27edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 239002347 - Original comment: ** |
Wikispaces>hstraub **Imported revision 239087289 - 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:hstraub|hstraub]] and made on <tt>2011-06-28 03:01:12 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>239087289</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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Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as [[12edo]], sharp 13 2/3 cents. The result is that [[6_5|6/5]], [[7_5|7/5]] and especially [[7_6|7/6]] are all tuned more accurately than this. | Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as [[12edo]], sharp 13 2/3 cents. The result is that [[6_5|6/5]], [[7_5|7/5]] and especially [[7_6|7/6]] are all tuned more accurately than this. | ||
27edo, with its 400 cent major third, tempers out the [[diesis]] of 128/125, and also the [[septimal comma]], 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with [[22edo]] tempering out the allegedly Bohlen-Pierce comma 245/243 as well as 64/63, so that they both support superpyth temperament, with quite sharp "superpythagorean" fifths giving a sharp 9/7 in place of meantone's 5/4. | 27edo, with its 400 cent major third, tempers out the [[diesis]] of 128/125, and also the [[septimal comma]], 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with [[22edo]] tempering out the allegedly Bohlen-Pierce comma 245/243 as well as 64/63, so that they both support superpyth temperament, with quite sharp "superpythagorean" fifths giving a sharp 9/7 in place of meantone's 5/4. | ||
Though the [[7-limit]] tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both | Though the [[7-limit]] tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both [[consistent]]ly and distinctly--that is, everything in the 7-limit [[Diamonds|diamond]] is uniquely represented by a certain number of steps of 27 equal. | ||
==Intervals== | ==Intervals== | ||
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||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||= || | ||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||= || | ||
=Music= | =Music= | ||
[[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] [[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]] by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]].</pre></div> | [[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] [[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]] by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]].</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as <a class="wiki_link" href="/12edo">12edo</a>, sharp 13 2/3 cents. The result is that <a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/7_5">7/5</a> and especially <a class="wiki_link" href="/7_6">7/6</a> are all tuned more accurately than this.<br /> | Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as <a class="wiki_link" href="/12edo">12edo</a>, sharp 13 2/3 cents. The result is that <a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/7_5">7/5</a> and especially <a class="wiki_link" href="/7_6">7/6</a> are all tuned more accurately than this.<br /> | ||
<br /> | <br /> | ||
27edo, with its 400 cent major third, tempers out the <a class="wiki_link" href="/diesis">diesis</a> of 128/125, and also the <a class="wiki_link" href="/septimal%20comma">septimal comma</a>, 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with <a class="wiki_link" href="/22edo">22edo</a> tempering out the allegedly Bohlen-Pierce comma 245/243 as well as 64/63, so that they both support superpyth temperament, with quite sharp &quot;superpythagorean&quot; fifths giving a sharp 9/7 in place of meantone's 5/4. <br /> | 27edo, with its 400 cent major third, tempers out the <a class="wiki_link" href="/diesis">diesis</a> of 128/125, and also the <a class="wiki_link" href="/septimal%20comma">septimal comma</a>, 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with <a class="wiki_link" href="/22edo">22edo</a> tempering out the allegedly Bohlen-Pierce comma 245/243 as well as 64/63, so that they both support superpyth temperament, with quite sharp &quot;superpythagorean&quot; fifths giving a sharp 9/7 in place of meantone's 5/4.<br /> | ||
<br /> | <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 | 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.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x27 tone equal tempertament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x27 tone equal tempertament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h1> | ||
<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>.</body></html></pre></div> | <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>.</body></html></pre></div> | ||