Luna and hemithirds/Chords: Difference between revisions

Revision as of 23:04, 20 December 2011

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2011-12-20 23:04:35 UTC.

The original revision id was 287833246.

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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 the [[Dyadic chord|dyadic chords]] of 11-limit [[Gamelismic clan#Hemithirds|hemithirds temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic.

=Triads=
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-5 || 1-5/4-7/4 || otonal ||
|| 2 || 0-3-5 || 1-7/5-7/4 || utonal ||
|| 3 || 0-2-7 || 1-5/4-12/11 || keenanismic ||
|| 4 || 0-5-7 || 1-7/4-12/11 || keenanismic ||
|| 5 || 0-3-8 || 1-7/5-11/9 || werckismic ||
|| 6 || 0-5-8 || 1-7/4-11/9 || werckismic ||
|| 7 || 0-7-15 || 1-12/11-4/3 || utonal ||
|| 8 || 0-8-15 || 1-11/9-4/3 || otonal ||
|| 9 || 0-2-17 || 1-5/4-5/3 || utonal ||
|| 10 || 0-15-17 || 1-4/3-5/3 || otonal ||
|| 11 || 0-3-20 || 1-7/5-7/6 || utonal ||
|| 12 || 0-5-20 || 1-7/4-7/6 || utonal ||
|| 13 || 0-15-20 || 1-4/3-7/6 || otonal ||
|| 14 || 0-17-20 || 1-5/3-7/6 || otonal ||
|| 15 || 0-2-22 || 1-5/4-16/11 || keenanismic ||
|| 16 || 0-5-22 || 1-7/4-16/11 || keenanismic ||
|| 17 || 0-7-22 || 1-12/11-16/11 || otonal ||
|| 18 || 0-15-22 || 1-4/3-16/11 || utonal ||
|| 19 || 0-17-22 || 1-5/3-16/11 || keenanismic ||
|| 20 || 0-20-22 || 1-7/6-16/11 || keenanismic ||
|| 21 || 0-2-24 || 1-5/4-20/11 || utonal ||
|| 22 || 0-7-24 || 1-12/11-20/11 || otonal ||
|| 23 || 0-17-24 || 1-5/3-20/11 || utonal ||
|| 24 || 0-22-24 || 1-16/11-20/11 || otonal ||
|| 25 || 0-3-27 || 1-7/5-14/11 || utonal ||
|| 26 || 0-5-27 || 1-7/4-14/11 || utonal ||
|| 27 || 0-7-27 || 1-12/11-14/11 || otonal ||
|| 28 || 0-20-27 || 1-7/6-14/11 || utonal ||
|| 29 || 0-22-27 || 1-16/11-14/11 || otonal ||
|| 30 || 0-24-27 || 1-20/11-14/11 || otonal ||
|| 31 || 0-3-30 || 1-7/5-16/9 || werckismic ||
|| 32 || 0-8-30 || 1-11/9-16/9 || otonal ||
|| 33 || 0-15-30 || 1-4/3-16/9 || ambitonal ||
|| 34 || 0-22-30 || 1-16/11-16/9 || utonal ||
|| 35 || 0-27-30 || 1-14/11-16/9 || werckismic ||
|| 36 || 0-2-32 || 1-5/4-10/9 || utonal ||
|| 37 || 0-5-32 || 1-7/4-10/9 || werckismic ||
|| 38 || 0-8-32 || 1-11/9-10/9 || otonal ||
|| 39 || 0-15-32 || 1-4/3-10/9 || otonal ||
|| 40 || 0-17-32 || 1-5/3-10/9 || utonal ||
|| 41 || 0-24-32 || 1-20/11-10/9 || utonal ||
|| 42 || 0-27-32 || 1-14/11-10/9 || werckismic ||
|| 43 || 0-30-32 || 1-16/9-10/9 || otonal ||
|| 44 || 0-3-35 || 1-7/5-14/9 || utonal ||
|| 45 || 0-5-35 || 1-7/4-14/9 || utonal ||
|| 46 || 0-8-35 || 1-11/9-14/9 || otonal ||
|| 47 || 0-15-35 || 1-4/3-14/9 || otonal ||
|| 48 || 0-20-35 || 1-7/6-14/9 || utonal ||
|| 49 || 0-27-35 || 1-14/11-14/9 || utonal ||
|| 50 || 0-30-35 || 1-16/9-14/9 || otonal ||
|| 51 || 0-32-35 || 1-10/9-14/9 || otonal ||

