63edo: 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:iamcamtaylor|iamcamtaylor]] and made on <tt>2016-07-08 00:53:04 UTC</tt>.<br>

: This revision was by author [[User:iamcamtaylor|iamcamtaylor]] and made on <tt>2016-07-08 01:06:56 UTC</tt>.<br>

: The original revision id was <tt>~~586694233~~</tt>.<br>

: The original revision id was <tt>586694489</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>

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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">The 63 equal division divides the octave into 63 equal parts of 19.048 cents each. It tempers out 3125/3072 in the 5-limit and 875/864, 225/224 and 245/243 in the 7-limit, so that it supports magic temperament. In the 11-limit it tempers out 100/99, supporting 11-limit magic, plus 896/891, 385/384 and 640/539. In the 13-limit it tempers put 275/273, 169/168, 640/637, 352/351, 364/363 and 676/675. It provides the optimal patent val for the 29&63 temperament in the 7-, 11- and 13-limit. It is divisible by 3, 7, 9 and 21.

63 is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning.</pre></div>

63 is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning. As a fifths-system, the diesis after 12 fifths can represent 32:33, 27:28, 88:91, and more, making chains of fifths 12 or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. A 17-tone fifths chain looks on the surface a little similar to 17edo, but as -17 fifths gets us to 64/63, observing the comma becomes an essential part in progressions favouring prime 7.

Audio:

https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts

https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams

https://archive.org/details/17_63EDOEarlyDreamsTwo

https://soundcloud.com/cam-taylor-2-1/12tone63edo1</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>63edo</title></head><body>The 63 equal division divides the octave into 63 equal parts of 19.048 cents each. It tempers out 3125/3072 in the 5-limit and 875/864, 225/224 and 245/243 in the 7-limit, so that it supports magic temperament. In the 11-limit it tempers out 100/99, supporting 11-limit magic, plus 896/891, 385/384 and 640/539. In the 13-limit it tempers put 275/273, 169/168, 640/637, 352/351, 364/363 and 676/675. It provides the optimal patent val for the 29&amp;63 temperament in the 7-, 11- and 13-limit. It is divisible by 3, 7, 9 and 21.<br />

<br />

63 is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning.</body></html></pre></div>

63 is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning. As a fifths-system, the diesis after 12 fifths can represent 32:33, 27:28, 88:91, and more, making chains of fifths 12 or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. A 17-tone fifths chain looks on the surface a little similar to 17edo, but as -17 fifths gets us to 64/63, observing the comma becomes an essential part in progressions favouring prime 7.<br />

<br />

Audio:<br />

<br />

<a class="wiki_link_ext" href="https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts" rel="nofollow">https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts</a><br />

<a class="wiki_link_ext" href="https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams" rel="nofollow">https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams</a><br />

<a class="wiki_link_ext" href="https://archive.org/details/17_63EDOEarlyDreamsTwo" rel="nofollow">https://archive.org/details/17_63EDOEarlyDreamsTwo</a><br />

<a class="wiki_link_ext" href="https://soundcloud.com/cam-taylor-2-1/12tone63edo1" rel="nofollow">https://soundcloud.com/cam-taylor-2-1/12tone63edo1</a></body></html></pre></div>

@@ Line 1: / Line 1: @@
 <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:iamcamtaylor|iamcamtaylor]] and made on <tt>2016-07-08 00:53:04 UTC</tt>.<br>
+: This revision was by author [[User:iamcamtaylor|iamcamtaylor]] and made on <tt>2016-07-08 01:06:56 UTC</tt>.<br>
-: The original revision id was <tt>586694233</tt>.<br>
+: The original revision id was <tt>586694489</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>
@@ Line 8: / Line 8: @@
 <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 63 equal division divides the octave into 63 equal parts of 19.048 cents each. It tempers out 3125/3072 in the 5-limit and 875/864, 225/224 and 245/243 in the 7-limit, so that it supports magic temperament. In the 11-limit it tempers out 100/99, supporting 11-limit magic, plus 896/891, 385/384 and 640/539. In the 13-limit it tempers put 275/273, 169/168, 640/637, 352/351, 364/363 and 676/675. It provides the optimal patent val for the 29&amp;63 temperament in the 7-, 11- and 13-limit. It is divisible by 3, 7, 9 and 21.
-is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning.</pre></div>
+is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning. As a fifths-system, the diesis after 12 fifths can represent 32:33, 27:28, 88:91, and more, making chains of fifths 12 or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. A 17-tone fifths chain looks on the surface a little similar to 17edo, but as -17 fifths gets us to 64/63, observing the comma becomes an essential part in progressions favouring prime 7.
+Audio:
+https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts
+https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams
+https://archive.org/details/17_63EDOEarlyDreamsTwo
+https://soundcloud.com/cam-taylor-2-1/12tone63edo1</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;63edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 63 equal division divides the octave into 63 equal parts of 19.048 cents each. It tempers out 3125/3072 in the 5-limit and 875/864, 225/224 and 245/243 in the 7-limit, so that it supports magic temperament. In the 11-limit it tempers out 100/99, supporting 11-limit magic, plus 896/891, 385/384 and 640/539. In the 13-limit it tempers put 275/273, 169/168, 640/637, 352/351, 364/363 and 676/675. It provides the optimal patent val for the 29&amp;amp;63 temperament in the 7-, 11- and 13-limit. It is divisible by 3, 7, 9 and 21.&lt;br /&gt;
 &lt;br /&gt;
-is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning.&lt;/body&gt;&lt;/html&gt;</pre></div>
+is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning. As a fifths-system, the diesis after 12 fifths can represent 32:33, 27:28, 88:91, and more, making chains of fifths 12 or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. A 17-tone fifths chain looks on the surface a little similar to 17edo, but as -17 fifths gets us to 64/63, observing the comma becomes an essential part in progressions favouring prime 7.&lt;br /&gt;
+&lt;br /&gt;
+&lt;br /&gt;
+Audio:&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextUrlRule:10:https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts --&gt;&lt;a class="wiki_link_ext" href="https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts" rel="nofollow"&gt;https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:10 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextUrlRule:11:https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams --&gt;&lt;a class="wiki_link_ext" href="https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams" rel="nofollow"&gt;https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:11 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextUrlRule:12:https://archive.org/details/17_63EDOEarlyDreamsTwo --&gt;&lt;a class="wiki_link_ext" href="https://archive.org/details/17_63EDOEarlyDreamsTwo" rel="nofollow"&gt;https://archive.org/details/17_63EDOEarlyDreamsTwo&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:12 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextUrlRule:13:https://soundcloud.com/cam-taylor-2-1/12tone63edo1 --&gt;&lt;a class="wiki_link_ext" href="https://soundcloud.com/cam-taylor-2-1/12tone63edo1" rel="nofollow"&gt;https://soundcloud.com/cam-taylor-2-1/12tone63edo1&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:13 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>