434 | 50.472 | ⟨⟨ 17 6 15 -30 -24 18 ]] | [⟨1 12 6 12], ⟨0 -17 -6 -15]] | 1728/1715 3136/3125 |
hemiwürschmidt | 6.598 | 0.560 | 20.307 | ⟨⟨ 16 2 5 -34 -37 6 ]] | [⟨1 15 4 7], ⟨0 -16 -2 -5]] | 2401/2400 3136/3125 |
hemikleismic | 6.704 | 1.390 | 52.054 | ⟨⟨ 12 10 -9 -12 -48 -49 ]] | [⟨1 0 1 4], ⟨0 12 10 -9]] | 4000/3969 6144/6125 |
sensei | 6.706 | 1.580 | 59.218 | ⟨⟨ 7 9 32 -2 31 49 ]] | [⟨1 6 8 23], ⟨0 -7 -9 -32]] | 225/224 78732/78125 |
hemififths | 6.812 | 0.575 | 22.243 | ⟨⟨ 2 25 13 35 15 -40 ]] | [⟨1 1 -5 -1], ⟨0 2 25 13]] | 2401/2400 5120/5103 |
pluto | 7.022 | 1.400 | 57.514 | ⟨⟨ 7 26 25 25 20 -15 ]] | [⟨1 5 15 15], ⟨0 -7 -26 -25]] | 4000/3969 10976/10935 |
amity | 7.127 | 0.559 | 23.649 | ⟨⟨ 5 13 -17 9 -41 -76 ]] | [⟨1 3 6 -2], ⟨0 -5 -13 17]] | 4375/4374 6144/6125 |
merman | 7.243 | 1.260 | 55.078 | ⟨⟨ 7 -15 -16 -40 -45 5 ]] | [⟨1 5 -5 -5], ⟨0 -7 15 16]] | 225/224 2500000/2470629 |
parakleismic | 7.343 | 0.610 | 27.431 | ⟨⟨ 13 14 35 -8 19 42 ]] | [⟨1 5 6 12], ⟨0 -13 -14 -35]] | 3136/3125 4375/4374 |
slender | 7.359 | 1.261 | 56.934 | ⟨⟨ 13 -10 6 -46 -27 42 ]] | [⟨1 2 2 3], ⟨0 -13 10 -6]] | 225/224 589824/588245 |
hemithirds | 7.385 | 0.974 | 44.284 | ⟨⟨ 15 -2 -5 -38 -50 -6 ]] | [⟨1 4 2 2], ⟨0 -15 2 5]] | 1029/1024 3136/3125 |
unidec | 7.662 | 0.785 | 38.393 | ⟨⟨ 12 22 -4 7 -40 -71 ]] | [⟨2 5 8 5], ⟨0 -6 -11 2]] | 1029/1024 4375/4374 |
ennealimmal | 7.714 | 0.073 | 3.610 | ⟨⟨ 18 27 18 1 -22 -34 ]] | [⟨9 1 1 12], ⟨0 2 3 2]] | 2401/2400 4375/4374 |
guiron | 7.795 | 0.939 | 47.544 | ⟨⟨ 3 -24 -1 -45 -10 65 ]] | [⟨1 1 7 3], ⟨0 3 -24 -1]] | 1029/1024 10976/10935 |
misty | 7.993 | 0.691 | 36.802 | ⟨⟨ 3 -12 -30 -26 -56 -36 ]] | [⟨3 0 26 56], ⟨0 1 -4 -10]] | 3136/3125 5120/5103 |
hendecatonic | 8.442 | 0.692 | 41.081 | ⟨⟨ 11 -11 22 -43 4 82 ]] | [⟨11 0 43 -4], ⟨0 1 -1 2]] | 6144/6125 10976/10935 |
harry | 8.457 | 0.572 | 34.077 | ⟨⟨ 12 34 20 26 -2 -49 ]] | [⟨2 4 7 7], ⟨0 -6 -17 -10]] | 2401/2400 19683/19600 |
hemiseven | 8.570 | 0.924 | 56.557 | ⟨⟨ 6 29 -2 32 -20 -86 ]] | [⟨1 4 14 2], ⟨0 -6 -29 2]] | 1029/1024 19683/19600 |
tritikleismic | 8.707 | 0.892 | 56.337 | ⟨⟨ 18 15 -6 -18 -60 -56 ]] | [⟨3 0 3 10], ⟨0 6 5 -2]] | 1029/1024 15625/15552 |
quadritikleismic | 8.908 | 0.593 | 39.231 | ⟨⟨ 24 20 16 -24 -42 -19 ]] | [⟨4 0 4 7], ⟨0 6 5 4]] | 2401/2400 15625/15552 |
