List of edo-distinct 72et rank two temperaments

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Revision as of 17:47, 11 February 2014 by Wikispaces>genewardsmith (**Imported revision 488875696 - Original comment: **)
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This revision was by author genewardsmith and made on 2014-02-11 17:47:51 UTC.
The original revision id was 488875696.
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The temperaments listed are 72edo-distinct, meaning that they are all different even if tuned in 72edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.

=5-limit temperaments= 
|| Period generator || Wedgie || Name || Complexity || Commas ||
|| 72 23 || <<30 1 -68]] || || 15.274 || 931322574615478515625/885443715538058477568 ||
|| 36 13 || <<12 -2 -31]] || || 6.558 || 2197265625/2147483648 ||
|| 24 1 || <<18 3 -37]] || || 8.789 || 3814697265625/3710851743744 ||
|| 18 5 || <<48 4 -105]] || || 24.043 || [[-105 -4 48>> ||
|| 72 19 || <<6 5 -6]] || Hanson || 2.685 || 15625/15552 ||
|| 12 1 || <<108 6 -241]] || || 54.584 || [[-241 -6 108>> ||
|| 72 7 || <<6 -7 -25]] || Ampersand || 4.815 || 34171875/33554432 ||
|| 9 4 || <<24 8 -43]] || || 11.22 || 59604644775390625/57711166318706688 ||
|| 8 1 || <<18 -9 -56]] || || 11.188 || 75084686279296875/72057594037927936 ||
|| 36 17 || <<60 62 -41]] || || 27.509 || [[-41 -62 60>> ||
|| 72 11 || <<30 -11 -87]] || || 17.697 || 164981000125408172607421875/154742504910672534362390528 ||
|| 6 1 || <<0 12 19]] || Compton || 4.218 || 531441/524288 ||
|| 72 35 || <<30 13 -49]] || || 13.746 || 931322574615478515625/897524058588526411776 ||
|| 36 7 || <<60 14 -117]] || || 28.753 ||  [[-117 -14 60>> ||
|| 24 5 || <<54 57 -35]] || || 24.859 ||  [[-35 -57 54>> ||
|| 9 2 || <<24 -16 -81]] || || 15.929 || 2565784513950347900390625/2417851639229258349412352 ||
|| 72 31 || <<6 17 13]] || || 5.177 || 129140163/128000000 ||
|| 4 1 || <<36 18 -55]] || || 16.323 || 14551915228366851806640625/13958294159168762755940352 ||
|| 72 5 || <<6 -19 -44]] || || 8.646 || 18160335421875/17592186044416 ||
|| 18 1 || <<48 52 -29]] || || 22.217 ||  [[-29 -52 48>> ||
|| 24 7 || <<54 21 -92]] || || 24.95 || [[-92 -21 54]]  ||
|| 36 11 || <<12 22 7]] || || 7.088 || 31381059609/31250000000 ||
|| 72 1 || <<30 49 8]] || || 16.415 || 239299329230617529590083/238418579101562500000000 ||
|| 3 1 || <<72 -24 -205]] || || 41.926 || [[-205 24 72>> ||
|| 72 25 || <<42 47 -23]] || || 19.587 || 227373675443232059478759765625/223043140842065783739956330496 ||
|| 36 1 || <<12 -26 -69]] || || 13.345 || 620572711994384765625/590295810358705651712 ||
|| 8 3 || <<18 27 1]] || || 9.386 || 7629394531250/7625597484987 ||
|| 18 7 || <<48 28 -67]] || || 21.556 || [[-67 -28 48>> ||
|| 72 29 || <<6 29 32]] || || 9.054 || 68630377364883/67108864000000 ||
|| 12 5 || <<36 42 -17]] || || 16.975 || 14551915228366851806640625/14341765743445587946242048 ||
|| 72 17 || <<6 -31 -63]] || || 12.723 || 9651146816936671875/9223372036854775808 ||
|| 9 1 || <<24 32 -5]] || || 11.847 || 59604644775390625/59296646043258912 ||
|| 24 11 || <<18 39 20]] || || 12.119 || 4052555153018976267/400 ||
|| 36 5 || <<60 38 -79]] || || 26.843 || [[-79 -38 60>> ||
|| 72 13 || <<30 37 -11]] || || 14.389 || 931322574615478515625/922181439264762599424 ||
|| 2 1 || <<144 36 -277]] || || 68.703 || [[-277 -36 144>> ||

Original HTML content:

