Huntmic chords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''Huntmic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the huntma, [[640/637]].
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>2011-08-01 16:38:57 UTC</tt>.<br>
: The original revision id was <tt>243776417</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">//Huntmic chords// are certain 13-limit [[Dyadic chord|essentially tempered chords]] which close at the octave by tempering out the huntma, 640/637. These include triads with steps of size (huntmic tempered) 5/4-16/13-8/7-8/7, 16/13-5/4-8/7-8/7 and 5/4-8/7-16/13-8/7, leading to the huntmic temperings of 5/4-20/13-7/4-2, 16/13-20/13-7/4-2 and 5/4-10/7-7/4-2. Note that the last chord can also be tempered by 441/440 to the [[werckismic chords|werckismic tetrad]]. Aside from tetrads, there are huntmic triads, the huntmic tempered versions of 1-16/13-7/5 and 1-8/7-7/5.


The name huntmic comes from the fact that the [[optimal patent val]] for huntmic temperament is [[205edo]], the basis of the Hunt System of [[Aaron Andrew Hunt]]. Other equal temperaments with huntmic chords include 22, 53, 68, 80, 94, 111, 121, 137 and 215.</pre></div>
There are three triads, six tetrads and two pentads as 2.5.7.13 [[subgroup]] [[13-odd-limit]] essentially tempered chords.
<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;huntmic chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;Huntmic chords&lt;/em&gt; are certain 13-limit &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;essentially tempered chords&lt;/a&gt; which close at the octave by tempering out the huntma, 640/637. These include triads with steps of size (huntmic tempered) 5/4-16/13-8/7-8/7, 16/13-5/4-8/7-8/7 and 5/4-8/7-16/13-8/7, leading to the huntmic temperings of 5/4-20/13-7/4-2, 16/13-20/13-7/4-2 and 5/4-10/7-7/4-2. Note that the last chord can also be tempered by 441/440 to the &lt;a class="wiki_link" href="/werckismic%20chords"&gt;werckismic tetrad&lt;/a&gt;. Aside from tetrads, there are huntmic triads, the huntmic tempered versions of 1-16/13-7/5 and 1-8/7-7/5.&lt;br /&gt;
For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is
&lt;br /&gt;
* 1-8/7-13/10 chord with steps of 8/7-8/7-20/13.
The name huntmic comes from the fact that the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for huntmic temperament is &lt;a class="wiki_link" href="/205edo"&gt;205edo&lt;/a&gt;, the basis of the Hunt System of &lt;a class="wiki_link" href="/Aaron%20Andrew%20Hunt"&gt;Aaron Andrew Hunt&lt;/a&gt;. Other equal temperaments with huntmic chords include 22, 53, 68, 80, 94, 111, 121, 137 and 215.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
The inversely related pair of chords is
* 1-16/13-7/5 with steps of 16/13-8/7-10/7, and its inverse
* 1-8/7-7/5 with steps of 8/7-16/13-10/7.
 
For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
* 1-16/13-7/5-7/4 chord with steps of 16/13-8/7-5/4-8/7;
* 1-8/7-16/13-7/5 chord with steps of 8/7-14/13-8/7-10/7.
 
The inversely related pairs of chords are
* 1-5/4-10/7-13/8 with steps of 5/4-8/7-8/7-16/13, and its inverse
* 1-8/7-13/10-13/8 with steps of 8/7-8/7-5/4-16/13;
* 1-8/7-13/10-13/7 with steps of 8/7-8/7-10/7-14/13, and its inverse
* 1-8/7-13/10-7/5 with steps of 8/7-8/7-14/13-10/7.
 
They can be extended to pentads:
* 1-8/7-10/7-13/8-7/4 with steps of 8/7-5/4-8/7-14/13-8/7, and its inverse
* 1-8/7-16/13-7/5-7/4 with steps of 8/7-14/13-8/7-5/4-8/7.
 
Equal temperaments with huntmic chords include {{Optimal ET sequence| 22, 53, 68, 80, 94, 111, 121, 137, 205 and 215 }}. The name huntmic comes from the fact that the [[optimal patent val]] for huntmic temperament is [[205edo]], the basis of the [[Hunt System]] of [[Aaron Andrew Hunt]].
 
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Huntmic]]