Neutral tetrad: Difference between revisions

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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>2011-09-~~21 11~~:51:16 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-13 14:50:43 UTC</tt>.<br>

: The original revision id was <tt>~~256601840~~</tt>.<br>

: The original revision id was <tt>285605592</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">~~The~~ //neutral tetrad//, or rastmic ~~tetrad, is an 11-limit~~ [[Dyadic chord#Essentially%20tempered%20dyadic%20chords|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

<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">A //neutral tetrad// is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords|rastmic]] [[Dyadic chord#Essentially%20tempered%20dyadic%20chords|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.

The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3_2|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.</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"><html><head><title>neutral tetrad</title></head><body>~~The~~ <em>neutral tetrad</em>, or rastmic ~~tetrad, is an 11-limit~~ <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it. <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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>neutral tetrad</title></head><body>A <em>neutral tetrad</em> is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the <a class="wiki_link" href="/rastmic%20chords">rastmic</a> <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it.<br />

<br />

A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49. <br />

<br />

The neutral tetrad is also available in <a class="wiki_link" href="/nonoctave">nonoctave</a> tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>). Nonoctave scales, naturally, cannot &quot;close at the octave,&quot; unless there is a tempered octave available.</body></html></pre></div>

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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>2011-09-21 11:51:16 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-13 14:50:43 UTC</tt>.<br>
-: The original revision id was <tt>256601840</tt>.<br>
+: The original revision id was <tt>285605592</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">The //neutral tetrad//, or rastmic tetrad, is an 11-limit [[Dyadic chord#Essentially%20tempered%20dyadic%20chords|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.
+<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">A //neutral tetrad// is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords|rastmic]] [[Dyadic chord#Essentially%20tempered%20dyadic%20chords|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.
+A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.
 The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3_2|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.</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;neutral tetrad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;neutral tetrad&lt;/em&gt;, or rastmic tetrad, is an 11-limit &lt;a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords"&gt;essentially tempered dyadic chord&lt;/a&gt; consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, which does an excellent version of it. &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;neutral tetrad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;neutral tetrad&lt;/em&gt; is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the &lt;a class="wiki_link" href="/rastmic%20chords"&gt;rastmic&lt;/a&gt; &lt;a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords"&gt;essentially tempered dyadic chord&lt;/a&gt; consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, which does an excellent version of it.&lt;br /&gt;
+&lt;br /&gt;
+A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49. &lt;br /&gt;
 &lt;br /&gt;
 The neutral tetrad is also available in &lt;a class="wiki_link" href="/nonoctave"&gt;nonoctave&lt;/a&gt; tunings which divide the &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; in half, including &lt;a class="wiki_link" href="/4edf"&gt;4edf&lt;/a&gt;, &lt;a class="wiki_link" href="/6edf"&gt;6edf&lt;/a&gt; (nonoctave miracle), 8edf or &lt;a class="wiki_link" href="/88cET"&gt;88cET&lt;/a&gt;, &lt;a class="wiki_link" href="/16edf"&gt;16edf&lt;/a&gt;, and 20edf (&lt;a class="wiki_link" href="/Carlos%20Gamma"&gt;Carlos Gamma&lt;/a&gt;). Nonoctave scales, naturally, cannot &amp;quot;close at the octave,&amp;quot; unless there is a tempered octave available.&lt;/body&gt;&lt;/html&gt;</pre></div>