<html><head><title>List of edo-distinct 72et rank two temperaments</title></head><body>The temperaments listed are 72edo-distinct, meaning that they are all different even if tuned in 72edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <td>Period generator<br />
</td>
        <td>Wedgie<br />
</td>
        <td>Name<br />
</td>
        <td>Complexity<br />
</td>
        <td>Commas<br />
</td>
    </tr>
    <tr>
        <td>72 23<br />
</td>
        <td>&lt;&lt;30 1 -68]]<br />
</td>
        <td><br />
</td>
        <td>15.274<br />
</td>
        <td>931322574615478515625/885443715538058477568<br />
</td>
    </tr>
    <tr>
        <td>36 13<br />
</td>
        <td>&lt;&lt;12 -2 -31]]<br />
</td>
        <td><br />
</td>
        <td>6.558<br />
</td>
        <td>2197265625/2147483648<br />
</td>
    </tr>
    <tr>
        <td>24 1<br />
</td>
        <td>&lt;&lt;18 3 -37]]<br />
</td>
        <td><br />
</td>
        <td>8.789<br />
</td>
        <td>3814697265625/3710851743744<br />
</td>
    </tr>
    <tr>
        <td>18 5<br />
</td>
        <td>&lt;&lt;48 4 -105]]<br />
</td>
        <td><br />
</td>
        <td>24.043<br />
</td>
        <td>[[-105 -4 48&gt;&gt;<br />
</td>
        <td colspan="2">72 19<br />
</td>
        <td>&lt;&lt;6 5 -6]]<br />
</td>
        <td>Hanson<br />
</td>
        <td>2.685<br />
</td>
        <td>15625/15552<br />
</td>
    </tr>
    <tr>
        <td>12 1<br />
</td>
        <td>&lt;&lt;108 6 -241]]<br />
</td>
        <td><br />
</td>
        <td>54.584<br />
</td>
        <td>[[-241 -6 108&gt;&gt;<br />
</td>
        <td colspan="2">72 7<br />
</td>
        <td>&lt;&lt;6 -7 -25]]<br />
</td>
        <td>Ampersand<br />
</td>
        <td>4.815<br />
</td>
        <td>34171875/33554432<br />
</td>
    </tr>
    <tr>
        <td>9 4<br />
</td>
        <td>&lt;&lt;24 8 -43]]<br />
</td>
        <td><br />
</td>
        <td>11.22<br />
</td>
        <td>59604644775390625/57711166318706688<br />
</td>
    </tr>
    <tr>
        <td>8 1<br />
</td>
        <td>&lt;&lt;18 -9 -56]]<br />
</td>
        <td><br />
</td>
        <td>11.188<br />
</td>
        <td>75084686279296875/72057594037927936<br />
</td>
    </tr>
    <tr>
        <td>36 17<br />
</td>
        <td>&lt;&lt;60 62 -41]]<br />
</td>
        <td><br />
</td>
        <td>27.509<br />
</td>
        <td>[[-41 -62 60&gt;&gt;<br />
</td>
        <td colspan="2">72 11<br />
</td>
        <td>&lt;&lt;30 -11 -87]]<br />
</td>
        <td><br />
</td>
        <td>17.697<br />
</td>
        <td>164981000125408172607421875/154742504910672534362390528<br />
</td>
    </tr>
    <tr>
        <td>6 1<br />
</td>
        <td>&lt;&lt;0 12 19]]<br />
</td>
        <td>Compton<br />
</td>
        <td>4.218<br />
</td>
        <td>531441/524288<br />
</td>
    </tr>
    <tr>
        <td>72 35<br />
</td>
        <td>&lt;&lt;30 13 -49]]<br />
</td>
        <td><br />
</td>
        <td>13.746<br />
</td>
        <td>931322574615478515625/897524058588526411776<br />
</td>
    </tr>
    <tr>
        <td>36 7<br />
</td>
        <td>&lt;&lt;60 14 -117]]<br />
</td>
        <td><br />
</td>
        <td>28.753<br />
</td>
        <td>[[-117 -14 60&gt;&gt;<br />
</td>
        <td colspan="2">24 5<br />
</td>
        <td>&lt;&lt;54 57 -35]]<br />
</td>
        <td><br />
</td>
        <td>24.859<br />
</td>
        <td>[[-35 -57 54&gt;&gt;<br />
</td>
        <td colspan="2">9 2<br />
</td>
        <td>&lt;&lt;24 -16 -81]]<br />
</td>
        <td><br />
</td>
        <td>15.929<br />
</td>
        <td>2565784513950347900390625/2417851639229258349412352<br />
</td>
    </tr>
    <tr>
        <td>72 31<br />
</td>
        <td>&lt;&lt;6 17 13]]<br />
</td>
        <td><br />
</td>
        <td>5.177<br />
</td>
        <td>129140163/128000000<br />
</td>
    </tr>
    <tr>
        <td>4 1<br />
</td>
        <td>&lt;&lt;36 18 -55]]<br />
</td>
        <td><br />
