List of 15et rank two temperaments by badness

Revision as of 00:52, 7 April 2012 by Wikispaces>genewardsmith (**Imported revision 318325226 - Original comment: **)

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Below are listed rank-two temperaments supported by the 15et patent val, below the indicated cutoff in TE badness.

=7-limit temperaments with badness below 0.06=
Listed is the wedgie and the TE badness times 1000 for 15 temperaments with badness less than 0.05.
|| Rank || Wedgie || Name || Badness || Commas ||
|| 1 || <<3 0 -6 -7 -18 -14]] || || 24.816 || 64/63 126/125 ||
|| 2 || <<0 5 0 8 0 -14]] || || 25.640 || 28/27 49/48 ||
|| 3 || <<6 5 3 -6 -12 -7]] || || 27.408 || 49/48 126/125 ||
|| 4 || <<9 5 -3 -13 -30 -21]] || || 31.056 || 126/125 1029/1024 ||
|| 5 || <<3 5 9 1 6 7]] || || 40.650 || 28/27 126/125 ||
|| 6 || <<3 5 -6 1 -18 -28]] || || 41.057 || 64/63 250/243 ||
|| 7 || <<21 15 -12 -25 -78 -70]] || || 45.048 || 6144/6125 250047/250000 ||
|| 8 || <<39 30 -18 -43 -138 -126]] || || 45.660 || 250047/250000 2100875/2097152 ||
|| 9 || <<9 10 -3 -5 -30 -35]] || || 47.932 || 875/864 1029/1024 ||
|| 10 || <<12 10 -9 -12 -48 -49]] || || 52.054 || 4000/3969 6144/6125 ||
|| 11 || <<3 0 9 -7 6 21]] || || 54.729 || 28/27 128/125 ||
|| 12 || <<6 0 3 -14 -12 7]] || || 54.988 || 49/48 128/125 ||
|| 13 || <<18 15 -6 -18 -60 -56]] || || 56.337 || 1029/1024 15625/15552 ||
|| 14 || <<6 10 3 2 -12 -21]] || || 57.420 || 49/48 250/243 ||
|| 15 || <<60 45 -30 -68 -216 -196]] || || 58.002 || 250047/250000 12884901888/12867859375 ||

