Keemic chords: Difference between revisions

Wikispaces>keenanpepper
**Imported revision 268608548 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 268628298 - Original comment: **
Line 1: Line 1:
<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:keenanpepper|keenanpepper]] and made on <tt>2011-10-25 22:28:33 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-25 23:58:20 UTC</tt>.<br>
: The original revision id was <tt>268608548</tt>.<br>
: The original revision id was <tt>268628298</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>
Line 10: Line 10:
In an optimized tuning for the 4&amp;7&amp;15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val ([[104edo]].) Hence [[magic]] (19&amp;22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a Graham complexity of 12, so it doesn't appear that often.
In an optimized tuning for the 4&amp;7&amp;15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val ([[104edo]].) Hence [[magic]] (19&amp;22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a Graham complexity of 12, so it doesn't appear that often.


Other temperaments that feature this chord prominently include 11-limit [[Keemun|keemun]], [[Superkleismic|superkleismic]], and [[Porcupine|porcupine]].</pre></div>
Other temperaments that feature this chord prominently include 11-limit [[Keemun|keemun]], [[Superkleismic|superkleismic]], [[Porcupine|porcupine]] and [[Jubilismic+clan#x-Doublewide|doublewide]].</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;magical seventh chord&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;magical seventh&lt;/em&gt; is an 11-limit essentially tempered dyadic chord consisting of three sharp minor thirds and an 8/7, in other words a 6/5-6/5-6/5-8/7 chord, which closes at the octave since both 100/99 and 385/384 (and therefore 875/864) are tempered out. This means that in the 11-limit 4&amp;amp;7&amp;amp;15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4.&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;magical seventh chord&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;magical seventh&lt;/em&gt; is an 11-limit essentially tempered dyadic chord consisting of three sharp minor thirds and an 8/7, in other words a 6/5-6/5-6/5-8/7 chord, which closes at the octave since both 100/99 and 385/384 (and therefore 875/864) are tempered out. This means that in the 11-limit 4&amp;amp;7&amp;amp;15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4.&lt;br /&gt;
Line 16: Line 16:
In an optimized tuning for the 4&amp;amp;7&amp;amp;15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val (&lt;a class="wiki_link" href="/104edo"&gt;104edo&lt;/a&gt;.) Hence &lt;a class="wiki_link" href="/magic"&gt;magic&lt;/a&gt; (19&amp;amp;22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a Graham complexity of 12, so it doesn't appear that often.&lt;br /&gt;
In an optimized tuning for the 4&amp;amp;7&amp;amp;15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val (&lt;a class="wiki_link" href="/104edo"&gt;104edo&lt;/a&gt;.) Hence &lt;a class="wiki_link" href="/magic"&gt;magic&lt;/a&gt; (19&amp;amp;22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a Graham complexity of 12, so it doesn't appear that often.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Other temperaments that feature this chord prominently include 11-limit &lt;a class="wiki_link" href="/Keemun"&gt;keemun&lt;/a&gt;, &lt;a class="wiki_link" href="/Superkleismic"&gt;superkleismic&lt;/a&gt;, and &lt;a class="wiki_link" href="/Porcupine"&gt;porcupine&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
Other temperaments that feature this chord prominently include 11-limit &lt;a class="wiki_link" href="/Keemun"&gt;keemun&lt;/a&gt;, &lt;a class="wiki_link" href="/Superkleismic"&gt;superkleismic&lt;/a&gt;, &lt;a class="wiki_link" href="/Porcupine"&gt;porcupine&lt;/a&gt; and [[Jubilismic+clan#x-Doublewide|doublewide]].&lt;/body&gt;&lt;/html&gt;</pre></div>