</td>
        <td>16.323<br />
</td>
        <td>14551915228366851806640625/13958294159168762755940352<br />
</td>
    </tr>
    <tr>
        <td>72 5<br />
</td>
        <td>&lt;&lt;6 -19 -44]]<br />
</td>
        <td><br />
</td>
        <td>8.646<br />
</td>
        <td>18160335421875/17592186044416<br />
</td>
    </tr>
    <tr>
        <td>18 1<br />
</td>
        <td>&lt;&lt;48 52 -29]]<br />
</td>
        <td><br />
</td>
        <td>22.217<br />
</td>
        <td>[[-29 -52 48&gt;&gt;<br />
</td>
        <td colspan="2">24 7<br />
</td>
        <td>&lt;&lt;54 21 -92]]<br />
</td>
        <td><br />
</td>
        <td>24.95<br />
</td>
        <td><a class="wiki_link" href="/-92%20-21%2054">-92 -21 54</a><br />
</td>
    </tr>
    <tr>
        <td>36 11<br />
</td>
        <td>&lt;&lt;12 22 7]]<br />
</td>
        <td><br />
</td>
        <td>7.088<br />
</td>
        <td>31381059609/31250000000<br />
</td>
    </tr>
    <tr>
        <td>72 1<br />
</td>
        <td>&lt;&lt;30 49 8]]<br />
</td>
        <td><br />
</td>
        <td>16.415<br />
</td>
        <td>239299329230617529590083/238418579101562500000000<br />
</td>
    </tr>
    <tr>
        <td>3 1<br />
</td>
        <td>&lt;&lt;72 -24 -205]]<br />
</td>
        <td><br />
</td>
        <td>41.926<br />
</td>
        <td>[[-205 24 72&gt;&gt;<br />
</td>
        <td colspan="2">72 25<br />
</td>
        <td>&lt;&lt;42 47 -23]]<br />
</td>
        <td><br />
</td>
        <td>19.587<br />
</td>
        <td>227373675443232059478759765625/223043140842065783739956330496<br />
</td>
    </tr>
    <tr>
        <td>36 1<br />
</td>
        <td>&lt;&lt;12 -26 -69]]<br />
</td>
        <td><br />
</td>
        <td>13.345<br />
</td>
        <td>620572711994384765625/590295810358705651712<br />
</td>
    </tr>
    <tr>
        <td>8 3<br />
</td>
        <td>&lt;&lt;18 27 1]]<br />
</td>
        <td><br />
</td>
        <td>9.386<br />
</td>
        <td>7629394531250/7625597484987<br />
</td>
    </tr>
    <tr>
        <td>18 7<br />
</td>
        <td>&lt;&lt;48 28 -67]]<br />
</td>
        <td><br />
</td>
        <td>21.556<br />
</td>
        <td>[[-67 -28 48&gt;&gt;<br />
</td>
        <td colspan="2">72 29<br />
</td>
        <td>&lt;&lt;6 29 32]]<br />
</td>
        <td><br />
</td>
        <td>9.054<br />
</td>
        <td>68630377364883/67108864000000<br />
</td>
    </tr>
    <tr>
        <td>12 5<br />
</td>
        <td>&lt;&lt;36 42 -17]]<br />
</td>
        <td><br />
</td>
        <td>16.975<br />
</td>
        <td>14551915228366851806640625/14341765743445587946242048<br />
</td>
    </tr>
    <tr>
        <td>72 17<br />
</td>
        <td>&lt;&lt;6 -31 -63]]<br />
</td>
        <td><br />
</td>
        <td>12.723<br />
</td>
        <td>9651146816936671875/9223372036854775808<br />
</td>
    </tr>
    <tr>
        <td>9 1<br />
</td>
        <td>&lt;&lt;24 32 -5]]<br />
</td>
        <td><br />
</td>
        <td>11.847<br />
</td>
        <td>59604644775390625/59296646043258912<br />
</td>
    </tr>
    <tr>
        <td>24 11<br />
</td>
        <td>&lt;&lt;18 39 20]]<br />
</td>
        <td><br />
</td>
        <td>12.119<br />
</td>
        <td>4052555153018976267/400<br />
</td>
    </tr>
    <tr>
        <td>36 5<br />
</td>
        <td>&lt;&lt;60 38 -79]]<br />
</td>
        <td><br />
</td>
        <td>26.843<br />
</td>
        <td>[[-79 -38 60&gt;&gt;<br />
</td>
        <td colspan="2">72 13<br />
</td>
        <td>&lt;&lt;30 37 -11]]<br />
</td>
        <td><br />
</td>
        <td>14.389<br />
</td>
        <td>931322574615478515625/922181439264762599424<br />
</td>
    </tr>
    <tr>
        <td>2 1<br />
</td>
        <td>&lt;&lt;144 36 -277]]<br />
</td>
        <td><br />
</td>
        <td>68.703<br />
</td>
        <td>[[-277 -36 144&gt;&gt;<br />
</td>
    </tr>
</table>

</body></html>
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