Porcupine/Chords
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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:<h1> --><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:<h1> --><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:<h1> --><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:<h1> --><h1 id="toc3"><a name="Hexads"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hexads</h1>
</body></html>