=Tetrads=
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-5-7 || 1-5/4-7/4-12/11 || keenanismic ||
|| 2 || 0-3-5-8 || 1-7/5-7/4-11/9 || werckismic ||
|| 3 || 0-3-5-20 || 1-7/5-7/4-7/6 || utonal ||
|| 4 || 0-15-17-20 || 1-4/3-5/3-7/6 || otonal ||
|| 5 || 0-2-5-22 || 1-5/4-7/4-16/11 || keenanismic ||
|| 6 || 0-2-7-22 || 1-5/4-12/11-16/11 || keenanismic ||
|| 7 || 0-5-7-22 || 1-7/4-12/11-16/11 || keenanismic ||
|| 8 || 0-7-15-22 || 1-12/11-4/3-16/11 || ambitonal ||
|| 9 || 0-2-17-22 || 1-5/4-5/3-16/11 || keenanismic ||
|| 10 || 0-15-17-22 || 1-4/3-5/3-16/11 || keenanismic ||
|| 11 || 0-5-20-22 || 1-7/4-7/6-16/11 || keenanismic ||
|| 12 || 0-15-20-22 || 1-4/3-7/6-16/11 || keenanismic ||
|| 13 || 0-17-20-22 || 1-5/3-7/6-16/11 || keenanismic ||
|| 14 || 0-2-7-24 || 1-5/4-12/11-20/11 || keenanismic ||
|| 15 || 0-2-17-24 || 1-5/4-5/3-20/11 || utonal ||
|| 16 || 0-2-22-24 || 1-5/4-16/11-20/11 || keenanismic ||
|| 17 || 0-7-22-24 || 1-12/11-16/11-20/11 || otonal ||
|| 18 || 0-17-22-24 || 1-5/3-16/11-20/11 || keenanismic ||
|| 19 || 0-3-5-27 || 1-7/5-7/4-14/11 || utonal ||
|| 20 || 0-5-7-27 || 1-7/4-12/11-14/11 || keenanismic ||
|| 21 || 0-3-20-27 || 1-7/5-7/6-14/11 || utonal ||
|| 22 || 0-5-20-27 || 1-7/4-7/6-14/11 || utonal ||
|| 23 || 0-5-22-27 || 1-7/4-16/11-14/11 || keenanismic ||
|| 24 || 0-7-22-27 || 1-12/11-16/11-14/11 || otonal ||
|| 25 || 0-20-22-27 || 1-7/6-16/11-14/11 || keenanismic ||
|| 26 || 0-7-24-27 || 1-12/11-20/11-14/11 || otonal ||
|| 27 || 0-22-24-27 || 1-16/11-20/11-14/11 || otonal ||
|| 28 || 0-3-8-30 || 1-7/5-11/9-16/9 || werckismic ||
|| 29 || 0-8-15-30 || 1-11/9-4/3-16/9 || otonal ||
|| 30 || 0-15-22-30 || 1-4/3-16/11-16/9 || utonal ||
|| 31 || 0-3-27-30 || 1-7/5-14/11-16/9 || werckismic ||
|| 32 || 0-22-27-30 || 1-16/11-14/11-16/9 || werckismic ||
|| 33 || 0-2-5-32 || 1-5/4-7/4-10/9 || werckismic ||
|| 34 || 0-5-8-32 || 1-7/4-11/9-10/9 || werckismic ||
|| 35 || 0-8-15-32 || 1-11/9-4/3-10/9 || otonal ||
|| 36 || 0-2-17-32 || 1-5/4-5/3-10/9 || utonal ||
|| 37 || 0-15-17-32 || 1-4/3-5/3-10/9 || ambitonal ||
|| 38 || 0-2-24-32 || 1-5/4-20/11-10/9 || utonal ||
|| 39 || 0-17-24-32 || 1-5/3-20/11-10/9 || utonal ||
|| 40 || 0-5-27-32 || 1-7/4-14/11-10/9 || werckismic ||
|| 41 || 0-24-27-32 || 1-20/11-14/11-10/9 || werckismic ||
|| 42 || 0-8-30-32 || 1-11/9-16/9-10/9 || otonal ||
|| 43 || 0-15-30-32 || 1-4/3-16/9-10/9 || otonal ||
|| 44 || 0-27-30-32 || 1-14/11-16/9-10/9 || werckismic ||
|| 45 || 0-3-5-35 || 1-7/5-7/4-14/9 || utonal ||
|| 46 || 0-3-8-35 || 1-7/5-11/9-14/9 || werckismic ||
|| 47 || 0-5-8-35 || 1-7/4-11/9-14/9 || werckismic ||
|| 48 || 0-8-15-35 || 1-11/9-4/3-14/9 || otonal ||
|| 49 || 0-3-20-35 || 1-7/5-7/6-14/9 || utonal ||
|| 50 || 0-5-20-35 || 1-7/4-7/6-14/9 || utonal ||
|| 51 || 0-15-20-35 || 1-4/3-7/6-14/9 || ambitonal ||
|| 52 || 0-3-27-35 || 1-7/5-14/11-14/9 || utonal ||
|| 53 || 0-5-27-35 || 1-7/4-14/11-14/9 || utonal ||
|| 54 || 0-20-27-35 || 1-7/6-14/11-14/9 || utonal ||
|| 55 || 0-3-30-35 || 1-7/5-16/9-14/9 || werckismic ||
|| 56 || 0-8-30-35 || 1-11/9-16/9-14/9 || otonal ||
|| 57 || 0-15-30-35 || 1-4/3-16/9-14/9 || otonal ||
|| 58 || 0-27-30-35 || 1-14/11-16/9-14/9 || werckismic ||
|| 59 || 0-5-32-35 || 1-7/4-10/9-14/9 || werckismic ||
|| 60 || 0-8-32-35 || 1-11/9-10/9-14/9 || otonal ||
|| 61 || 0-15-32-35 || 1-4/3-10/9-14/9 || otonal ||
|| 62 || 0-27-32-35 || 1-14/11-10/9-14/9 || werckismic ||
|| 63 || 0-30-32-35 || 1-16/9-10/9-14/9 || otonal ||

