List of 12et rank two temperaments by badness

From Xenharmonic Wiki
Revision as of 08:47, 7 April 2012 by Wikispaces>genewardsmith (**Imported revision 318361266 - Original comment: **)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2012-04-07 08:47:29 UTC.
The original revision id was 318361266.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

Below are listed rank-two temperaments supported by the 12et patent val, below the indicated cutoff in TE badness.

=11-limit temperaments with badness below 0.05=
Listed is the wedgie and the TE badness times 1000 for 40 temperaments with badness less than 0.05.
|| Rank || Wedgie || Name || Badness || Commas ||
|| 1 || <<1 4 10 18 4 13 25 12 28 16]] || || 17.027 || 81/80 99/98 126/125 ||
|| 2 || <<3 0 -6 -6 -7 -18 -20 -14 -14 4]] || || 19.613 || 56/55 64/63 100/99 ||
|| 3 || <<3 0 6 6 -7 1 -1 14 14 -4]] || || 20.191 || 36/35 45/44 56/55 ||
|| 4 || <<2 -4 -4 -12 -11 -12 -26 2 -14 -20]] || || 20.343 || 50/49 64/63 99/98 ||
|| 5 || <<1 4 10 6 4 13 6 12 0 -18]] || || 21.423 || 45/44 56/55 81/80 ||
|| 6 || <<1 4 -2 6 4 -6 6 -16 0 24]] || || 21.978 || 36/35 45/44 64/63 ||
|| 7 || <<4 4 4 0 -3 -5 -14 -2 -14 -14]] || || 22.132 || 36/35 50/49 56/55 ||
|| 8 || <<0 12 24 36 19 38 57 22 42 18]] || || 22.235 || 225/224 441/440 4375/4356 ||
|| 9 || <<2 8 8 12 8 7 12 -4 0 6]] || || 23.124 || 45/44 50/49 99/98 ||
|| 10 || <<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]] || || 23.556 || 100/99 225/224 245/242 ||
|| 11 || <<2 -4 -4 0 -11 -12 -7 2 14 14]] || || 23.798 || 45/44 50/49 56/55 ||
|| 12 || <<1 4 -2 -6 4 -6 -13 -16 -28 -10]] || || 24.18 || 36/35 56/55 64/63 ||
|| 13 || <<2 -4 -16 -24 -11 -31 -45 -26 -42 -12]] || || 25.034 || 126/125 176/175 5488/5445 ||
|| 14 || <<4 4 4 12 -3 -5 5 -2 14 20]] || || 26.574 || 36/35 45/44 50/49 ||
|| 15 || <<2 -16 -40 -60 -30 -69 -102 -48 -84 -30]] || || 28.160 || 441/440 3136/3125 8019/8000 ||
|| 16 || <<0 0 0 12 0 0 19 0 28 34]] || || 30.536 || 36/35 50/49 64/63 ||
|| 17 || <<0 0 12 12 0 19 19 28 28 -8]] || || 34.478 || 56/55 81/80 128/125 ||
|| 18 || <<4 -20 -44 -72 -41 -81 -128 -46 -98 -50]] || || 34.837 || 1375/1372 5120/5103 5632/5625 ||
|| 19 || <<1 -8 -14 -30 -15 -25 -51 -10 -42 -36]] || || 35.637 || 99/98 176/175 3125/3087 ||
|| 20 || <<3 -12 -30 -42 -26 -56 -77 -36 -56 -14]] || || 35.932 || 441/440 3136/3125 4375/4356 ||
|| 21 || <<1 -8 -2 -6 -15 -6 -13 18 14 -10]] || || 37.482 || 45/44 64/63 99/98 ||
|| 22 || <<2 8 20 24 8 26 31 24 28 -2]] || || 38.122 || 81/80 126/125 245/242 ||
|| 23 || <<6 0 0 0 -14 -17 -21 0 0 0]] || || 38.412 || 50/49 56/55 125/121 ||
|| 24 || <<5 8 2 6 1 -11 -8 -18 -14 10]] || || 38.811 || 36/35 80/77 126/121 ||
|| 25 || <<3 0 6 -6 -7 1 -20 14 -14 -38]] || || 39.764 || 36/35 80/77 128/125 ||
|| 26 || <<4 -8 -20 -36 -22 -43 -71 -24 -56 -32]] || || 40.191 || 176/175 896/891 1375/1372 ||
|| 27 || <<5 8 14 18 1 8 11 10 14 2]] || || 40.347 || 45/44 99/98 126/125 ||
|| 28 || <<5 -4 -10 -18 -18 -30 -46 -12 -28 -16]] || || 40.809 || 64/63 100/99 1375/1372 ||
|| 29 || <<3 0 -6 -18 -7 -18 -39 -14 -42 -30]] || || 40.832 || 64/63 99/98 126/125 ||