=11-limit temperaments with badness below 0.05=
Listed is the wedgie and the TE badness times 1000 for 33 temperaments with badness less than 0.05.
|| Rank || Wedgie || Name || Badness || Commas ||
|| 1 || <<9 5 -3 7 -13 -30 -20 -21 -1 30]] || Valentine || 16.687 || 121/120 126/125 176/175 ||
|| 2 || <<18 15 -6 9 -18 -60 -48 -56 -31 46]] || Tritikleismic || 19.333 || 385/384 441/440 4000/3993 ||
|| 3 || <<3 0 -6 -6 -7 -18 -20 -14 -14 4]] || Augene || 19.613 || 56/55 64/63 100/99 ||
|| 4 || <<3 5 -6 4 1 -18 -4 -28 -8 32]] || Porcupine || 21.562 || 55/54 64/63 100/99 ||
|| 5 || <<3 5 9 4 1 6 -4 7 -8 -20]] || Opossum || 22.325 || 28/27 55/54 77/75 ||
|| 6 || <<0 5 0 -5 8 0 -8 -14 -29 -14]] || Blacksmith || 24.641 || 28/27 49/48 55/54 ||
|| 7 || <<9 10 -3 2 -5 -30 -28 -35 -30 16]] || Superkleismic || 25.659 || 100/99 245/242 385/384 ||
|| 8 || <<6 10 3 8 2 -12 -8 -21 -16 12]] || Nautilus || 26.023 || 49/48 55/54 100/99 ||
|| 9 || <<6 0 3 3 -14 -12 -16 7 7 -2]] || Triforce || 26.152 || 49/48 56/55 77/75 ||
|| 10 || <<6 5 3 -2 -6 -12 -24 -7 -22 -16]] || Keemun || 27.41 || 49/48 56/55 100/99 ||
|| 11 || <<6 5 3 13 -6 -12 0 -7 13 26]] || Darjeeling || 27.648 || 49/48 55/54 77/75 ||
|| 12 || <<0 5 0 10 8 0 16 -14 6 28]] || Ferrier || 29.2 || 28/27 49/48 77/75 ||
|| 13 || <<3 -5 -6 -1 -15 -18 -12 0 15 18]] || Progress || 31.036 || 56/55 64/63 77/75 ||
|| 14 || <<3 0 9 9 -7 6 4 21 21 -6]] || Inflated || 31.171 || 28/27 55/54 128/125 ||
|| 15 || <<12 5 -9 1 -20 -48 -40 -35 -15 34]] || Thuja || 33.078 || 126/125 176/175 1344/1331 ||
|| 16 || <<27 20 -9 16 -31 -90 -68 -77 -32 76]] || Tritriple || 35.350 || 385/384 441/440 43923/43750 ||
|| 17 || <<3 0 -6 9 -7 -18 4 -14 21 46]] || || 35.554 || 55/54 64/63 77/75 ||
|| 18 || <<6 5 -12 -2 -6 -36 -24 -42 -22 36]] || || 36.894 || 64/63 100/99 1331/1323 ||
|| 19 || <<12 10 -9 11 -12 -48 -24 -49 -9 62]] || || 38.230 || 121/120 176/175 4000/3969 ||
|| 20 || <<12 10 6 11 -12 -24 -24 -14 -9 10]] || || 42.696 || 49/48 121/120 126/125 ||
|| 21 || <<3 10 9 14 9 6 12 -7 -2 8]] || || 43.195 || 28/27 77/75 245/242 ||
|| 22 || <<15 10 -15 5 -19 -66 -44 -63 -23 66]] || || 43.508 || 176/175 1331/1323 4000/3969 ||
|| 23 || <<33 25 -21 14 -37 -126 -92 -119 -54 112]] || || 43.743 || 3025/3024 4000/3993 6144/6125 ||
|| 24 || <<15 15 0 15 -11 -42 -28 -42 -17 42]] || || 44.405 || 121/120 441/440 875/864 ||
|| 25 || <<6 0 -12 3 -14 -36 -16 -28 7 50]] || || 44.448 || 64/63 121/120 126/125 ||
|| 26 || <<15 10 0 5 -19 -42 -44 -28 -23 14]] || || 45.070 || 126/125 245/242 385/384 ||
|| 27 || <<0 10 0 5 16 0 8 -28 -23 14]] || || 45.972 || 28/27 49/48 121/120 ||
|| 28 || <<30 20 -15 10 -38 -108 -88 -91 -46 80]] || || 47.990 || 441/440 4000/3993 6144/6125 ||
|| 29 || <<9 0 -3 -3 -21 -30 -36 -7 -7 2]] || || 48.345 || 56/55 128/125 2541/2500 ||
|| 30 || <<3 0 9 -6 -7 6 -20 21 -14 -48]] || || 48.744 || 28/27 77/75 128/125 ||
|| 31 || <<21 15 -12 3 -25 -78 -68 -70 -45 50]] || || 48.836 || 441/440 1344/1331 4375/4356 ||
|| 32 || <<0 5 15 10 8 24 16 21 6 -24]] || || 49.486 || 56/55 100/99 256/243 ||
|| 33 || <<3 10 -6 -1 9 -18 -12 -42 -37 18]] || || 49.863 || 55/54 64/63 245/242 ||

Original HTML content:

