26edo: Difference between revisions
Wikispaces>igliashon **Imported revision 242831105 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 250376628 - 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>2011-09-02 15:00:28 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>250376628</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">//26edo// divides the [[octave]] into 26 equal parts of 46.154 [[cent]]s each. It tempers out 81/80 in the [[5-limit]], making it a meantone tuning with a very flat fifth. In the [[7-limit]], it tempers out 50/49, 525/512 and 875/864, and supports [[Meantone family|injera]] and [[Meantone family|flattone]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-limit|13 odd limit]] [[consistent| consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7_4|7/4]]). | <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">[[toc|flat]] | ||
//26edo// divides the [[octave]] into 26 equal parts of 46.154 [[cent]]s each. It tempers out 81/80 in the [[5-limit]], making it a meantone tuning with a very flat fifth. In the [[7-limit]], it tempers out 50/49, 525/512 and 875/864, and supports [[Meantone family|injera]] and [[Meantone family|flattone]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-limit|13 odd limit]] [[consistent| consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7_4|7/4]]). | |||
=**Structure**= | =**Structure**= | ||
| Line 121: | Line 123: | ||
[[http://www.io.com/%7Ehmiller/midi/26tet.mid|Etude in 26-tone equal temperament]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/26tet.mp3|play]] by [[Herman Miller]] | [[http://www.io.com/%7Ehmiller/midi/26tet.mid|Etude in 26-tone equal temperament]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/26tet.mp3|play]] by [[Herman Miller]] | ||
[[http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html|A New Recording of Organ Study #1]] [[http://www.microtonalmusic.net/audio/organstudyremix26edo.mp3|play]] by [[Daniel Thompson]] | [[http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html|A New Recording of Organ Study #1]] [[http://www.microtonalmusic.net/audio/organstudyremix26edo.mp3|play]] by [[Daniel Thompson]] | ||
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/LittleFugueIn26_CBobro.mp3|Little Fugue in 26]] by [[Cameron Bobro]]</pre></div> | [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/LittleFugueIn26_CBobro.mp3|Little Fugue in 26]] by [[Cameron Bobro]] | ||
[[http://www.96edo.com/music/micro900607.mp3|Mcicrotonal music in 26-EDO]] by [[Shaahin Mohajeri]]</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><em>26edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 26 equal parts of 46.154 <a class="wiki_link" href="/cent">cent</a>s each. It tempers out 81/80 in the <a class="wiki_link" href="/5-limit">5-limit</a>, making it a meantone tuning with a very flat fifth. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it tempers out 50/49, 525/512 and 875/864, and supports <a class="wiki_link" href="/Meantone%20family">injera</a> and <a class="wiki_link" href="/Meantone%20family">flattone</a> temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the <a class="wiki_link" href="/13-limit">13 odd limit</a> <a class="wiki_link" href="/consistent"> consistent</a>ly. 26edo has a very good approximation of the harmonic seventh (<a class="wiki_link" href="/7_4">7/4</a>).<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>26edo</title></head><body><!-- ws:start:WikiTextTocRule:16:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Structure">Structure</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Orgone Temperament">Orgone Temperament</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#toc4"> </a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Additional Scalar Bases Available in 26-EDO:">Additional Scalar Bases Available in 26-EDO:</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Literature">Literature</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | ||
<!-- ws:end:WikiTextTocRule:25 --><br /> | |||
<em>26edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 26 equal parts of 46.154 <a class="wiki_link" href="/cent">cent</a>s each. It tempers out 81/80 in the <a class="wiki_link" href="/5-limit">5-limit</a>, making it a meantone tuning with a very flat fifth. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it tempers out 50/49, 525/512 and 875/864, and supports <a class="wiki_link" href="/Meantone%20family">injera</a> and <a class="wiki_link" href="/Meantone%20family">flattone</a> temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the <a class="wiki_link" href="/13-limit">13 odd limit</a> <a class="wiki_link" href="/consistent"> consistent</a>ly. 26edo has a very good approximation of the harmonic seventh (<a class="wiki_link" href="/7_4">7/4</a>).<br /> | |||
<br /> | <br /> | ||
<!-- 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> | ||
| Line 866: | Line 871: | ||
Orgone has a minimax tuning which sharpens both 7 and 11 by 1/5 of an orgonisma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgonisma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.<br /> | Orgone has a minimax tuning which sharpens both 7 and 11 by 1/5 of an orgonisma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgonisma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:726:&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:726 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --> </h1> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --> </h1> | ||
| Line 883: | Line 888: | ||
<a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/26tet.mid" rel="nofollow">Etude in 26-tone equal temperament</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/26tet.mp3" rel="nofollow">play</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 temperament</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/26tet.mp3" rel="nofollow">play</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> <a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/organstudyremix26edo.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Daniel%20Thompson">Daniel Thompson</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> <a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/organstudyremix26edo.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Daniel%20Thompson">Daniel Thompson</a><br /> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/LittleFugueIn26_CBobro.mp3" rel="nofollow">Little Fugue in 26</a> by <a class="wiki_link" href="/Cameron%20Bobro">Cameron Bobro</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/LittleFugueIn26_CBobro.mp3" rel="nofollow">Little Fugue in 26</a> by <a class="wiki_link" href="/Cameron%20Bobro">Cameron Bobro</a><br /> | ||
<a class="wiki_link_ext" href="http://www.96edo.com/music/micro900607.mp3" rel="nofollow">Mcicrotonal music in 26-EDO</a> by <a class="wiki_link" href="/Shaahin%20Mohajeri">Shaahin Mohajeri</a></body></html></pre></div> | |||