|| 30 || <<2 8 8 0 8 7 -7 -4 -28 -28]] || || 43.062 || 50/49 56/55 81/77 ||
|| 31 || <<3 0 -6 6 -7 -18 -1 -14 14 38]] || || 44.048 || 45/44 64/63 126/125 ||
|| 32 || <<4 -32 -68 -108 -60 -119 -185 -68 -140 -68]] || || 45.738 || 1375/1372 6250/6237 496125/495616 ||
|| 33 || <<3 12 18 30 12 20 37 8 28 22]] || || 46.794 || 81/80 99/98 625/616 ||
|| 34 || <<2 -4 8 0 -11 7 -7 30 14 -28]] || || 47.882 || 36/35 45/44 128/121 ||
|| 35 || <<2 -4 -16 -12 -11 -31 -26 -26 -14 22]] || || 48.070 || 56/55 100/99 2048/2025 ||
|| 36 || <<2 -16 -28 -48 -30 -50 -83 -20 -56 -38]] || ||48.712 || 225/224 2420/2401 3125/3087 ||
|| 37 || <<2 8 8 24 8 7 31 -4 28 40]] || || 48.739 || 50/49 81/80 176/175 ||
|| 38 || <<1 -8 -26 -42 -15 -44 -70 -38 -70 -28]] || || 48.887 || 126/125 176/175 539055/537824 ||
|| 39 || <<1 16 34 54 23 51 82 34 70 34]] || || 49.725 || 225/224 441/440 78408/78125 ||
|| 40 || <<7 4 10 6 -10 -4 -15 12 0 -18]] || || 49.914 || 36/35 56/55 125/121 ||

Original HTML content:

<html><head><title>List of 12et rank two temperaments by badness</title></head><body>Below are listed rank-two temperaments supported by the 12et patent val, below the indicated cutoff in TE badness.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x11-limit temperaments with badness below 0.05"></a><!-- ws:end:WikiTextHeadingRule:0 -->11-limit temperaments with badness below 0.05</h1>
Listed is the wedgie and the TE badness times 1000 for 40 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;1 4 10 18 4 13 25 12 28 16]]<br />
</td>
        <td><br />
</td>
        <td>17.027<br />
</td>
        <td>81/80 99/98 126/125<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;3 0 -6 -6 -7 -18 -20 -14 -14 4]]<br />
</td>
        <td><br />
</td>
        <td>19.613<br />
</td>
        <td>56/55 64/63 100/99<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;3 0 6 6 -7 1 -1 14 14 -4]]<br />
</td>
        <td><br />
</td>
        <td>20.191<br />
</td>
        <td>36/35 45/44 56/55<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;2 -4 -4 -12 -11 -12 -26 2 -14 -20]]<br />
</td>
        <td><br />
</td>
        <td>20.343<br />
</td>
        <td>50/49 64/63 99/98<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;1 4 10 6 4 13 6 12 0 -18]]<br />
</td>
        <td><br />
</td>
        <td>21.423<br />
</td>
        <td>45/44 56/55 81/80<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;1 4 -2 6 4 -6 6 -16 0 24]]<br />
</td>
        <td><br />
</td>
        <td>21.978<br />
</td>
        <td>36/35 45/44 64/63<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>&lt;&lt;4 4 4 0 -3 -5 -14 -2 -14 -14]]<br />
</td>
        <td><br />
</td>
        <td>22.132<br />
</td>
        <td>36/35 50/49 56/55<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>&lt;&lt;0 12 24 36 19 38 57 22 42 18]]<br />
</td>
        <td><br />
</td>
        <td>22.235<br />
</td>
        <td>225/224 441/440 4375/4356<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>&lt;&lt;2 8 8 12 8 7 12 -4 0 6]]<br />
</td>
        <td><br />
</td>
        <td>23.124<br />
</td>
