48edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~seraph57~~|~~seraph57~~]] and made on <tt>~~2009~~-06-~~12 16~~:40:00 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-29 13:51:02 UTC</tt>.<br>

: The original revision id was <tt>~~77952179~~</tt>.<br>

: The original revision id was <tt>215141180</tt>.<br>

: The revision comment was: <tt>~~new piece uploaded~~</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>

<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">=Compositions=

<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">The //48 equal division// divides the octave into 48 1/8th tones of precisely 25 cents each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the 5-limit, but tempers out 2401/2400 in the 7-limit, making it a tuning for [[Meantone family|squares temperament]]. In the 11-limit we can add 99/98 and 121/120 to the list, and in the 13-limit, 66/65. While [[31edo]] can also do 13-limit squares, 48 might be preferred for some purposes.

Using its best major third, 48 tempers out 20000/19683, but [[34edo]] does a much better job for this temperament, known as [[Tetracot family|tetracot]]. If 48 is treated as a no-fives system, it still tempers out 99/98 and 243/242 in the 11-limit, leading to a no-fives version of squares for which it does well as a tuning. In the 13 no-fives limit, we can add 144/143 to the list of commas, and we get the no-fives version of 13-limit squares, for which 48 actually defines the [[optimal patent val]]. No-fives squares should probably be considered by anyone interested in 48edo; the generator is 17\48, a 425 cent interval serving as both 9/7 and 14/11.

=Compositions=

Quincunx by [[http://artistgigs.com/artist.pl?id=1487|Jon Lyle Smith]]

Two At Once by [[http://www.seraph.it/blog_files/a0aafbec9519cfe9600e7a82118da2ee-26.html|Carlo Serafini]]

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</pre></div>

<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>48edo</title></head><body><h1 id="toc0"><a name="Compositions"></a>Compositions</h1>

<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>48edo</title></head><body>The <em>48 equal division</em> divides the octave into 48 1/8th tones of precisely 25 cents each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the 5-limit, but tempers out 2401/2400 in the 7-limit, making it a tuning for <a class="wiki_link" href="/Meantone%20family">squares temperament</a>. In the 11-limit we can add 99/98 and 121/120 to the list, and in the 13-limit, 66/65. While <a class="wiki_link" href="/31edo">31edo</a> can also do 13-limit squares, 48 might be preferred for some purposes.<br />

<br />

Using its best major third, 48 tempers out 20000/19683, but <a class="wiki_link" href="/34edo">34edo</a> does a much better job for this temperament, known as <a class="wiki_link" href="/Tetracot%20family">tetracot</a>. If 48 is treated as a no-fives system, it still tempers out 99/98 and 243/242 in the 11-limit, leading to a no-fives version of squares for which it does well as a tuning. In the 13 no-fives limit, we can add 144/143 to the list of commas, and we get the no-fives version of 13-limit squares, for which 48 actually defines the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>. No-fives squares should probably be considered by anyone interested in 48edo; the generator is 17\48, a 425 cent interval serving as both 9/7 and 14/11.<br />

<br />

<h1 id="toc0"><a name="Compositions"></a>Compositions</h1>

Quincunx by <a class="wiki_link_ext" href="http://artistgigs.com/artist.pl?id=1487" rel="nofollow">Jon Lyle Smith</a><br />

Two At Once by <a class="wiki_link_ext" href="http://www.seraph.it/blog_files/a0aafbec9519cfe9600e7a82118da2ee-26.html" rel="nofollow">Carlo Serafini</a><br />

Tim's Flutes by <a class="wiki_link_ext" href="http://www.seraph.it/blog_files/a8435fb03236157e8a60b047e9892594-27.html" rel="nofollow">Carlo Serafini</a></body></html></pre></div>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:seraph57|seraph57]] and made on <tt>2009-06-12 16:40:00 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-29 13:51:02 UTC</tt>.<br>
-: The original revision id was <tt>77952179</tt>.<br>
+: The original revision id was <tt>215141180</tt>.<br>
-: The revision comment was: <tt>new piece uploaded</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>
 <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">=Compositions=
+<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">The //48 equal division// divides the octave into 48 1/8th tones of precisely 25 cents each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the 5-limit, but tempers out 2401/2400 in the 7-limit, making it a tuning for [[Meantone family|squares temperament]]. In the 11-limit we can add 99/98 and 121/120 to the list, and in the 13-limit, 66/65. While [[31edo]] can also do 13-limit squares, 48 might be preferred for some purposes.
+Using its best major third, 48 tempers out 20000/19683, but [[34edo]] does a much better job for this temperament, known as [[Tetracot family|tetracot]]. If 48 is treated as a no-fives system, it still tempers out 99/98 and 243/242 in the 11-limit, leading to a no-fives version of squares for which it does well as a tuning. In the 13 no-fives limit, we can add 144/143 to the list of commas, and we get the no-fives version of 13-limit squares, for which 48 actually defines the [[optimal patent val]]. No-fives squares should probably be considered by anyone interested in 48edo; the generator is 17\48, a 425 cent interval serving as both 9/7 and 14/11.
+=Compositions=
 Quincunx by [[http://artistgigs.com/artist.pl?id=1487|Jon Lyle Smith]]
 Two At Once by [[http://www.seraph.it/blog_files/a0aafbec9519cfe9600e7a82118da2ee-26.html|Carlo Serafini]]
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 </pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;48edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Compositions&lt;/h1&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;48edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;48 equal division&lt;/em&gt; divides the octave into 48 1/8th tones of precisely 25 cents each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the 5-limit, but tempers out 2401/2400 in the 7-limit, making it a tuning for &lt;a class="wiki_link" href="/Meantone%20family"&gt;squares temperament&lt;/a&gt;. In the 11-limit we can add 99/98 and 121/120 to the list, and in the 13-limit, 66/65. While &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; can also do 13-limit squares, 48 might be preferred for some purposes.&lt;br /&gt;
+&lt;br /&gt;
+Using its best major third, 48 tempers out 20000/19683, but &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; does a much better job for this temperament, known as &lt;a class="wiki_link" href="/Tetracot%20family"&gt;tetracot&lt;/a&gt;. If 48 is treated as a no-fives system, it still tempers out 99/98 and 243/242 in the 11-limit, leading to a no-fives version of squares for which it does well as a tuning. In the 13 no-fives limit, we can add 144/143 to the list of commas, and we get the no-fives version of 13-limit squares, for which 48 actually defines the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt;. No-fives squares should probably be considered by anyone interested in 48edo; the generator is 17\48, a 425 cent interval serving as both 9/7 and 14/11.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Compositions&lt;/h1&gt;
   Quincunx by &lt;a class="wiki_link_ext" href="http://artistgigs.com/artist.pl?id=1487" rel="nofollow"&gt;Jon Lyle Smith&lt;/a&gt;&lt;br /&gt;
 Two At Once by &lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/a0aafbec9519cfe9600e7a82118da2ee-26.html" rel="nofollow"&gt;Carlo Serafini&lt;/a&gt;&lt;br /&gt;
 Tim's Flutes by &lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/a8435fb03236157e8a60b047e9892594-27.html" rel="nofollow"&gt;Carlo Serafini&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>