Porcupine/Chords: Difference between revisions

Revision as of 18:14, 28 July 2012

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This revision was by author phylingual and made on 2012-07-28 18:14:58 UTC.

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Original Wikitext content:

Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Porcupine|porcupine temperament]] that do not have generator steps 7 or 13 as dyads. <span style="background-color: #ffffff;">Typing the chords requires consideration of the fact that porcupine conflates 10/9, 11/10 and 12/11 and also 16/9 and 7/4. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal.</span> If a chord is essentially tempered, the chord is analyzed in terms of the transversals 11/10, 6/5, 16/11 and 7/4. Chords that require only 64/63 tempering are marked archytas, by 100/99 ptolemismic, by 121/120 biyatismic, 176/175 valinorsmic, and by 385/384 keenanismic. Chords that require 64/63 and 176/175 tempering are marked ares, and 176/175 and 385/384 tempered chords are marked zeus. Chords that receive tempering by three independent commas above are labeled porcupine.


=Triads= 
|| Chord || Transversal || Type ||
|| 0-1-2 || 1-11/10-6/5 || otonal ||
|| 0-1-3 || 1-10/9-4/3 || otonal ||
|| 0-2-3 || 1-11/9-4/3 || otonal ||
|| 0-1-4 || 1-12/11-16/11 || otonal ||
|| 0-2-4 || 1-6/5-16/11 || otonal ||
|| 0-3-4 || 1-4/3-16/11 || utonal ||
|| 0-1-5 || 1-11/10-8/5 || otonal ||
|| 0-2-5 || 1-6/5-8/5 || otonal ||
|| 0-3-5 || 1-4/3-8/5 || utonal ||
|| 0-4-5 || 1-16/11-8/5 || utonal ||
|| 0-1-6 || 1-11/10-7/4 || valinorsmic ||
|| 0-2-6 || 1-10/9-16/9 || otonal ||
|| 0-3-6 || 1-4/3-16/9 || ambitonal ||
|| 0-4-6 || 1-16/11-16/9 || utonal ||
|| 0-5-6 || 1-8/5-7/4 || valinorsmic ||
|| 0-2-8 || 1-6/5-16/15 || ambitonal ||
|| 0-3-8 || 1-4/3-16/15 || ambitonal ||
|| 0-4-8 || 1-22/15-16/15 || otonal ||
|| 0-5-8 || 1-8/5-16/15 || ambitonal ||
|| 0-6-8 || 1-16/9-16/15 || ambitonal ||
|| 0-1-9 || 1-11/10-7/6 || valinorsmic ||
|| 0-3-9 || 1-4/3-7/6 || otonal ||
|| 0-4-9 || 1-16/11-7/6 || keenanismic ||
|| 0-5-9 || 1-8/5-7/6 || keenanismic ||
|| 0-6-9 || 1-7/4-7/6 || utonal ||
|| 0-8-9 || 1-16/15-7/6 || valinorsmic ||
|| 0-1-10 || 1-12/11-14/11 || otonal ||
|| 0-2-10 || 1-6/5-14/11 || valinorsmic ||
|| 0-4-10 || 1-16/11-14/11 || otonal ||
|| 0-5-10 || 1-8/5-14/11 || valinorsmic ||
|| 0-6-10 || 1-7/4-14/11 || utonal ||
|| 0-8-10 || 1-16/15-14/11 || valinorsmic ||
|| 0-9-10 || 1-7/6-14/11 || utonal ||
|| 0-1-11 || 1-11/10-7/5 || otonal ||
|| 0-2-11 || 1-6/5-7/5 || otonal ||
|| 0-3-11 || 1-4/3-7/5 || archytas ||
|| 0-5-11 || 1-8/5-7/5 || otonal ||
|| 0-6-11 || 1-7/4-7/5 || utonal ||
|| 0-8-11 || 1-16/15-7/5 || archytas ||
|| 0-9-11 || 1-7/6-7/5 || utonal ||
|| 0-10-11 || 1-14/11-7/5 || utonal ||
|| 0-1-12 || 1-10/9-14/9 || otonal ||
|| 0-2-12 || 1-11/9-14/9 || otonal ||
|| 0-3-12 || 1-4/3-14/9 || otonal ||
|| 0-4-12 || 1-16/11-14/9 || keenanismic ||
|| 0-6-12 || 1-16/9-14/9 || otonal ||
|| 0-8-12 || 1-16/15-14/9 || keenanismic ||
|| 0-9-12 || 1-7/6-14/9 || utonal ||
|| 0-10-12 || 1-14/11-14/9 || utonal ||
|| 0-11-12 || 1-7/5-14/9 || utonal ||
|| 0-2-14 || 1-6/5-28/15 || otonal ||
|| 0-3-14 || 1-4/3-28/15 || otonal ||
|| 0-4-14 || 1-22/15-28/15 || otonal ||
|| 0-5-14 || 1-8/5-28/15 || otonal ||
|| 0-6-14 || 1-7/4-28/15 || utonal ||
|| 0-8-14 || 1-16/15-28/15 || otonal ||
|| 0-9-14 || 1-7/6-28/15 || utonal ||
|| 0-10-14 || 1-14/11-28/15 || utonal ||
|| 0-11-14 || 1-7/5-28/15 || utonal ||
|| 0-12-14 || 1-14/9-28/15 || utonal ||