=Pentads=
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-5-7-22 || 1-5/4-7/4-12/11-16/11 || keenanismic ||
|| 2 || 0-15-17-20-22 || 1-4/3-5/3-7/6-16/11 || keenanismic ||
|| 3 || 0-2-7-22-24 || 1-5/4-12/11-16/11-20/11 || keenanismic ||
|| 4 || 0-2-17-22-24 || 1-5/4-5/3-16/11-20/11 || keenanismic ||
|| 5 || 0-3-5-20-27 || 1-7/5-7/4-7/6-14/11 || utonal ||
|| 6 || 0-5-7-22-27 || 1-7/4-12/11-16/11-14/11 || keenanismic ||
|| 7 || 0-5-20-22-27 || 1-7/4-7/6-16/11-14/11 || keenanismic ||
|| 8 || 0-7-22-24-27 || 1-12/11-16/11-20/11-14/11 || otonal ||
|| 9 || 0-2-17-24-32 || 1-5/4-5/3-20/11-10/9 || utonal ||
|| 10 || 0-8-15-30-32 || 1-11/9-4/3-16/9-10/9 || otonal ||
|| 11 || 0-3-5-8-35 || 1-7/5-7/4-11/9-14/9 || werckismic ||
|| 12 || 0-3-5-20-35 || 1-7/5-7/4-7/6-14/9 || utonal ||
|| 13 || 0-3-5-27-35 || 1-7/5-7/4-14/11-14/9 || utonal ||
|| 14 || 0-3-20-27-35 || 1-7/5-7/6-14/11-14/9 || utonal ||
|| 15 || 0-5-20-27-35 || 1-7/4-7/6-14/11-14/9 || utonal ||
|| 16 || 0-3-8-30-35 || 1-7/5-11/9-16/9-14/9 || werckismic ||
|| 17 || 0-8-15-30-35 || 1-11/9-4/3-16/9-14/9 || otonal ||
|| 18 || 0-3-27-30-35 || 1-7/5-14/11-16/9-14/9 || werckismic ||
|| 19 || 0-5-8-32-35 || 1-7/4-11/9-10/9-14/9 || werckismic ||
|| 20 || 0-8-15-32-35 || 1-11/9-4/3-10/9-14/9 || otonal ||
|| 21 || 0-5-27-32-35 || 1-7/4-14/11-10/9-14/9 || werckismic ||
|| 22 || 0-8-30-32-35 || 1-11/9-16/9-10/9-14/9 || otonal ||
|| 23 || 0-15-30-32-35 || 1-4/3-16/9-10/9-14/9 || otonal ||
|| 24 || 0-27-30-32-35 || 1-14/11-16/9-10/9-14/9 || werckismic ||

