43edo: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 288886953 - Original comment: ** |
Wikispaces>Kosmorsky **Imported revision 311993404 - Original comment: ** |
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<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:Kosmorsky|Kosmorsky]] and made on <tt>2012-03-17 20:38:30 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>311993404</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> | ||
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<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">=<span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span>= | <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">=<span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span>= | ||
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//43edo// divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, being a good tuning system in the 5, 7 | //43edo// divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. It has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician [[@http://en.wikipedia.org/wiki/Joseph_Sauveur|Joseph Saveur]] based his system on 43 equal tones to the octave, calling them "merides". Further information: [[http://tonalsoft.com/enc/m/meride.aspx]] | ||
In the 13-limit, we get two versions of meantone equivalent in 43et, one tempering out 78/77, the other 144/143. The first has generator mapping <0 1 4 10 18 27|, and the second <0 1 4 10 18 -16|. | In the 13-limit, we get two versions of meantone equivalent in 43et, one tempering out 78/77, the other 144/143. The first has generator mapping <0 1 4 10 18 27|, and the second <0 1 4 10 18 -16|. | ||
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|| 42 || 1172,093 ||</pre></div> | || 42 || 1172,093 || | ||
[[media type="file" key="43 edo counterpoint.mid"]] Peter Kosmorsky (late 2011)</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>43edo</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>43edo</title></head><body><!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="x43 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:1 --><span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span></h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><!-- ws:end:WikiTextHeadingRule:3 --> </h1> | ||
<em>43edo</em> divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, being a good tuning system in the 5, 7 | <em>43edo</em> divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. It has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joseph_Sauveur" rel="nofollow" target="_blank">Joseph Saveur</a> based his system on 43 equal tones to the octave, calling them &quot;merides&quot;. Further information: <a class="wiki_link_ext" href="http://tonalsoft.com/enc/m/meride.aspx" rel="nofollow">http://tonalsoft.com/enc/m/meride.aspx</a><br /> | ||
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In the 13-limit, we get two versions of meantone equivalent in 43et, one tempering out 78/77, the other 144/143. The first has generator mapping &lt;0 1 4 10 18 27|, and the second &lt;0 1 4 10 18 -16|.<br /> | In the 13-limit, we get two versions of meantone equivalent in 43et, one tempering out 78/77, the other 144/143. The first has generator mapping &lt;0 1 4 10 18 27|, and the second &lt;0 1 4 10 18 -16|.<br /> | ||
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43edo is the 14th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/41edo">41edo</a> and coming before <a class="wiki_link" href="/47edo">47edo</a>.<br /> | 43edo is the 14th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/41edo">41edo</a> and coming before <a class="wiki_link" href="/47edo">47edo</a>.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="x43 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 -->Intervals</h2> | ||
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</table> | </table> | ||
</body></html></pre></div> | <br /> | ||
<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/43%20edo%20counterpoint.mid?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;43 edo counterpoint.mid&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/43+edo+counterpoint.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:0 --> Peter Kosmorsky (late 2011)</body></html></pre></div> | |||