=Tetrads= 
|| Chord || Transversal || Type ||
|| 0-1-2-3 || 1-10/9-11/9-4/3 || otonal ||
|| 0-1-2-4 || 1-11/10-11/9-22/15 || utonal ||
|| 0-1-3-4 || 1-10/9-4/3-22/15 || otonal ||
|| 0-1-2-5 || 1-11/10-6/5-8/5 || otonal ||
|| 0-1-3-5 || 1-11/10-4/3-8/5 || ptolemismic ||
|| 0-1-4-5 || 1-11/10-16/11-8/5 || biyatismic ||
|| 0-2-3-5 || 1-6/5-4/3-8/5 || ambitonal ||

=Pentads= 
|| Chord || Transversal || Type ||
||   ||   ||   ||
|| 0-1-2-3-6 || 1-10/9-11/9-4/3-16/9 || otonal ||
|| 0-2-3-4-6 ||   ||   ||
|| 0-3-4-5-6 ||   ||   ||
|| 0-2-4-6-8 ||   ||   ||

=Hexads=

Original HTML content:

<html><head><title>Chords of porcupine</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="/Porcupine">porcupine temperament</a> that do not have generator steps 7 or 13 as dyads. <span style="background-color: #ffffff;">Typing the chords requires consideration of the fact that porcupine conflates 10/9, 11/10 and 12/11 and also 16/9 and 7/4. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal.</span> If a chord is essentially tempered, the chord is analyzed in terms of the transversals 11/10, 6/5, 16/11 and 7/4. Chords that require only 64/63 tempering are marked archytas, by 100/99 ptolemismic, by 121/120 biyatismic, 176/175 valinorsmic, and by 385/384 keenanismic. Chords that require 64/63 and 176/175 tempering are marked ares, and 176/175 and 385/384 tempered chords are marked zeus. Chords that receive tempering by three independent commas above are labeled porcupine.<br />
<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>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td>0-1-2<br />
</td>
        <td>1-11/10-6/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-3<br />
</td>
        <td>1-10/9-4/3<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-2-3<br />
</td>
        <td>1-11/9-4/3<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-4<br />
</td>
        <td>1-12/11-16/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-2-4<br />
</td>
        <td>1-6/5-16/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-3-4<br />
</td>
        <td>1-4/3-16/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-5<br />
</td>
        <td>1-11/10-8/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-2-5<br />
</td>
        <td>1-6/5-8/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-3-5<br />
</td>
        <td>1-4/3-8/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-4-5<br />
</td>
        <td>1-16/11-8/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-6<br />
</td>
        <td>1-11/10-7/4<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>0-2-6<br />
</td>
        <td>1-10/9-16/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-3-6<br />
</td>
        <td>1-4/3-16/9<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>0-4-6<br />
</td>
        <td>1-16/11-16/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-5-6<br />
</td>
        <td>1-8/5-7/4<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>0-2-8<br />
</td>
        <td>1-6/5-16/15<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>0-3-8<br />
</td>
        <td>1-4/3-16/15<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>0-4-8<br />
</td>
        <td>1-22/15-16/15<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-5-8<br />
</td>
        <td>1-8/5-16/15<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>0-6-8<br />
</td>
        <td>1-16/9-16/15<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-9<br />
</td>
        <td>1-11/10-7/6<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>0-3-9<br />
</td>
        <td>1-4/3-7/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-4-9<br />
</td>
        <td>1-16/11-7/6<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>0-5-9<br />
</td>
        <td>1-8/5-7/6<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>0-6-9<br />
</td>
        <td>1-7/4-7/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-8-9<br />
</td>
        <td>1-16/15-7/6<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>0-1-10<br />
</td>
        <td>1-12/11-14/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-2-10<br />
</td>
        <td>1-6/5-14/11<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>0-4-10<br />
</td>
        <td>1-16/11-14/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-5-10<br />
</td>
        <td>1-8/5-14/11<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>0-6-10<br />
</td>
        <td>1-7/4-14/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-8-10<br />
</td>
        <td>1-16/15-14/11<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>0-9-10<br />
</td>
        <td>1-7/6-14/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-11<br />
</td>
        <td>1-11/10-7/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-2-11<br />
</td>
        <td>1-6/5-7/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-3-11<br />
</td>
        <td>1-4/3-7/5<br />
</td>
        <td>archytas<br />
</td>
    </tr>
    <tr>
        <td>0-5-11<br />
</td>
        <td>1-8/5-7/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-6-11<br />
</td>
        <td>1-7/4-7/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-8-11<br />
</td>
        <td>1-16/15-7/5<br />
</td>
        <td>archytas<br />
</td>
    </tr>
    <tr>
        <td>0-9-11<br />
</td>
        <td>1-7/6-7/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-10-11<br />
</td>
        <td>1-14/11-7/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-12<br />
</td>
        <td>1-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-2-12<br />
</td>
        <td>1-11/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-3-12<br />
</td>
        <td>1-4/3-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-4-12<br />
</td>
        <td>1-16/11-14/9<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>0-6-12<br />
</td>
        <td>1-16/9-14/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-8-12<br />
</td>
        <td>1-16/15-14/9<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>0-9-12<br />
</td>
        <td>1-7/6-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-10-12<br />
</td>
        <td>1-14/11-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-11-12<br />
</td>
        <td>1-7/5-14/9<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-2-14<br />
</td>
        <td>1-6/5-28/15<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-3-14<br />
</td>
        <td>1-4/3-28/15<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-4-14<br />
</td>
        <td>1-22/15-28/15<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-5-14<br />
</td>
        <td>1-8/5-28/15<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-6-14<br />
</td>
        <td>1-7/4-28/15<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-8-14<br />
</td>
        <td>1-16/15-28/15<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-9-14<br />
</td>
        <td>1-7/6-28/15<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-10-14<br />
</td>
        <td>1-14/11-28/15<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-11-14<br />
</td>
        <td>1-7/5-28/15<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-12-14<br />
</td>
        <td>1-14/9-28/15<br />
</td>
        <td>utonal<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>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td>0-1-2-3<br />
</td>
        <td>1-10/9-11/9-4/3<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-2-4<br />
</td>
        <td>1-11/10-11/9-22/15<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-3-4<br />
</td>
        <td>1-10/9-4/3-22/15<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-2-5<br />
</td>
        <td>1-11/10-6/5-8/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-1-3-5<br />
</td>
        <td>1-11/10-4/3-8/5<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>0-1-4-5<br />
</td>
        <td>1-11/10-16/11-8/5<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>0-2-3-5<br />
</td>
        <td>1-6/5-4/3-8/5<br />
</td>
        <td>ambitonal<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>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>0-1-2-3-6<br />
</td>
        <td>1-10/9-11/9-4/3-16/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>0-2-3-4-6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>0-3-4-5-6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>0-2-4-6-8<br />
</td>
        <td><br />
</td>
        <td><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>
</body></html>

