74edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 215740136 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 277565016 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-11-21 00:46:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>277565016</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">//74edo// divides the [[octave]] into 74 equal parts of size 16.216 [[cent]]s each. It is most notable as a [[meantone]] tuning, tempering out 81/80 in the [[5-limit]]; 81/80 and 126/125 (and hence 225/224) in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and 144/143 and 847/845 in the [[13-limit]]. Discarding 847/845 from that gives [[Meantone family|13-limit meantone]], aka 13-limit huygens, for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone.</pre></div> | <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">//74edo// divides the [[octave]] into 74 equal parts of size 16.216 [[cent]]s each. It is most notable as a [[meantone]] tuning, tempering out 81/80 in the [[5-limit]]; 81/80 and 126/125 (and hence 225/224) in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and 144/143 and 847/845 in the [[13-limit]]. Discarding 847/845 from that gives [[Meantone family|13-limit meantone]], aka 13-limit huygens, for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone. | ||
74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.</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>74edo</title></head><body><em>74edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 74 equal parts of size 16.216 <a class="wiki_link" href="/cent">cent</a>s each. It is most notable as a <a class="wiki_link" href="/meantone">meantone</a> tuning, tempering out 81/80 in the <a class="wiki_link" href="/5-limit">5-limit</a>; 81/80 and 126/125 (and hence 225/224) in the <a class="wiki_link" href="/7-limit">7-limit</a>; 99/98, 176/175 and 441/440 in the <a class="wiki_link" href="/11-limit">11-limit</a>; and 144/143 and 847/845 in the <a class="wiki_link" href="/13-limit">13-limit</a>. Discarding 847/845 from that gives <a class="wiki_link" href="/Meantone%20family">13-limit meantone</a>, aka 13-limit huygens, for which 74edo gives the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>; and discarding 144/143 gives a 13-limit 62&amp;74 temperament with half-octave period and two parallel tracks of meantone.</body></html></pre></div> | <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>74edo</title></head><body><em>74edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 74 equal parts of size 16.216 <a class="wiki_link" href="/cent">cent</a>s each. It is most notable as a <a class="wiki_link" href="/meantone">meantone</a> tuning, tempering out 81/80 in the <a class="wiki_link" href="/5-limit">5-limit</a>; 81/80 and 126/125 (and hence 225/224) in the <a class="wiki_link" href="/7-limit">7-limit</a>; 99/98, 176/175 and 441/440 in the <a class="wiki_link" href="/11-limit">11-limit</a>; and 144/143 and 847/845 in the <a class="wiki_link" href="/13-limit">13-limit</a>. Discarding 847/845 from that gives <a class="wiki_link" href="/Meantone%20family">13-limit meantone</a>, aka 13-limit huygens, for which 74edo gives the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>; and discarding 144/143 gives a 13-limit 62&amp;74 temperament with half-octave period and two parallel tracks of meantone.<br /> | ||
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74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.</body></html></pre></div> | |||