hemischis | 9.155 | 0.656 | 45.817 | ⟨⟨ 2 -16 25 -30 34 103 ]] | [⟨1 0 15 -17], ⟨0 2 -16 25]] | 6144/6125 19683/19600 |
subpental | 9.279 | 0.757 | 54.303 | ⟨⟨ 14 18 45 -4 32 54 ]] | [⟨1 6 8 17], ⟨0 -14 -18 -45]] | 3136/3125 19683/19600 |
countercata | 9.466 | 0.698 | 52.128 | ⟨⟨ 6 5 -31 -6 -66 -86 ]] | [⟨1 0 1 11], ⟨0 6 5 -31]] | 5120/5103 15625/15552 |
grendel | 9.823 | 0.645 | 51.834 | ⟨⟨ 23 -1 13 -55 -44 33 ]] | [⟨1 9 2 7], ⟨0 -23 1 -13]] | 6144/6125 16875/16807 |
kwai | 9.844 | 0.675 | 54.476 | ⟨⟨ 1 33 27 50 40 -30 ]] | [⟨1 0 -50 -40], ⟨0 1 33 27]] | 5120/5103 16875/16807 |
bischismic | 10.11 | 0.643 | 54.744 | ⟨⟨ 2 -16 -40 -30 -69 -48 ]] | [⟨2 0 30 69], ⟨0 1 -8 -20]] | 3136/3125 32805/32768 |
sesquiquartififths | 10.196 | 0.130 | 11.244 | ⟨⟨ 4 -32 -15 -60 -35 55 ]] | [⟨1 1 7 5], ⟨0 4 -32 -15]] | 2401/2400 32805/32768 |
octoid | 10.207 | 0.491 | 42.670 | ⟨⟨ 24 32 40 -5 -4 3 ]] | [⟨8 1 3 3], ⟨0 3 4 5]] | 4375/4374 16875/16807 |
tertiaseptal | 10.247 | 0.149 | 12.995 | ⟨⟨ 22 -5 3 -59 -57 21 ]] | [⟨1 3 2 3], ⟨0 -22 5 -3]] | 2401/2400 65625/65536 |
mirkat | 10.652 | 0.628 | 59.376 | ⟨⟨ 18 39 42 20 16 -12 ]] | [⟨3 2 1 2], ⟨0 6 13 14]] | 16875/16807 19683/19600 |
pontiac | 10.787 | 0.146 | 14.133 | ⟨⟨ 1 -8 39 -15 59 113 ]] | [⟨1 0 15 -59], ⟨0 1 -8 39]] | 4374/4375 32805/32768 |
nessafof | 10.834 | 0.461 | 45.048 | ⟨⟨ 21 15 -12 -25 -78 -70 ]] | [⟨3 2 5 10], ⟨0 7 5 -4]] | 6144/6125 250047/250000 |
chromat | 11.375 | 0.533 | 57.499 | ⟨⟨ 15 39 48 27 34 2 ]] | [⟨3 4 5 6], ⟨0 5 13 16]] | 10976/10935 235298/234375 |
septiquarter | 11.425 | 0.494 | 53.760 | ⟨⟨ 7 38 -4 44 -26 -116 ]] | [⟨1 3 10 2], ⟨0 -7 -38 4]] | 5120/5103 420175/419904 |
sengagen | 11.446 | 0.531 | 57.978 | ⟨⟨ 29 16 40 -42 -18 48 ]] | [⟨1 1 2 2], ⟨0 29 16 40]] | 3136/3125 420175/419904 |
enneadecal | 11.926 | 0.092 | 10.954 | ⟨⟨ 19 19 57 -14 37 79 ]] | [⟨19 0 14 -37], ⟨0 1 1 3]] | 4375/4374 703125/702464 |
septisuperfourth | 11.986 | 0.495 | 59.241 | ⟨⟨ 18 -14 30 -64 -3 109 ]] | [⟨2 4 4 7], ⟨0 -9 7 -15]] | 6144/6125 118098/117649 |
quinmite | 12.636 | 0.281 | 37.322 | ⟨⟨ 34 29 23 -33 -59 -28 ]] | [⟨1 27 24 20], ⟨0 -34 -29 -23]] | 2401/2400 1959552/1953125 |
gamera | 12.911 | 0.271 | 37.648 | ⟨⟨ 23 40 1 10 -63 -110 ]] | [⟨1 6 10 3], ⟨0 -23 -40 -1]] | 4375/4374 589824/588245 |
amicable | 12.973 | 0.324 | 45.473 | ⟨⟨ 20 52 31 36 -7 -74 ]] | [⟨1 3 6 5], ⟨0 -20 -52 -31]] | 2401/2400 1600000/1594323 |
