Hecate hexad: 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>2011-10-28 01:08:48 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-28 01:28:39 UTC</tt>.<br>

: The original revision id was <tt>~~269470162~~</tt>.<br>

: The original revision id was <tt>269472232</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 hecate hexad is a [[Dyadic chord|essentially tempered chord]] is the 1-9/8-5/4-7/5-14/9-7/4 chord, tempered in the [[Marvel family#Hecate|hecate]] ({225/224, 385/384, 325/324}) temperament, which makes the steps of the scale 9/8-10/9-9/8-10/9-9/8-8/7. Another way of viewing the hecate hexad is that it is the hecate tempering of the Euler genus consisting of ~~the~~ divisors of 75, ~~reeduced~~ to an octave. ~~From~~ this ~~it is easy~~ to ~~see that three hecate hexads, stacked on a chain of fifths, make up~~ the marveldene--the ~~marvel~~-tempered duodene.</pre></div>

<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 hecate hexad is a [[Dyadic chord|essentially tempered chord]] is the 1-9/8-5/4-7/5-14/9-7/4 chord, tempered in the [[Marvel family#Hecate|hecate]] ({225/224, 385/384, 325/324}) temperament, which makes the steps of the scale 9/8-10/9-9/8-10/9-9/8-8/7. Another way of viewing the hecate hexad is that it is the hecate tempering of

two [[marvel triads]] separated by an interval of 9/8. This can be filled in with a third augmented triad at the fifth, leading to the hecate tempering of the nine-note Euler genus consisting of divisors of 225, reduced to an octave. Extending this to the marveldene, the hecate-tempered Ellis duodene which is the hecate tempering of the divisors of 675 reduced to an octave.

</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>hecate hexad</title></head><body>The hecate hexad is a <a class="wiki_link" href="/Dyadic%20chord">essentially tempered chord</a> is the 1-9/8-5/4-7/5-14/9-7/4 chord, tempered in the <a class="wiki_link" href="/Marvel%20family#Hecate">hecate</a> ({225/224, 385/384, 325/324}) temperament, which makes the steps of the scale 9/8-10/9-9/8-10/9-9/8-8/7. Another way of viewing the hecate hexad is that it is the hecate tempering of the Euler genus consisting of ~~the~~ divisors of 75, ~~reeduced~~ to an octave. ~~From~~ this ~~it is easy~~ to ~~see that three hecate hexads, stacked on a chain of fifths, make up~~ the marveldene--the ~~marvel~~-tempered duodene.</body></html></pre></div>

<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>hecate hexad</title></head><body>The hecate hexad is a <a class="wiki_link" href="/Dyadic%20chord">essentially tempered chord</a> is the 1-9/8-5/4-7/5-14/9-7/4 chord, tempered in the <a class="wiki_link" href="/Marvel%20family#Hecate">hecate</a> ({225/224, 385/384, 325/324}) temperament, which makes the steps of the scale 9/8-10/9-9/8-10/9-9/8-8/7. Another way of viewing the hecate hexad is that it is the hecate tempering of<br />

two <a class="wiki_link" href="/marvel%20triads">marvel triads</a> separated by an interval of 9/8. This can be filled in with a third augmented triad at the fifth, leading to the hecate tempering of the nine-note Euler genus consisting of divisors of 225, reduced to an octave. Extending this to the marveldene, the hecate-tempered Ellis duodene which is the hecate tempering of the divisors of 675 reduced to an octave.</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>2011-10-28 01:08:48 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-28 01:28:39 UTC</tt>.<br>
-: The original revision id was <tt>269470162</tt>.<br>
+: The original revision id was <tt>269472232</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 hecate hexad is a [[Dyadic chord|essentially tempered chord]] is the 1-9/8-5/4-7/5-14/9-7/4 chord, tempered in the [[Marvel family#Hecate|hecate]] ({225/224, 385/384, 325/324}) temperament, which makes the steps of the scale 9/8-10/9-9/8-10/9-9/8-8/7. Another way of viewing the hecate hexad is that it is the hecate tempering of the Euler genus consisting of the divisors of 75, reeduced to an octave. From this it is easy to see that three hecate hexads, stacked on a chain of fifths, make up the marveldene--the marvel-tempered duodene.</pre></div>
+<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 hecate hexad is a [[Dyadic chord|essentially tempered chord]] is the 1-9/8-5/4-7/5-14/9-7/4 chord, tempered in the [[Marvel family#Hecate|hecate]] ({225/224, 385/384, 325/324}) temperament, which makes the steps of the scale 9/8-10/9-9/8-10/9-9/8-8/7. Another way of viewing the hecate hexad is that it is the hecate tempering of
+two [[marvel triads]] separated by an interval of 9/8. This can be filled in with a third augmented triad at the fifth, leading to the hecate tempering of the nine-note Euler genus consisting of divisors of 225, reduced to an octave. Extending this to the marveldene, the hecate-tempered Ellis duodene which is the hecate tempering of the divisors of 675 reduced to an octave.
+</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;hecate hexad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The hecate hexad is a &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;essentially tempered chord&lt;/a&gt; is the 1-9/8-5/4-7/5-14/9-7/4 chord, tempered in the &lt;a class="wiki_link" href="/Marvel%20family#Hecate"&gt;hecate&lt;/a&gt; ({225/224, 385/384, 325/324}) temperament, which makes the steps of the scale 9/8-10/9-9/8-10/9-9/8-8/7. Another way of viewing the hecate hexad is that it is the hecate tempering of the Euler genus consisting of the divisors of 75, reeduced to an octave. From this it is easy to see that three hecate hexads, stacked on a chain of fifths, make up the marveldene--the marvel-tempered duodene.&lt;/body&gt;&lt;/html&gt;</pre></div>
+<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;hecate hexad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The hecate hexad is a &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;essentially tempered chord&lt;/a&gt; is the 1-9/8-5/4-7/5-14/9-7/4 chord, tempered in the &lt;a class="wiki_link" href="/Marvel%20family#Hecate"&gt;hecate&lt;/a&gt; ({225/224, 385/384, 325/324}) temperament, which makes the steps of the scale 9/8-10/9-9/8-10/9-9/8-8/7. Another way of viewing the hecate hexad is that it is the hecate tempering of&lt;br /&gt;
+two &lt;a class="wiki_link" href="/marvel%20triads"&gt;marvel triads&lt;/a&gt; separated by an interval of 9/8. This can be filled in with a third augmented triad at the fifth, leading to the hecate tempering of the nine-note Euler genus consisting of divisors of 225, reduced to an octave. Extending this to the marveldene, the hecate-tempered Ellis duodene which is the hecate tempering of the divisors of 675 reduced to an octave.&lt;/body&gt;&lt;/html&gt;</pre></div>