<html><head><title>List of 15et rank two temperaments by badness</title></head><body>Below are listed rank-two temperaments supported by the 15et patent val, below the indicated cutoff in TE badness.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x7-limit temperaments with badness below 0.06"></a><!-- ws:end:WikiTextHeadingRule:0 -->7-limit temperaments with badness below 0.06</h1>
Listed is the wedgie and the TE badness times 1000 for 15 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>&lt;&lt;3 0 -6 -7 -18 -14]]<br />
</td>
        <td><br />
</td>
        <td>24.816<br />
</td>
        <td>64/63 126/125<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;0 5 0 8 0 -14]]<br />
</td>
        <td><br />
</td>
        <td>25.640<br />
</td>
        <td>28/27 49/48<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;6 5 3 -6 -12 -7]]<br />
</td>
        <td><br />
</td>
        <td>27.408<br />
</td>
        <td>49/48 126/125<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;9 5 -3 -13 -30 -21]]<br />
</td>
        <td><br />
</td>
        <td>31.056<br />
</td>
        <td>126/125 1029/1024<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;3 5 9 1 6 7]]<br />
</td>
        <td><br />
</td>
        <td>40.650<br />
</td>
        <td>28/27 126/125<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;3 5 -6 1 -18 -28]]<br />
</td>
        <td><br />
</td>
        <td>41.057<br />
</td>
        <td>64/63 250/243<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>&lt;&lt;21 15 -12 -25 -78 -70]]<br />
</td>
        <td><br />
</td>
        <td>45.048<br />
</td>
        <td>6144/6125 250047/250000<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>&lt;&lt;39 30 -18 -43 -138 -126]]<br />
</td>
        <td><br />
</td>
        <td>45.660<br />
</td>
        <td>250047/250000 2100875/2097152<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>&lt;&lt;9 10 -3 -5 -30 -35]]<br />
</td>
        <td><br />
</td>
        <td>47.932<br />
</td>
        <td>875/864 1029/1024<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>&lt;&lt;12 10 -9 -12 -48 -49]]<br />
</td>
        <td><br />
</td>
        <td>52.054<br />
</td>
        <td>4000/3969 6144/6125<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>&lt;&lt;3 0 9 -7 6 21]]<br />
</td>
        <td><br />
</td>
        <td>54.729<br />
</td>
        <td>28/27 128/125<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>&lt;&lt;6 0 3 -14 -12 7]]<br />
</td>
        <td><br />
</td>
        <td>54.988<br />
</td>
        <td>49/48 128/125<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>&lt;&lt;18 15 -6 -18 -60 -56]]<br />
</td>
        <td><br />
</td>
        <td>56.337<br />
</td>
        <td>1029/1024 15625/15552<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>&lt;&lt;6 10 3 2 -12 -21]]<br />
</td>
        <td><br />
</td>
        <td>57.420<br />
</td>
        <td>49/48 250/243<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>&lt;&lt;60 45 -30 -68 -216 -196]]<br />
</td>
        <td><br />
</td>
        <td>58.002<br />
</td>
        <td>250047/250000 12884901888/12867859375<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x11-limit temperaments with badness below 0.05"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit temperaments with badness below 0.05</h1>
Listed is the wedgie and the TE badness times 1000 for 33 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>&lt;&lt;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>2<br />
</td>
        <td>&lt;&lt;18 15 -6 9 -18 -60 -48 -56 -31 46]]<br />
</td>
        <td>Tritikleismic<br />
</td>
        <td>19.333<br />
</td>
        <td>385/384 441/440 4000/3993<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;3 0 -6 -6 -7 -18 -20 -14 -14 4]]<br />
</td>
        <td>Augene<br />
</td>
        <td>19.613<br />
</td>
        <td>56/55 64/63 100/99<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;3 5 -6 4 1 -18 -4 -28 -8 32]]<br />
</td>
        <td>Porcupine<br />
</td>
        <td>21.562<br />
</td>
        <td>55/54 64/63 100/99<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;3 5 9 4 1 6 -4 7 -8 -20]]<br />
</td>
        <td>Opossum<br />
</td>
        <td>22.325<br />
</td>
        <td>28/27 55/54 77/75<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;0 5 0 -5 8 0 -8 -14 -29 -14]]<br />
</td>
        <td>Blacksmith<br />
</td>
        <td>24.641<br />
</td>
        <td>28/27 49/48 55/54<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>&lt;&lt;9 10 -3 2 -5 -30 -28 -35 -30 16]]<br />
</td>
        <td>Superkleismic<br />
</td>
        <td>25.659<br />
</td>
        <td>100/99 245/242 385/384<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>&lt;&lt;6 10 3 8 2 -12 -8 -21 -16 12]]<br />
</td>
        <td>Nautilus<br />
</td>
        <td>26.023<br />
</td>
        <td>49/48 55/54 100/99<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>&lt;&lt;6 0 3 3 -14 -12 -16 7 7 -2]]<br />
