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>2013-01-31 15:53:00 UTC</tt>.<br>
: The original revision id was <tt>403175216</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 tetrads 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 1-5/4-20/13-7/4, 1-16/13-20/13-7/4 and 1-5/4-10/7-7/4. 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, 205 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 tetrads 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 1-5/4-20/13-7/4, 1-16/13-20/13-7/4 and 1-5/4-10/7-7/4. 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, 205 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]]

Latest revision as of 00:47, 3 November 2023

Huntmic chords are essentially tempered chords tempered by the huntma, 640/637.

There are three triads, six tetrads and two pentads as 2.5.7.13 subgroup 13-odd-limit essentially tempered chords.

For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is

  • 1-8/7-13/10 chord with steps of 8/7-8/7-20/13.

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 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.

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