26edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 214920252 - Original comment: ** |
Wikispaces>guest **Imported revision 229057036 - Original comment: ** |
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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:guest|guest]] and made on <tt>2011-05-16 21:44:03 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>229057036</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> | ||
<h4>Original Wikitext content:</h4> | <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"> | <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">=**Structure**= | ||
=**Structure**= | |||
The structure of 26-EDO is an interesting beast, and I find three particular manners of understanding the chords and chordal relationships in it; | The structure of 26-EDO is an interesting beast, and I find three particular manners of understanding the chords and chordal relationships in it; | ||
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= | =Additional Scalar Bases Available in 26-EDO:= | ||
Since the perfect 5th in 26-EDO spans 15 degrees, it can be divided into three equal parts (each approximately an 8/7) as well as five equal parts (each approximately a 13/12). The former approach produces MOS at 1L+4s, 5L+1s, and 5L+6s (5 5 5 5 6, 5 5 5 5 5 1, and 4 1 4 1 4 1 4 1 4 1 1 respectively), and is excellent for 4:6:7 triads. The latter produces MOS at 1L+7s and 8L+1s (3 3 3 3 3 3 3 5 and 3 3 3 3 3 3 3 3 2 respectively), and is fairly well-supplied with 4:6:7:11:13 pentads. It also works well for more conventional (thought further from Just) 6:7:9 triads, as well as 4:5:6 triads that use the worse mapping for 5 (making 5/4 the 415.38-cent interval). | |||
-Igs | |||
=Literature= | |||
[[http://www.ronsword.com|Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]] | [[http://www.ronsword.com|Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]] | ||
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[[http://soundclick.com/share?songid=5683791|A Time-Yellowed Photo of the Cliffs Hangs on the Wall ]] by [[Igliashon Jones]] | [[http://soundclick.com/share?songid=5683791|A Time-Yellowed Photo of the Cliffs Hangs on the Wall ]] by [[Igliashon Jones]] | ||
[[http://www.io.com/%7Ehmiller/midi/26tet.mid|Etude in 26-tone equal tuning]] by [[Herman Miller]] | [[http://www.io.com/%7Ehmiller/midi/26tet.mid|Etude in 26-tone equal tuning]] by [[Herman Miller]] | ||
[[http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html|A New Recording of Organ Study #1]] by [[Daniel Thompson]] | [[http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html|A New Recording of Organ Study #1]] by [[Daniel Thompson]]</pre></div> | ||
</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>26edo</title></head><body> | <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>26edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Structure"></a><!-- ws:end:WikiTextHeadingRule:0 --><strong>Structure</strong></h1> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Structure"></a><!-- ws:end:WikiTextHeadingRule:0 --><strong>Structure</strong></h1> | |||
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The structure of 26-EDO is an interesting beast, and I find three particular manners of understanding the chords and chordal relationships in it;<br /> | The structure of 26-EDO is an interesting beast, and I find three particular manners of understanding the chords and chordal relationships in it;<br /> | ||
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If a name already exists for this temperament, I'd be interested to know about it. As far as I know, temperaments which ignore lower primes (in this case 3 and 5) in favor of higher ones (in this case 7 and 11) are still largely uncharted, but I am interested in finding out if someone has walked this path before.<br /> | If a name already exists for this temperament, I'd be interested to know about it. As far as I know, temperaments which ignore lower primes (in this case 3 and 5) in favor of higher ones (in this case 7 and 11) are still largely uncharted, but I am interested in finding out if someone has walked this path before.<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:382:&lt;img src=&quot;/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg" alt="orgone_heptatonic.jpg" title="orgone_heptatonic.jpg" /><!-- ws:end:WikiTextLocalImageRule:382 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name=" | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Additional Scalar Bases Available in 26-EDO:"></a><!-- ws:end:WikiTextHeadingRule:6 -->Additional Scalar Bases Available in 26-EDO:</h1> | ||
Since the perfect 5th in 26-EDO spans 15 degrees, it can be divided into three equal parts (each approximately an 8/7) as well as five equal parts (each approximately a 13/12). The former approach produces MOS at 1L+4s, 5L+1s, and 5L+6s (5 5 5 5 6, 5 5 5 5 5 1, and 4 1 4 1 4 1 4 1 4 1 1 respectively), and is excellent for 4:6:7 triads. The latter produces MOS at 1L+7s and 8L+1s (3 3 3 3 3 3 3 5 and 3 3 3 3 3 3 3 3 2 respectively), and is fairly well-supplied with 4:6:7:11:13 pentads. It also works well for more conventional (thought further from Just) 6:7:9 triads, as well as 4:5:6 triads that use the worse mapping for 5 (making 5/4 the 415.38-cent interval).<br /> | |||
<br /> | |||
-Igs<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Literature"></a><!-- ws:end:WikiTextHeadingRule:8 -->Literature</h1> | |||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow">Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.</a><br /> | <a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow">Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Compositions</h1> | ||
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<a class="wiki_link_ext" href="http://soundclick.com/share?songid=5683791" rel="nofollow">A Time-Yellowed Photo of the Cliffs Hangs on the Wall </a> by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br /> | <a class="wiki_link_ext" href="http://soundclick.com/share?songid=5683791" rel="nofollow">A Time-Yellowed Photo of the Cliffs Hangs on the Wall </a> by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br /> | ||
<a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/26tet.mid" rel="nofollow">Etude in 26-tone equal tuning</a> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br /> | <a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/26tet.mid" rel="nofollow">Etude in 26-tone equal tuning</a> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br /> | ||
<a class="wiki_link_ext" href="http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html" rel="nofollow">A New Recording of Organ Study #1</a> by <a class="wiki_link" href="/Daniel%20Thompson">Daniel Thompson</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html" rel="nofollow">A New Recording of Organ Study #1</a> by <a class="wiki_link" href="/Daniel%20Thompson">Daniel Thompson</a></body></html></pre></div> | ||