semidimfourth | 13.269 | 0.377 | 55.249 | ⟨⟨ 31 41 53 -7 -3 8 ]] | [⟨1 21 28 36], ⟨0 -31 -41 -53]] | 4375/4374 235298/234375 |
term | 13.877 | 0.124 | 19.950 | ⟨⟨ 3 -24 -54 -45 -94 -58 ]] | [⟨3 0 45 94], ⟨0 1 -8 -18]] | 32805/32768 250000/250047 |
mitonic | 14.474 | 0.144 | 25.184 | ⟨⟨ 17 35 -21 16 -81 -147 ]] | [⟨1 16 32 -15], ⟨0 -17 -35 21]] | 4375/4374 2100875/2097152 |
fifthplus | 14.679 | 0.144 | 25.840 | ⟨⟨ 23 -13 42 -74 2 134 ]] | [⟨1 11 -3 20], ⟨0 -23 13 -42]] | 65625/65536 420175/419904 |
emmthird | 14.897 | 0.090 | 16.736 | ⟨⟨ 14 59 33 61 13 -89 ]] | [⟨1 11 42 25], ⟨0 -14 -59 -33]] | 2401/2400 14348907/14336000 |
decoid | 14.948 | 0.182 | 33.902 | ⟨⟨ 20 -30 -10 -94 -72 61 ]] | [⟨10 0 47 36], ⟨0 2 -3 -1]] | 2400/2401 67108864/66976875 |
neptune | 15.001 | 0.125 | 23.427 | ⟨⟨ 40 22 21 -58 -79 -13 ]] | [⟨1 21 13 13], ⟨0 -40 -22 -21]] | 2401/2400 48828125/48771072 |
mutt | 15.075 | 0.150 | 28.406 | ⟨⟨ 21 3 -36 -44 -116 -92 ]] | [⟨3 5 7 8], ⟨0 -7 -1 12]] | 65625/65536 250047/250000 |
tsaharuk | 15.750 | 0.148 | 30.697 | ⟨⟨ 5 -40 24 -75 24 168 ]] | [⟨1 1 7 0], ⟨0 5 -40 24]] | 32805/32768 420175/419904 |
septichrome | 16.640 | 0.073 | 16.814 | ⟨⟨ 15 51 72 46 72 24 ]] | [⟨3 3 1 0], ⟨0 5 17 24]] | 250047/250000 2460375/2458624 |
quasiorwell | 16.766 | 0.153 | 35.832 | ⟨⟨ 38 -3 8 -93 -94 27 ]] | [⟨1 31 0 9], ⟨0 -38 3 -8]] | 2401/2400 29360128/29296875 |
vishnu | 16.789 | 0.178 | 41.912 | ⟨⟨ 14 6 74 -23 78 155 ]] | [⟨2 4 5 10], ⟨0 -7 -3 -37]] | 4375/4374 29360128/29296875 |
newt | 16.876 | 0.176 | 41.878 | ⟨⟨ 2 -57 -28 -95 -50 95 ]] | [⟨1 1 19 11], ⟨0 2 -57 -28]] | 2401/2400 33554432/33480783 |
supermajor | 16.944 | 0.045 | 10.836 | ⟨⟨ 37 46 75 -13 15 45 ]] | [⟨1 15 19 30], ⟨0 -37 -46 -75]] | 4375/4374 52734375/52706752 |
qak | 17.375 | 0.116 | 29.267 | ⟨⟨ 41 14 60 -73 -20 100 ]] | [⟨1 27 11 40], ⟨0 -41 -14 -60]] | 420175/419904 703125/702464 |
vulture | 17.675 | 0.142 | 36.985 | ⟨⟨ 4 21 -56 24 -100 -189 ]] | [⟨1 0 -6 25], ⟨0 4 21 -56]] | 4375/4374 33554432/33480783 |
septidiasemi | 18.931 | 0.148 | 44.115 | ⟨⟨ 26 -37 -12 -119 -92 76 ]] | [⟨1 25 -31 -8], ⟨0 -26 37 12]] | 2401/2400 2152828125/2147483648 |
acrokleismic | 19.245 | 0.182 | 56.184 | ⟨⟨ 32 33 92 -22 56 121 ]] | [⟨1 10 11 27], ⟨0 -32 -33 -92]] | 4375/4374 2202927104/2197265625 |
