Keemic chords: Difference between revisions

Line 1:

<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>2011-10-25 18:02:53 UTC</tt>.<br>

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-25 22:21:47 UTC</tt>.<br>

: The original revision id was <tt>~~268530672~~</tt>.<br>

: The original revision id was <tt>268606826</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">A //magical seventh// 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 99~~/98~~ and 385/384 (and therefore 875/864) are tempered out. This means that in the 11-limit 4&7&15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4. 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 while it by definition it merely requires the 4&7&15 temperament, it can for the most part be regarded as a chord of [[magic]] (19&22) temperament.

<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">A //magical seventh// 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&7&15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4.

~~However~~, this ~~chord also exists and has low complexity~~ in 11-limit [[~~Superpyth#Suprapyth|suprapyth~~]] ~~temperament~~. ~~One is found in~~ the 7~~-note MOS~~.</pre></div>

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 while it by definition it merely requires the 4&7&15 temperament, it can for the most part be regarded as a chord of [[magic]] (19&22) temperament.</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>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 99~~/98~~ 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. 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 while it by definition it merely requires the 4&amp;7&amp;15 temperament, it can for the most part be regarded as a chord of <a class="wiki_link" href="/magic">magic</a> (19&amp;22) temperament.<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 />

<br />

~~However~~, this ~~chord also exists and has low complexity~~ in 11-limit <a class="wiki_link" href="/~~Superpyth#Suprapyth~~">~~suprapyth~~</a> ~~temperament~~. ~~One is found in~~ the 7~~-note MOS~~.</body></html></pre></div>

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 while it by definition it merely requires the 4&amp;7&amp;15 temperament, it can for the most part be regarded as a chord of <a class="wiki_link" href="/magic">magic</a> (19&amp;22) temperament.</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <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>2011-10-25 18:02:53 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-25 22:21:47 UTC</tt>.<br>
-: The original revision id was <tt>268530672</tt>.<br>
+: The original revision id was <tt>268606826</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">A //magical seventh// 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 99/98 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. 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 while it by definition it merely requires the 4&amp;7&amp;15 temperament, it can for the most part be regarded as a chord of [[magic]] (19&amp;22) temperament.
+<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">A //magical seventh// 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.
-However, this chord also exists and has low complexity in 11-limit [[Superpyth#Suprapyth|suprapyth]] temperament. One is found in the 7-note MOS.</pre></div>
+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 while it by definition it merely requires the 4&amp;7&amp;15 temperament, it can for the most part be regarded as a chord of [[magic]] (19&amp;22) temperament.</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;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 99/98 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. 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 while it by definition it merely requires the 4&amp;amp;7&amp;amp;15 temperament, it can for the most part be regarded as a chord of &lt;a class="wiki_link" href="/magic"&gt;magic&lt;/a&gt; (19&amp;amp;22) temperament.&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;
 &lt;br /&gt;
-However, this chord also exists and has low complexity in 11-limit &lt;a class="wiki_link" href="/Superpyth#Suprapyth"&gt;suprapyth&lt;/a&gt; temperament. One is found in the 7-note MOS.&lt;/body&gt;&lt;/html&gt;</pre></div>
+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 while it by definition it merely requires the 4&amp;amp;7&amp;amp;15 temperament, it can for the most part be regarded as a chord of &lt;a class="wiki_link" href="/magic"&gt;magic&lt;/a&gt; (19&amp;amp;22) temperament.&lt;/body&gt;&lt;/html&gt;</pre></div>