Dyadic chord: Difference between revisions
Wikispaces>mbattaglia1 **Imported revision 255293206 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 255434612 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-18 22:09:59 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>255434612</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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">[[toc|flat]] | <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">[[toc|flat]] | ||
=Definitions= | =Definitions= | ||
By a //dyadic chord// is meant a chord each of whose intervals belongs to a specified set of intervals considered to be consonant; it is therefore relative to the set of intervals in question. By a //just// dyadic chord is meant a chord in rational intonation which is dyadic, so that each of its notes in relation to the lowest note is a rational number belonging to the set of consonances, and moreover each interval between the notes belongs to the set of consonances. By an //essentially just// dyadic chord is meant a chord which is considered to be an approximation of a just dyadic chord, such that each of its intervals is considered to be an approximation of the corresponding interval in the just dyadic chord. So, for instance, 1-5/4-3/2 is a just dyadic chord when the consonance set is the 5-limit diamond with octave equivalence, and 0-10-18 in 31edo with consonance set {8, 10, 13, 18, 21, 23, 31} modulo 31 is an essentially just dyadic chord approximating 1-5/4-3/2. | By a //dyadic chord// is meant a chord each of whose intervals belongs to a specified set of intervals considered to be consonant; it is therefore relative to the set of intervals in question. By a //just// dyadic chord is meant a chord in rational intonation which is dyadic, so that each of its notes in relation to the lowest note is a rational number belonging to the set of consonances, and moreover each interval between the notes belongs to the set of consonances. By an //essentially just// dyadic chord is meant a chord which is considered to be an approximation of a just dyadic chord, such that each of its intervals is considered to be an approximation of the corresponding interval in the just dyadic chord. So, for instance, 1-5/4-3/2 is a just dyadic chord when the consonance set is the 5-limit diamond with octave equivalence, and 0-10-18 in 31edo with consonance set {8, 10, 13, 18, 21, 23, 31} modulo 31 is an essentially just dyadic chord approximating 1-5/4-3/2. | ||
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[[battaglia chord]] | [[battaglia chord]] | ||
=19-limit= | ==19-limit== | ||
[[hendrix chord]] | [[hendrix chord]] | ||
[[rootminor triad]] | [[rootminor triad]] | ||
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[[gamelismic pentad]]</pre></div> | [[gamelismic pentad]]</pre></div> | ||
<h4>Original HTML content:</h4> | <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"><html><head><title>Dyadic chord</title></head><body><!-- ws:start:WikiTextTocRule:22:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><a href="#Definitions">Definitions</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Anomalous Saturated Suspensions">Anomalous Saturated Suspensions</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Just intonation tetrads">Just intonation tetrads</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Essentially tempered dyadic chords">Essentially tempered dyadic chords</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: -- | <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"><html><head><title>Dyadic chord</title></head><body><!-- ws:start:WikiTextTocRule:22:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><a href="#Definitions">Definitions</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Anomalous Saturated Suspensions">Anomalous Saturated Suspensions</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Just intonation tetrads">Just intonation tetrads</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Essentially tempered dyadic chords">Essentially tempered dyadic chords</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | ||
<!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Definitions"></a><!-- ws:end:WikiTextHeadingRule:0 -->Definitions</h1> | <!-- ws:end:WikiTextTocRule:34 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Definitions"></a><!-- ws:end:WikiTextHeadingRule:0 -->Definitions</h1> | |||
By a <em>dyadic chord</em> is meant a chord each of whose intervals belongs to a specified set of intervals considered to be consonant; it is therefore relative to the set of intervals in question. By a <em>just</em> dyadic chord is meant a chord in rational intonation which is dyadic, so that each of its notes in relation to the lowest note is a rational number belonging to the set of consonances, and moreover each interval between the notes belongs to the set of consonances. By an <em>essentially just</em> dyadic chord is meant a chord which is considered to be an approximation of a just dyadic chord, such that each of its intervals is considered to be an approximation of the corresponding interval in the just dyadic chord. So, for instance, 1-5/4-3/2 is a just dyadic chord when the consonance set is the 5-limit diamond with octave equivalence, and 0-10-18 in 31edo with consonance set {8, 10, 13, 18, 21, 23, 31} modulo 31 is an essentially just dyadic chord approximating 1-5/4-3/2.<br /> | By a <em>dyadic chord</em> is meant a chord each of whose intervals belongs to a specified set of intervals considered to be consonant; it is therefore relative to the set of intervals in question. By a <em>just</em> dyadic chord is meant a chord in rational intonation which is dyadic, so that each of its notes in relation to the lowest note is a rational number belonging to the set of consonances, and moreover each interval between the notes belongs to the set of consonances. By an <em>essentially just</em> dyadic chord is meant a chord which is considered to be an approximation of a just dyadic chord, such that each of its intervals is considered to be an approximation of the corresponding interval in the just dyadic chord. So, for instance, 1-5/4-3/2 is a just dyadic chord when the consonance set is the 5-limit diamond with octave equivalence, and 0-10-18 in 31edo with consonance set {8, 10, 13, 18, 21, 23, 31} modulo 31 is an essentially just dyadic chord approximating 1-5/4-3/2.<br /> | ||
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<a class="wiki_link" href="/battaglia%20chord">battaglia chord</a><br /> | <a class="wiki_link" href="/battaglia%20chord">battaglia chord</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:18:&lt; | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Essentially tempered dyadic chords-19-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->19-limit</h2> | ||
<a class="wiki_link" href="/hendrix%20chord">hendrix chord</a><br /> | <a class="wiki_link" href="/hendrix%20chord">hendrix chord</a><br /> | ||
<a class="wiki_link" href="/rootminor%20triad">rootminor triad</a><br /> | <a class="wiki_link" href="/rootminor%20triad">rootminor triad</a><br /> | ||
<a class="wiki_link" href="/rootsubminor%20triad">rootsubminor triad</a><br /> | <a class="wiki_link" href="/rootsubminor%20triad">rootsubminor triad</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name=" | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Essentially tempered dyadic chords-21-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->21-limit</h2> | ||
<a class="wiki_link" href="/gamelismic%20pentad">gamelismic pentad</a></body></html></pre></div> | <a class="wiki_link" href="/gamelismic%20pentad">gamelismic pentad</a></body></html></pre></div> | ||