=Hexads=
|| Number || Chord || Transversal || Type ||
|| 1 || 0-3-5-20-27-35 || 1-7/5-7/4-7/6-14/11-14/9 || utonal ||
|| 2 || 0-8-15-30-32-35 || 1-11/9-4/3-16/9-10/9-14/9 || otonal ||

Original HTML content:

<html><head><title>Chords of hemithirds</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Gamelismic%20clan#Hemithirds">hemithirds temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>


<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-5<br />
</td>
        <td>1-5/4-7/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-3-5<br />
</td>
        <td>1-7/5-7/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-2-7<br />
</td>
        <td>1-5/4-12/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-5-7<br />
</td>
        <td>1-7/4-12/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-3-8<br />
</td>
        <td>1-7/5-11/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-5-8<br />
</td>
        <td>1-7/4-11/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-7-15<br />
</td>
        <td>1-12/11-4/3<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-8-15<br />
</td>
        <td>1-11/9-4/3<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-2-17<br />
</td>
        <td>1-5/4-5/3<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-15-17<br />
</td>
        <td>1-4/3-5/3<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-3-20<br />
</td>
        <td>1-7/5-7/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-5-20<br />
</td>
        <td>1-7/4-7/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-15-20<br />
</td>
        <td>1-4/3-7/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-17-20<br />
</td>
        <td>1-5/3-7/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-2-22<br />
</td>
        <td>1-5/4-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-5-22<br />
</td>
        <td>1-7/4-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-7-22<br />
</td>
        <td>1-12/11-16/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-15-22<br />
</td>
        <td>1-4/3-16/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-17-22<br />
</td>
        <td>1-5/3-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-20-22<br />
</td>
        <td>1-7/6-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-2-24<br />
</td>
        <td>1-5/4-20/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-7-24<br />
</td>
        <td>1-12/11-20/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-17-24<br />
</td>
        <td>1-5/3-20/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-22-24<br />
</td>
        <td>1-16/11-20/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-3-27<br />
</td>
        <td>1-7/5-14/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-5-27<br />
</td>
        <td>1-7/4-14/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-7-27<br />
</td>
        <td>1-12/11-14/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-20-27<br />
</td>
        <td>1-7/6-14/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-22-27<br />
</td>
        <td>1-16/11-14/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-24-27<br />
</td>
        <td>1-20/11-14/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-3-30<br />
</td>
        <td>1-7/5-16/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-8-30<br />
</td>
        <td>1-11/9-16/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-15-30<br />
</td>
        <td>1-4/3-16/9<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-22-30<br />
</td>
        <td>1-16/11-16/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-27-30<br />
</td>
        <td>1-14/11-16/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-2-32<br />
</td>
        <td>1-5/4-10/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-5-32<br />
</td>
        <td>1-7/4-10/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-8-32<br />
</td>
        <td>1-11/9-10/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-15-32<br />
</td>
        <td>1-4/3-10/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-17-32<br />
</td>
        <td>1-5/3-10/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-24-32<br />
</td>
        <td>1-20/11-10/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-27-32<br />
</td>
        <td>1-14/11-10/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-30-32<br />
</td>
        <td>1-16/9-10/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-3-35<br />
</td>
        <td>1-7/5-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-5-35<br />
</td>
        <td>1-7/4-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-8-35<br />
</td>
        <td>1-11/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-15-35<br />
</td>
        <td>1-4/3-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-20-35<br />
</td>
        <td>1-7/6-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-27-35<br />
</td>
        <td>1-14/11-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-30-35<br />
</td>
        <td>1-16/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-32-35<br />
</td>
        <td>1-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Tetrads"></a><!-- ws:end:WikiTextHeadingRule:2 -->Tetrads</h1>


