Porcupine/Chords: Difference between revisions

: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-28 17:06:28 UTC</tt>.<br>

: The original revision id was <tt>355203380</tt>.<br>

<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 [[Porcupine|porcupine temperament]] 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 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.

||  || 0-2-4 || 1-6/5-16/11 || otonal ||

||  || 0-1-5 || 1-11/10-8/5 || otonal ||

||  || 0-2-5 || 1-6/5-8/5 || otonal ||

||  || 0-4-5 || 1-16/11-8/5 || utonal ||

||  || 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 ||

||  || 0-2-4-6 || 1-6/5-11/6-7/4 ||   ||

<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 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;

         &lt;td&gt;1-6/5-16/11&lt;br /&gt;

        &lt;td&gt;1-11/10-8/5&lt;br /&gt;

        &lt;td&gt;1-6/5-8/5&lt;br /&gt;

        &lt;td&gt;0-3-5&lt;br /&gt;

         &lt;td&gt;1-4/3-8/5&lt;br /&gt;

        &lt;td&gt;utonal&lt;br /&gt;

         &lt;td&gt;1-10/9-16/9&lt;br /&gt;

         &lt;td&gt;otonal&lt;br /&gt;

         &lt;td&gt;1-4/3-16/9&lt;br /&gt;

         &lt;td&gt;ambitonal&lt;br /&gt;

         &lt;td&gt;1-16/11-16/9&lt;br /&gt;

         &lt;td&gt;utonal&lt;br /&gt;

         &lt;td&gt;&lt;br /&gt;