        <td>45/44 50/49 99/98<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>&lt;&lt;1 -8 -14 -18 -15 -25 -32 -10 -14 -2]]<br />
</td>
        <td><br />
</td>
        <td>23.556<br />
</td>
        <td>100/99 225/224 245/242<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>&lt;&lt;2 -4 -4 0 -11 -12 -7 2 14 14]]<br />
</td>
        <td><br />
</td>
        <td>23.798<br />
</td>
        <td>45/44 50/49 56/55<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>&lt;&lt;1 4 -2 -6 4 -6 -13 -16 -28 -10]]<br />
</td>
        <td><br />
</td>
        <td>24.18<br />
</td>
        <td>36/35 56/55 64/63<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>&lt;&lt;2 -4 -16 -24 -11 -31 -45 -26 -42 -12]]<br />
</td>
        <td><br />
</td>
        <td>25.034<br />
</td>
        <td>126/125 176/175 5488/5445<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>&lt;&lt;4 4 4 12 -3 -5 5 -2 14 20]]<br />
</td>
        <td><br />
</td>
        <td>26.574<br />
</td>
        <td>36/35 45/44 50/49<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>&lt;&lt;2 -16 -40 -60 -30 -69 -102 -48 -84 -30]]<br />
</td>
        <td><br />
</td>
        <td>28.160<br />
</td>
        <td>441/440 3136/3125 8019/8000<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>&lt;&lt;0 0 0 12 0 0 19 0 28 34]]<br />
</td>
        <td><br />
</td>
        <td>30.536<br />
</td>
        <td>36/35 50/49 64/63<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>&lt;&lt;0 0 12 12 0 19 19 28 28 -8]]<br />
</td>
        <td><br />
</td>
        <td>34.478<br />
</td>
        <td>56/55 81/80 128/125<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>&lt;&lt;4 -20 -44 -72 -41 -81 -128 -46 -98 -50]]<br />
</td>
        <td><br />
</td>
        <td>34.837<br />
</td>
        <td>1375/1372 5120/5103 5632/5625<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>&lt;&lt;1 -8 -14 -30 -15 -25 -51 -10 -42 -36]]<br />
</td>
        <td><br />
</td>
        <td>35.637<br />
</td>
        <td>99/98 176/175 3125/3087<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>&lt;&lt;3 -12 -30 -42 -26 -56 -77 -36 -56 -14]]<br />
</td>
        <td><br />
</td>
        <td>35.932<br />
</td>
        <td>441/440 3136/3125 4375/4356<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>&lt;&lt;1 -8 -2 -6 -15 -6 -13 18 14 -10]]<br />
</td>
        <td><br />
</td>
        <td>37.482<br />
</td>
        <td>45/44 64/63 99/98<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>&lt;&lt;2 8 20 24 8 26 31 24 28 -2]]<br />
</td>
        <td><br />
</td>
        <td>38.122<br />
</td>
        <td>81/80 126/125 245/242<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>&lt;&lt;6 0 0 0 -14 -17 -21 0 0 0]]<br />
</td>
        <td><br />
</td>
        <td>38.412<br />
</td>
        <td>50/49 56/55 125/121<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>&lt;&lt;5 8 2 6 1 -11 -8 -18 -14 10]]<br />
</td>
        <td><br />
</td>
        <td>38.811<br />
</td>
        <td>36/35 80/77 126/121<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>&lt;&lt;3 0 6 -6 -7 1 -20 14 -14 -38]]<br />
</td>
        <td><br />
</td>