<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-5-7<br />
</td>
        <td>1-5/4-7/4-12/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-3-5-8<br />
</td>
        <td>1-7/5-7/4-11/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-3-5-20<br />
</td>
        <td>1-7/5-7/4-7/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-15-17-20<br />
</td>
        <td>1-4/3-5/3-7/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-2-5-22<br />
</td>
        <td>1-5/4-7/4-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-2-7-22<br />
</td>
        <td>1-5/4-12/11-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-5-7-22<br />
</td>
        <td>1-7/4-12/11-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-7-15-22<br />
</td>
        <td>1-12/11-4/3-16/11<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-2-17-22<br />
</td>
        <td>1-5/4-5/3-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-15-17-22<br />
</td>
        <td>1-4/3-5/3-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-5-20-22<br />
</td>
        <td>1-7/4-7/6-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-15-20-22<br />
</td>
        <td>1-4/3-7/6-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-17-20-22<br />
</td>
        <td>1-5/3-7/6-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-2-7-24<br />
</td>
        <td>1-5/4-12/11-20/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-2-17-24<br />
</td>
        <td>1-5/4-5/3-20/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-2-22-24<br />
</td>
        <td>1-5/4-16/11-20/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-7-22-24<br />
</td>
        <td>1-12/11-16/11-20/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-17-22-24<br />
</td>
        <td>1-5/3-16/11-20/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-3-5-27<br />
</td>
        <td>1-7/5-7/4-14/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-5-7-27<br />
</td>
        <td>1-7/4-12/11-14/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-3-20-27<br />
</td>
        <td>1-7/5-7/6-14/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-5-20-27<br />
</td>
        <td>1-7/4-7/6-14/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-5-22-27<br />
</td>
        <td>1-7/4-16/11-14/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-7-22-27<br />
</td>
        <td>1-12/11-16/11-14/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-20-22-27<br />
</td>
        <td>1-7/6-16/11-14/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-7-24-27<br />
</td>
        <td>1-12/11-20/11-14/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-22-24-27<br />
</td>
        <td>1-16/11-20/11-14/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-3-8-30<br />
</td>
        <td>1-7/5-11/9-16/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-8-15-30<br />
</td>
        <td>1-11/9-4/3-16/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-15-22-30<br />
</td>
        <td>1-4/3-16/11-16/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-3-27-30<br />
</td>
        <td>1-7/5-14/11-16/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-22-27-30<br />
</td>
        <td>1-16/11-14/11-16/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-2-5-32<br />
</td>
        <td>1-5/4-7/4-10/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-5-8-32<br />
</td>
        <td>1-7/4-11/9-10/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-8-15-32<br />
</td>
        <td>1-11/9-4/3-10/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-2-17-32<br />
</td>
        <td>1-5/4-5/3-10/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-15-17-32<br />
</td>
        <td>1-4/3-5/3-10/9<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-2-24-32<br />
</td>
        <td>1-5/4-20/11-10/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-17-24-32<br />
</td>
        <td>1-5/3-20/11-10/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-5-27-32<br />
</td>
        <td>1-7/4-14/11-10/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-24-27-32<br />
</td>
        <td>1-20/11-14/11-10/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-8-30-32<br />
</td>
        <td>1-11/9-16/9-10/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-15-30-32<br />
</td>
        <td>1-4/3-16/9-10/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-27-30-32<br />
</td>
        <td>1-14/11-16/9-10/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-3-5-35<br />
</td>
        <td>1-7/5-7/4-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-3-8-35<br />
</td>
        <td>1-7/5-11/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-5-8-35<br />
</td>
        <td>1-7/4-11/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-8-15-35<br />
</td>
        <td>1-11/9-4/3-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-3-20-35<br />
</td>
        <td>1-7/5-7/6-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-5-20-35<br />
</td>
        <td>1-7/4-7/6-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-15-20-35<br />
</td>
        <td>1-4/3-7/6-14/9<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-3-27-35<br />
</td>
        <td>1-7/5-14/11-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-5-27-35<br />
</td>
        <td>1-7/4-14/11-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-20-27-35<br />
</td>
        <td>1-7/6-14/11-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-3-30-35<br />
</td>
        <td>1-7/5-16/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-8-30-35<br />
</td>
        <td>1-11/9-16/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-15-30-35<br />
</td>
        <td>1-4/3-16/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-27-30-35<br />
</td>
        <td>1-14/11-16/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-5-32-35<br />
</td>
        <td>1-7/4-10/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-8-32-35<br />
</td>
        <td>1-11/9-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-15-32-35<br />
</td>
        <td>1-4/3-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-27-32-35<br />
</td>
        <td>1-14/11-10/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-30-32-35<br />
</td>
        <td>1-16/9-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Pentads"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pentads</h1>


