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: | : 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> | : 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&7&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&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&7&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&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]], | 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"><html><head><title>magical seventh chord</title></head><body>A <em>magical seventh</em> 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;7&amp;15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4.<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>magical seventh chord</title></head><body>A <em>magical seventh</em> 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;7&amp;15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4.<br /> | ||
| Line 16: | Line 16: | ||
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 (<a class="wiki_link" href="/104edo">104edo</a>.) Hence <a class="wiki_link" href="/magic">magic</a> (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.<br /> | 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 (<a class="wiki_link" href="/104edo">104edo</a>.) Hence <a class="wiki_link" href="/magic">magic</a> (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.<br /> | ||
<br /> | <br /> | ||
Other temperaments that feature this chord prominently include 11-limit <a class="wiki_link" href="/Keemun">keemun</a>, <a class="wiki_link" href="/Superkleismic">superkleismic</a>, | Other temperaments that feature this chord prominently include 11-limit <a class="wiki_link" href="/Keemun">keemun</a>, <a class="wiki_link" href="/Superkleismic">superkleismic</a>, <a class="wiki_link" href="/Porcupine">porcupine</a> and [[Jubilismic+clan#x-Doublewide|doublewide]].</body></html></pre></div> | ||