</td>
        <td>Triforce<br />
</td>
        <td>26.152<br />
</td>
        <td>49/48 56/55 77/75<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>&lt;&lt;6 5 3 -2 -6 -12 -24 -7 -22 -16]]<br />
</td>
        <td>Keemun<br />
</td>
        <td>27.41<br />
</td>
        <td>49/48 56/55 100/99<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>&lt;&lt;6 5 3 13 -6 -12 0 -7 13 26]]<br />
</td>
        <td>Darjeeling<br />
</td>
        <td>27.648<br />
</td>
        <td>49/48 55/54 77/75<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>&lt;&lt;0 5 0 10 8 0 16 -14 6 28]]<br />
</td>
        <td>Ferrier<br />
</td>
        <td>29.2<br />
</td>
        <td>28/27 49/48 77/75<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>&lt;&lt;3 -5 -6 -1 -15 -18 -12 0 15 18]]<br />
</td>
        <td>Progress<br />
</td>
        <td>31.036<br />
</td>
        <td>56/55 64/63 77/75<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>&lt;&lt;3 0 9 9 -7 6 4 21 21 -6]]<br />
</td>
        <td>Inflated<br />
</td>
        <td>31.171<br />
</td>
        <td>28/27 55/54 128/125<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>&lt;&lt;12 5 -9 1 -20 -48 -40 -35 -15 34]]<br />
</td>
        <td>Thuja<br />
</td>
        <td>33.078<br />
</td>
        <td>126/125 176/175 1344/1331<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>&lt;&lt;27 20 -9 16 -31 -90 -68 -77 -32 76]]<br />
</td>
        <td>Tritriple<br />
</td>
        <td>35.350<br />
</td>
        <td>385/384 441/440 43923/43750<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>&lt;&lt;3 0 -6 9 -7 -18 4 -14 21 46]]<br />
</td>
        <td><br />
</td>
        <td>35.554<br />
</td>
        <td>55/54 64/63 77/75<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>&lt;&lt;6 5 -12 -2 -6 -36 -24 -42 -22 36]]<br />
</td>
        <td><br />
</td>
        <td>36.894<br />
</td>
        <td>64/63 100/99 1331/1323<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>&lt;&lt;12 10 -9 11 -12 -48 -24 -49 -9 62]]<br />
</td>
        <td><br />
</td>
        <td>38.230<br />
</td>
        <td>121/120 176/175 4000/3969<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>&lt;&lt;12 10 6 11 -12 -24 -24 -14 -9 10]]<br />
</td>
        <td><br />
</td>
        <td>42.696<br />
</td>
        <td>49/48 121/120 126/125<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>&lt;&lt;3 10 9 14 9 6 12 -7 -2 8]]<br />
</td>
        <td><br />
</td>
        <td>43.195<br />
</td>
        <td>28/27 77/75 245/242<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>&lt;&lt;15 10 -15 5 -19 -66 -44 -63 -23 66]]<br />
</td>
        <td><br />
</td>
        <td>43.508<br />
</td>
        <td>176/175 1331/1323 4000/3969<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>&lt;&lt;33 25 -21 14 -37 -126 -92 -119 -54 112]]<br />
</td>
        <td><br />
</td>
        <td>43.743<br />
</td>
        <td>3025/3024 4000/3993 6144/6125<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>&lt;&lt;15 15 0 15 -11 -42 -28 -42 -17 42]]<br />
</td>
        <td><br />
</td>
        <td>44.405<br />
</td>
        <td>121/120 441/440 875/864<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>&lt;&lt;6 0 -12 3 -14 -36 -16 -28 7 50]]<br />
</td>
        <td><br />
</td>
        <td>44.448<br />
</td>
        <td>64/63 121/120 126/125<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>&lt;&lt;15 10 0 5 -19 -42 -44 -28 -23 14]]<br />
</td>
        <td><br />
</td>
        <td>45.070<br />
</td>
        <td>126/125 245/242 385/384<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>&lt;&lt;0 10 0 5 16 0 8 -28 -23 14]]<br />
</td>
        <td><br />
</td>
        <td>45.972<br />
</td>
        <td>28/27 49/48 121/120<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>&lt;&lt;30 20 -15 10 -38 -108 -88 -91 -46 80]]<br />
</td>
        <td><br />
</td>
        <td>47.990<br />
</td>
        <td>441/440 4000/3993 6144/6125<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>&lt;&lt;9 0 -3 -3 -21 -30 -36 -7 -7 2]]<br />
</td>
        <td><br />
</td>
        <td>48.345<br />
</td>
        <td>56/55 128/125 2541/2500<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>&lt;&lt;3 0 9 -6 -7 6 -20 21 -14 -48]]<br />
</td>
        <td><br />
</td>
        <td>48.744<br />
</td>
        <td>28/27 77/75 128/125<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>&lt;&lt;21 15 -12 3 -25 -78 -68 -70 -45 50]]<br />
</td>
        <td><br />
</td>
        <td>48.836<br />
</td>
        <td>441/440 1344/1331 4375/4356<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>&lt;&lt;0 5 15 10 8 24 16 21 6 -24]]<br />
</td>
        <td><br />
</td>
        <td>49.486<br />
</td>
        <td>56/55 100/99 256/243<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>&lt;&lt;3 10 -6 -1 9 -18 -12 -42 -37 18]]<br />
</td>
        <td><br />
</td>
        <td>49.863<br />
</td>
        <td>55/54 64/63 245/242<br />
</td>
    </tr>
</table>

</body></html>