27edo: Difference between revisions
Wikispaces>Kosmorsky **Imported revision 248749997 - Original comment: ** |
Wikispaces>vaisvil **Imported revision 266625938 - 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:vaisvil|vaisvil]] and made on <tt>2011-10-19 20:26:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>266625938</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 92: | Line 92: | ||
[[http://www.youtube.com/watch?v=7QcwKlK6z4c|miniature prelude and fugue]] by Kosmorsky</pre></div> | [[http://www.youtube.com/watch?v=7QcwKlK6z4c|miniature prelude and fugue]] by Kosmorsky[[media type="custom" key="10942764"]]</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>27edo</title></head><body><!-- ws:start:WikiTextHeadingRule: | <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>27edo</title></head><body><!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="x27 tone equal tempertament"></a><!-- ws:end:WikiTextHeadingRule:1 --><span style="color: #0061ff; font-size: 103%;">27 tone equal tempertament</span></h1> | ||
<br /> | <br /> | ||
If octaves are kept pure, 27edo divides the <a class="wiki_link" href="/octave">octave</a> in 27 equal parts each exactly 44.444... <a class="wiki_link" href="/cent">cent</a>s in size. However, 27 is a prime candidate for <a class="wiki_link" href="/octave%20shrinking">octave shrinking</a>, and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the <a class="wiki_link" href="/5_4">third</a>, <a class="wiki_link" href="/3_2">fifth</a> and <a class="wiki_link" href="/7_4">7/4</a> sharply.<br /> | If octaves are kept pure, 27edo divides the <a class="wiki_link" href="/octave">octave</a> in 27 equal parts each exactly 44.444... <a class="wiki_link" href="/cent">cent</a>s in size. However, 27 is a prime candidate for <a class="wiki_link" href="/octave%20shrinking">octave shrinking</a>, and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the <a class="wiki_link" href="/5_4">third</a>, <a class="wiki_link" href="/3_2">fifth</a> and <a class="wiki_link" href="/7_4">7/4</a> sharply.<br /> | ||
| Line 104: | Line 104: | ||
Though the <a class="wiki_link" href="/7-limit">7-limit</a> tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both <a class="wiki_link" href="/consistent">consistent</a>ly and distinctly--that is, everything in the 7-limit <a class="wiki_link" href="/Diamonds">diamond</a> is uniquely represented by a certain number of steps of 27 equal. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13 temperament<br /> | Though the <a class="wiki_link" href="/7-limit">7-limit</a> tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both <a class="wiki_link" href="/consistent">consistent</a>ly and distinctly--that is, everything in the 7-limit <a class="wiki_link" href="/Diamonds">diamond</a> is uniquely represented by a certain number of steps of 27 equal. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13 temperament<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="x27 tone equal tempertament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:3 -->Intervals</h2> | ||
| Line 344: | Line 344: | ||
*based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.<br /> | *based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="x27 tone equal tempertament-Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:5 -->Linear temperaments</h2> | ||
| Line 463: | Line 463: | ||
</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="x27 tone equal tempertament-Commas"></a><!-- ws:end:WikiTextHeadingRule:7 -->Commas</h2> | ||
27 EDO tempers out the following commas. (Note: This assumes the val &lt; 27 43 63 76 93 100 |.)<br /> | 27 EDO tempers out the following commas. (Note: This assumes the val &lt; 27 43 63 76 93 100 |.)<br /> | ||
| Line 751: | Line 751: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc4"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:9 -->Music</h1> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a> <a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a> The central portion is in 27edo, the rest in <a class="wiki_link" href="/46edo">46edo</a>.<br /> | <a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a> <a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a> The central portion is in 27edo, the rest in <a class="wiki_link" href="/46edo">46edo</a>.<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=7QcwKlK6z4c" rel="nofollow">miniature prelude and fugue</a> by Kosmorsky</body></html></pre></div> | <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=7QcwKlK6z4c" rel="nofollow">miniature prelude and fugue</a> by Kosmorsky<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/10942764?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;10942764&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js"> | ||
</script><!-- ws:end:WikiTextMediaRule:0 --></body></html></pre></div> | |||