@@ Line 1: / Line 1: @@
 <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:phylingual|phylingual]] and made on <tt>2012-07-28 18:09:55 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-28 18:14:58 UTC</tt>.<br>
-: The original revision id was <tt>355208100</tt>.<br>
+: The original revision id was <tt>355208480</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>
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 || 0-2-4-6-8 ||   ||   ||
-=Hexads=
+=Hexads= </pre></div>
-|| Chord || Transversal || Type ||
-|| 0-1-2-5-11 ||   ||   ||</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 porcupine&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="/Porcupine"&gt;porcupine temperament&lt;/a&gt; that do not have generator steps 7 or 13 as dyads. &lt;span style="background-color: #ffffff;"&gt;Typing the chords requires consideration of the fact that porcupine conflates 10/9, 11/10 and 12/11 and also 16/9 and 7/4. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal.&lt;/span&gt; If a chord is essentially tempered, the chord is analyzed in terms of the transversals 11/10, 6/5, 16/11 and 7/4. Chords that require only 64/63 tempering are marked archytas, by 100/99 ptolemismic, by 121/120 biyatismic, 176/175 valinorsmic, and by 385/384 keenanismic. Chords that require 64/63 and 176/175 tempering are marked ares, and 176/175 and 385/384 tempered chords are marked zeus. Chords that receive tempering by three independent commas above are labeled porcupine.&lt;br /&gt;
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 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Hexads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Hexads&lt;/h1&gt;
-&lt;table class="wiki_table"&gt;
-    &lt;tr&gt;
-        &lt;td&gt;Chord&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Transversal&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Type&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;0-1-2-5-11&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-&lt;/table&gt;
 &lt;/body&gt;&lt;/html&gt;</pre></div>

Porcupine/Chords: Difference between revisions

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