pnict | 19.517 | 0.144 | 45.660 | ⟨⟨ 39 30 -18 -43 -138 -126 ]] | [⟨3 10 11 6], ⟨0 -13 -10 6]] | 250047/250000 2100875/2097152 |
maviloid | 19.870 | 0.175 | 57.632 | ⟨⟨ 52 56 41 -32 -81 -62 ]] | [⟨1 31 34 26], ⟨0 -52 -56 -41]] | 2401/2400 1224440064/1220703125 |
tokko | 19.992 | 0.133 | 44.417 | ⟨⟨ 13 67 -6 76 -46 -202 ]] | [⟨1 12 56 -2], ⟨0 -13 -67 6]] | 420175/419904 5250987/5242880 |
Junk temperaments
Name | Complexity | Error (¢) | Badness (k) | Wedgie | Mapping | Commas |
---|---|---|---|---|---|---|
0.266 | 400.986 | 23.561 | ⟨⟨ 0 0 1 0 2 2 ]] | [⟨1 2 2 0], ⟨0 0 0 1]] | 4/3 5/3 | |
0.340 | 252.955 | 24.334 | ⟨⟨ 0 1 0 2 0 -3 ]] | [⟨1 2 0 3], ⟨0 0 1 0]] | 4/3 7/6 | |
0.367 | 309.005 | 34.752 | ⟨⟨ 0 1 1 2 2 0 ]] | [⟨1 2 0 0], ⟨0 0 1 1]] | 4/3 7/5 | |
0.373 | 199.358 | 23.114 | ⟨⟨ 1 1 1 -1 -1 0 ]] | [⟨1 0 1 1], ⟨0 1 1 1]] | 6/5 7/5 | |
0.401 | 168.811 | 22.624 | ⟨⟨ 1 0 1 -2 -1 2 ]] | [⟨1 0 2 1], ⟨0 1 0 1]] | 5/4 7/6 | |
0.437 | 223.834 | 35.689 | ⟨⟨ 1 0 0 -2 -3 0 ]] | [⟨1 0 2 3], ⟨0 1 0 0]] | 5/4 8/7 | |
0.458 | 152.797 | 26.720 | ⟨⟨ 1 1 2 -1 0 2 ]] | [⟨1 0 1 0], ⟨0 1 1 2]] | 6/5 9/7 | |
0.470 | 135.120 | 24.843 | ⟨⟨ 1 1 0 -1 -3 -3 ]] | [⟨1 0 1 3], ⟨0 1 1 0]] | 6/5 8/7 | |
0.508 | 134.886 | 29.047 | ⟨⟨ 0 0 2 0 3 5 ]] | [⟨2 3 5 0], ⟨0 0 0 1]] | 6/5 9/8 | |
0.517 | 100.760 | 22.434 | ⟨⟨ 1 2 1 1 -1 -3 ]] | [⟨1 0 -1 1], ⟨0 1 2 1]] | 7/6 10/9 | |
0.536 | 159.295 | 38.111 | ⟨⟨ 1 0 -1 -2 -4 -2 ]] | [⟨1 0 2 4], ⟨0 1 0 -1]] | 5/4 21/16 | |
0.603 | 180.305 | 54.612 | ⟨⟨ 1 1 -1 -1 -4 -5 ]] | [⟨1 0 1 4], ⟨0 1 1 -1]] | 6/5 21/16 | |
0.613 | 126.550 | 39.612 | ⟨⟨ 0 2 0 3 0 -6 ]] | [⟨2 3 0 6], ⟨0 0 1 0]] | 8/7 9/7 | |
antitonic | 0.631 | 58.311 | 19.373 | ⟨⟨ 0 2 2 3 3 -1 ]] | [⟨2 3 0 1], ⟨0 0 1 1]] | 9/8 15/14 |
0.637 | 70.842 | 23.922 | ⟨⟨ 1 -1 0 -4 -3 3 ]] | [⟨1 0 4 3], ⟨0 1 -1 0]] | 8/7 15/14 | |
0.648 | 81.437 | 28.454 | ⟨⟨ 1 2 0 1 -3 -6 ]] | [⟨1 0 -1 3], ⟨0 1 2 0]] | 8/7 10/9 | |
0.649 | 103.614 | 36.419 | ⟨⟨ 1 -1 1 -4 -1 5 ]] | [⟨1 0 4 1], ⟨0 1 -1 1]] | 7/6 16/15 | |
0.656 | 66.836 | 23.962 | ⟨⟨ 1 2 3 1 2 1 ]] | [⟨1 0 -1 -2], ⟨0 1 2 3]] | 10/9 15/14 | |
0.724 | 136.735 | 59.654 | ⟨⟨ 2 2 2 -1 -2 -1 ]] | [⟨2 0 1 2], ⟨0 1 1 1]] | 7/6 25/18 | |
0.736 | 97.698 | 44.046 | ⟨⟨ 2 1 2 -3 -2 2 ]] | [⟨1 1 2 2], ⟨0 2 1 2]] | 7/6 25/24 | |
0.736 | 132.937 | 59.948 | ⟨⟨ 1 3 2 2 0 -4 ]] | [⟨1 0 -2 0], ⟨0 1 3 2]] | 9/7 21/20 |