        <td>39.764<br />
</td>
        <td>36/35 80/77 128/125<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>&lt;&lt;4 -8 -20 -36 -22 -43 -71 -24 -56 -32]]<br />
</td>
        <td><br />
</td>
        <td>40.191<br />
</td>
        <td>176/175 896/891 1375/1372<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>&lt;&lt;5 8 14 18 1 8 11 10 14 2]]<br />
</td>
        <td><br />
</td>
        <td>40.347<br />
</td>
        <td>45/44 99/98 126/125<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>&lt;&lt;5 -4 -10 -18 -18 -30 -46 -12 -28 -16]]<br />
</td>
        <td><br />
</td>
        <td>40.809<br />
</td>
        <td>64/63 100/99 1375/1372<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>&lt;&lt;3 0 -6 -18 -7 -18 -39 -14 -42 -30]]<br />
</td>
        <td><br />
</td>
        <td>40.832<br />
</td>
        <td>64/63 99/98 126/125<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>&lt;&lt;2 8 8 0 8 7 -7 -4 -28 -28]]<br />
</td>
        <td><br />
</td>
        <td>43.062<br />
</td>
        <td>50/49 56/55 81/77<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>&lt;&lt;3 0 -6 6 -7 -18 -1 -14 14 38]]<br />
</td>
        <td><br />
</td>
        <td>44.048<br />
</td>
        <td>45/44 64/63 126/125<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>&lt;&lt;4 -32 -68 -108 -60 -119 -185 -68 -140 -68]]<br />
</td>
        <td><br />
</td>
        <td>45.738<br />
</td>
        <td>1375/1372 6250/6237 496125/495616<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>&lt;&lt;3 12 18 30 12 20 37 8 28 22]]<br />
</td>
        <td><br />
</td>
        <td>46.794<br />
</td>
        <td>81/80 99/98 625/616<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>&lt;&lt;2 -4 8 0 -11 7 -7 30 14 -28]]<br />
</td>
        <td><br />
</td>
        <td>47.882<br />
</td>
        <td>36/35 45/44 128/121<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>&lt;&lt;2 -4 -16 -12 -11 -31 -26 -26 -14 22]]<br />
</td>
        <td><br />
</td>
        <td>48.070<br />
</td>
        <td>56/55 100/99 2048/2025<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>&lt;&lt;2 -16 -28 -48 -30 -50 -83 -20 -56 -38]]<br />
</td>
        <td><br />
</td>
        <td>48.712<br />
</td>
        <td>225/224 2420/2401 3125/3087<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>&lt;&lt;2 8 8 24 8 7 31 -4 28 40]]<br />
</td>
        <td><br />
</td>
        <td>48.739<br />
</td>
        <td>50/49 81/80 176/175<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>&lt;&lt;1 -8 -26 -42 -15 -44 -70 -38 -70 -28]]<br />
</td>
        <td><br />
</td>
        <td>48.887<br />
</td>
        <td>126/125 176/175 539055/537824<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>&lt;&lt;1 16 34 54 23 51 82 34 70 34]]<br />
</td>
        <td><br />
</td>
        <td>49.725<br />
</td>
        <td>225/224 441/440 78408/78125<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>&lt;&lt;7 4 10 6 -10 -4 -15 12 0 -18]]<br />
</td>
        <td><br />
</td>
        <td>49.914<br />
</td>
        <td>36/35 56/55 125/121<br />
</td>
    </tr>
</table>

</body></html>