<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-5-7-22<br />
</td>
        <td>1-5/4-7/4-12/11-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-15-17-20-22<br />
</td>
        <td>1-4/3-5/3-7/6-16/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-2-7-22-24<br />
</td>
        <td>1-5/4-12/11-16/11-20/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-2-17-22-24<br />
</td>
        <td>1-5/4-5/3-16/11-20/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-3-5-20-27<br />
</td>
        <td>1-7/5-7/4-7/6-14/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-5-7-22-27<br />
</td>
        <td>1-7/4-12/11-16/11-14/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-5-20-22-27<br />
</td>
        <td>1-7/4-7/6-16/11-14/11<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-7-22-24-27<br />
</td>
        <td>1-12/11-16/11-20/11-14/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-2-17-24-32<br />
</td>
        <td>1-5/4-5/3-20/11-10/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-8-15-30-32<br />
</td>
        <td>1-11/9-4/3-16/9-10/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-3-5-8-35<br />
</td>
        <td>1-7/5-7/4-11/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-3-5-20-35<br />
</td>
        <td>1-7/5-7/4-7/6-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-3-5-27-35<br />
</td>
        <td>1-7/5-7/4-14/11-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-3-20-27-35<br />
</td>
        <td>1-7/5-7/6-14/11-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-5-20-27-35<br />
</td>
        <td>1-7/4-7/6-14/11-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-3-8-30-35<br />
</td>
        <td>1-7/5-11/9-16/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-8-15-30-35<br />
</td>
        <td>1-11/9-4/3-16/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-3-27-30-35<br />
</td>
        <td>1-7/5-14/11-16/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-5-8-32-35<br />
</td>
        <td>1-7/4-11/9-10/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-8-15-32-35<br />
</td>
        <td>1-11/9-4/3-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-5-27-32-35<br />
</td>
        <td>1-7/4-14/11-10/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-8-30-32-35<br />
</td>
        <td>1-11/9-16/9-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-15-30-32-35<br />
</td>
        <td>1-4/3-16/9-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-27-30-32-35<br />
</td>
        <td>1-14/11-16/9-10/9-14/9<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Hexads"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hexads</h1>


<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-3-5-20-27-35<br />
</td>
        <td>1-7/5-7/4-7/6-14/11-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-8-15-30-32-35<br />
</td>
        <td>1-11/9-4/3-16/9-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
</table>

</body></html>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-20 19:41:15 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-20 23:04:35 UTC</tt>.<br>
-: The original revision id was <tt>287805802</tt>.<br>
+: The original revision id was <tt>287833246</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Gamelismic clan#Hemithirds|hemithirds temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic.
 =Triads=
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 </pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Chords of hemithirds&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Chords of hemithirds&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed the &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;dyadic chords&lt;/a&gt; of 11-limit &lt;a class="wiki_link" href="/Gamelismic%20clan#Hemithirds"&gt;hemithirds temperament&lt;/a&gt;. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Triads&lt;/h1&gt;

Luna and hemithirds/Chords: Difference between revisions

Revision as of 23:04, 20 December 2011

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