List of 19et rank two temperaments by badness

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This revision was by author genewardsmith and made on 2012-04-07 18:56:13 UTC.
The original revision id was 318442142.
The revision comment was:

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Original Wikitext content:

Below are listed rank-two temperaments supported by the 19et 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 six temperaments with badness less than 0.1.
|| Rank || Wedgie || Name || Badness || Commas ||

=7-limit temperaments with badness below 0.06=
Listed is the wedgie and the TE badness times 1000 for 18 temperaments with badness less than 0.06.
|| Rank || Wedgie || Name || Badness || Commas ||

=11-limit temperaments with badness below 0.05=
Listed is the wedgie and the TE badness times 1000 for 27 temperaments with badness less than 0.05.
|| Rank || Wedgie || Name || Badness || Commas ||
|| 1 || <<5 1 12 11 -10 5 0 25 22 -11]] || || 20.352 || 45/44 56/55 245/243 ||
|| 2 || <<2 8 1 -7 8 -4 -18 -20 -44 -23]] || || 21.423 || 49/48 56/55 81/80 ||
|| 3 || <<1 4 10 6 4 13 6 12 0 -18]] || || 21.543 || 45/44 56/55 81/80 ||
|| 4 || <<6 5 22 -2 -6 18 -24 37 -22 -82]] || || 21.849 || 100/99 225/224 864/847 ||
|| 5 || <<5 1 -7 11 -10 -25 0 -19 22 55]] || || 26.190 || 45/44 126/125 385/384 ||
|| 6 || <<6 5 3 17 -6 -12 6 -7 22 37]] || || 27.410 || 45/44 49/48 126/125 ||
|| 7 || <<8 13 23 -9 2 14 -42 17 -66 -105]] || || 28.680 || 126/125 540/539 896/891 ||
|| 8 || <<2 8 20 -7 8 26 -18 24 -44 -89]] || || 28.947 || 81/80 126/125 864/847 ||
|| 9 || <<1 4 10 -13 4 13 -24 12 -44 -71]] || || 33.839 || 81/80 126/125 540/539 ||
|| 10 || <<2 8 1 12 8 -4 12 -20 0 30]] || || 35.673 || 45/44 49/48 81/80 ||
|| 11 || <<1 4 -9 6 4 -17 6 -32 0 48]] || || 36.387 || 45/44 81/80 385/384 ||
|| 12 || <<38 38 114 -95 -28 74 -282 158 -352 -661]] || || 36.878 || 4375/4374 41503/41472 703125/702464 ||
|| 13 || <<7 9 13 4 -2 1 -18 5 -22 -34]] || || 37.942 || 56/55 100/99 245/243 ||
|| 14 || <<4 -3 2 5 -14 -8 -6 13 22 7]] || || 38.679 || 45/44 49/48 56/55 ||
|| 15 || <<12 10 25 -23 -12 6 -78 30 -88 -151]] || || 39.156 || 245/243 385/384 3136/3125 ||
|| 16 || <<6 5 3 -2 -6 -12 -24 -7 -22 -16]] || || 39.282 || 49/48 56/55 100/99 ||
|| 17 || <<6 5 22 -21 -6 18 -54 37 -66 -135]] || || 39.701 || 225/224 385/384 4375/4374 ||
|| 18 || <<4 -3 2 -14 -14 -8 -36 13 -22 -46]] || || 40.056 || 49/48 100/99 225/224 ||
|| 19 || <<14 18 45 -30 -4 32 -96 54 -132 -240]] || || 40.721 || 540/539 3136/3125 8019/8000 ||
|| 20 || <<32 33 92 -74 -22 56 -228 121 -286 -526]] || || 41.720 || 4375/4374 41503/41472 172032/171875 ||
|| 21 || <<7 9 13 -15 -2 1 -48 5 -66 -87]] || || 43.734 || 126/125 245/243 385/384 ||
|| 22 || <<19 19 57 -38 -14 37 -126 79 -154 -304]] || || 44.335 || 540/539 4375/4374 16384/16335 ||
|| 23 || <<3 12 11 -1 12 9 -12 -8 -44 -41]] || || 45.352 || 56/55 81/80 540/539 ||
|| 24 || <<13 14 35 -36 -8 19 -102 42 -132 -222]] || || 45.675 || 385/384 3136/3125 4375/4374 ||
|| 25 || <<5 1 12 -8 -10 5 -30 25 -22 -64]] || || 47.417 || 100/99 225/224 245/243 ||
|| 26 || <<3 -7 -8 -1 -18 -21 -12 1 22 25]] || || 48.038 || 45/44 56/55 1029/1000 ||
|| 27 || <<13 14 35 -17 -8 19 -72 42 -88 -169]] || || 49.303 || 540/539 896/891 3136/3125 ||

Original HTML content:

<html><head><title>List of 19et rank two temperaments by badness</title></head><body>Below are listed rank-two temperaments supported by the 19et patent val, below the indicated cutoff in TE badness.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><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 six temperaments with badness less than 0.1.<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>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><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 18 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>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><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 27 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;5 1 12 11 -10 5 0 25 22 -11]]<br />
</td>
        <td><br />
</td>
        <td>20.352<br />
</td>
        <td>45/44 56/55 245/243<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;2 8 1 -7 8 -4 -18 -20 -44 -23]]<br />
</td>
        <td><br />
</td>
        <td>21.423<br />
</td>
        <td>49/48 56/55 81/80<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;1 4 10 6 4 13 6 12 0 -18]]<br />
</td>
        <td><br />
</td>
        <td>21.543<br />
</td>
        <td>45/44 56/55 81/80<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;6 5 22 -2 -6 18 -24 37 -22 -82]]<br />
</td>
        <td><br />
</td>
        <td>21.849<br />
</td>
        <td>100/99 225/224 864/847<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;5 1 -7 11 -10 -25 0 -19 22 55]]<br />
</td>
        <td><br />
</td>
        <td>26.190<br />
</td>
        <td>45/44 126/125 385/384<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;6 5 3 17 -6 -12 6 -7 22 37]]<br />
</td>
        <td><br />
</td>
        <td>27.410<br />
</td>
        <td>45/44 49/48 126/125<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>&lt;&lt;8 13 23 -9 2 14 -42 17 -66 -105]]<br />
</td>
        <td><br />
</td>
        <td>28.680<br />
</td>
        <td>126/125 540/539 896/891<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>&lt;&lt;2 8 20 -7 8 26 -18 24 -44 -89]]<br />
</td>
        <td><br />
</td>
        <td>28.947<br />
</td>
        <td>81/80 126/125 864/847<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>&lt;&lt;1 4 10 -13 4 13 -24 12 -44 -71]]<br />
</td>
        <td><br />
</td>
        <td>33.839<br />
</td>
        <td>81/80 126/125 540/539<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>&lt;&lt;2 8 1 12 8 -4 12 -20 0 30]]<br />
</td>
        <td><br />
</td>
        <td>35.673<br />
</td>
        <td>45/44 49/48 81/80<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>&lt;&lt;1 4 -9 6 4 -17 6 -32 0 48]]<br />
</td>
        <td><br />
</td>
        <td>36.387<br />
</td>
        <td>45/44 81/80 385/384<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>&lt;&lt;38 38 114 -95 -28 74 -282 158 -352 -661]]<br />
</td>
        <td><br />
</td>
        <td>36.878<br />
</td>
        <td>4375/4374 41503/41472 703125/702464<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>&lt;&lt;7 9 13 4 -2 1 -18 5 -22 -34]]<br />
</td>
        <td><br />
</td>
        <td>37.942<br />
</td>
        <td>56/55 100/99 245/243<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>&lt;&lt;4 -3 2 5 -14 -8 -6 13 22 7]]<br />
</td>
        <td><br />
</td>
        <td>38.679<br />
</td>
        <td>45/44 49/48 56/55<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>&lt;&lt;12 10 25 -23 -12 6 -78 30 -88 -151]]<br />
</td>
        <td><br />
</td>
        <td>39.156<br />
</td>
        <td>245/243 385/384 3136/3125<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>&lt;&lt;6 5 3 -2 -6 -12 -24 -7 -22 -16]]<br />
</td>
        <td><br />
</td>
        <td>39.282<br />
</td>
        <td>49/48 56/55 100/99<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>&lt;&lt;6 5 22 -21 -6 18 -54 37 -66 -135]]<br />
</td>
        <td><br />
</td>
        <td>39.701<br />
</td>
        <td>225/224 385/384 4375/4374<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>&lt;&lt;4 -3 2 -14 -14 -8 -36 13 -22 -46]]<br />
</td>
        <td><br />
</td>
        <td>40.056<br />
</td>
        <td>49/48 100/99 225/224<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>&lt;&lt;14 18 45 -30 -4 32 -96 54 -132 -240]]<br />
</td>
        <td><br />
</td>
        <td>40.721<br />
</td>
        <td>540/539 3136/3125 8019/8000<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>&lt;&lt;32 33 92 -74 -22 56 -228 121 -286 -526]]<br />
</td>
        <td><br />
</td>
        <td>41.720<br />
</td>
        <td>4375/4374 41503/41472 172032/171875<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>&lt;&lt;7 9 13 -15 -2 1 -48 5 -66 -87]]<br />
</td>
        <td><br />
</td>
        <td>43.734<br />
</td>
        <td>126/125 245/243 385/384<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>&lt;&lt;19 19 57 -38 -14 37 -126 79 -154 -304]]<br />
</td>
        <td><br />
</td>
        <td>44.335<br />
</td>
        <td>540/539 4375/4374 16384/16335<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>&lt;&lt;3 12 11 -1 12 9 -12 -8 -44 -41]]<br />
</td>
        <td><br />
</td>
        <td>45.352<br />
</td>
        <td>56/55 81/80 540/539<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>&lt;&lt;13 14 35 -36 -8 19 -102 42 -132 -222]]<br />
</td>
        <td><br />
</td>
        <td>45.675<br />
</td>
        <td>385/384 3136/3125 4375/4374<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>&lt;&lt;5 1 12 -8 -10 5 -30 25 -22 -64]]<br />
</td>
        <td><br />
</td>
        <td>47.417<br />
</td>
        <td>100/99 225/224 245/243<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>&lt;&lt;3 -7 -8 -1 -18 -21 -12 1 22 25]]<br />
</td>
        <td><br />
</td>
        <td>48.038<br />
</td>
        <td>45/44 56/55 1029/1000<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>&lt;&lt;13 14 35 -17 -8 19 -72 42 -88 -169]]<br />
</td>
        <td><br />
</td>
        <td>49.303<br />
</td>
        <td>540/539 896/891 3136/3125<br />
</td>
    </tr>
</table>

</body></html>