39edt: Difference between revisions

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-04 14:05:29 UTC</tt>.<br>

: The original revision id was <tt>250636156</tt>.<br>

<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 39 equal division of 3, the tritave, divides it into 39 equal parts of 48.678 cents each, corresponding to 24.606 edo. It is a strong no-twos 13-limit system, a fact first noted by [[Paul Erlich]], and like [[26edt]] and [[52edt]] it is a multiple of [[13edt]] and so contains the [[Bohlen-Pierce]] scale. It is contorted in the 7-limit, tempering out the same BP commas 245/243 and 3125/3087 as 13edt. In the 11-limit it tempers out 1331/1323 and in the 13-limit 275/273, 847/845 and 1575/1573. It is related to the 49f&amp;172f temperament tempering out 245/243, 275/273, 847/845 and 1575/1573, which has map [&lt;1 0 0 0 0 0|, &lt;0 39 57 69 85 91|]. This has a POTE generator which is an approximate 77/75 of 48.822 cents. 39edt is the ninth [[The Riemann Zeta Function and Tuning#Removing primes|no-twos zeta peak edt]].  

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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;39edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 39 equal division of 3, the tritave, divides it into 39 equal parts of 48.678 cents each, corresponding to 24.606 edo. It is a strong no-twos 13-limit system, a fact first noted by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;, and like &lt;a class="wiki_link" href="/26edt"&gt;26edt&lt;/a&gt; and &lt;a class="wiki_link" href="/52edt"&gt;52edt&lt;/a&gt; it is a multiple of &lt;a class="wiki_link" href="/13edt"&gt;13edt&lt;/a&gt; and so contains the &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; scale. It is contorted in the 7-limit, tempering out the same BP commas 245/243 and 3125/3087 as 13edt. In the 11-limit it tempers out 1331/1323 and in the 13-limit 275/273, 847/845 and 1575/1573. It is related to the 49f&amp;amp;172f temperament tempering out 245/243, 275/273, 847/845 and 1575/1573, which has map [&amp;lt;1 0 0 0 0 0|, &amp;lt;0 39 57 69 85 91|]. This has a POTE generator which is an approximate 77/75 of 48.822 cents. 39edt is the ninth &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing primes"&gt;no-twos zeta peak edt&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>