The Riemann zeta function and tuning: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:~~mbattaglia1~~|~~mbattaglia1~~]] and made on <tt>2011-09-03 18:17:10 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-03 21:05:14 UTC</tt>.<br>

: The original revision id was <tt>~~250535182~~</tt>.<br>

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Multiplying the Z-function by this factor of adjustment gives a Z-function with the prime p removed from consideration. Zeta peak and zeta integral tunings may then be found as before.

Removing 2 leads to increasing adjusted peak values corresponding to the division of 3 (the "tritave") into 4, 7, 9, 13, 15, 17, 26, 32, 39, 45, 52, 56, 71, 75, 88, 131, 245, 316 ... parts. A striking feature of this list is the appearance not only of [[13edt]], the [[Bohlen-Pierce]] division of thr tritave, but the multiples 26, 39 and 52 also.

=Computing zeta=

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<br />

Multiplying the Z-function by this factor of adjustment gives a Z-function with the prime p removed from consideration. Zeta peak and zeta integral tunings may then be found as before.<br />

<br />

Removing 2 leads to increasing adjusted peak values corresponding to the division of 3 (the &quot;tritave&quot;) into 4, 7, 9, 13, 15, 17, 26, 32, 39, 45, 52, 56, 71, 75, 88, 131, 245, 316 ... parts. A striking feature of this list is the appearance not only of <a class="wiki_link" href="/13edt">13edt</a>, the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> division of thr tritave, but the multiples 26, 39 and 52 also.<br />

<br />

<h1 id="toc5"><a name="Computing zeta"></a>Computing zeta</h1>

@@ 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:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-03 18:17:10 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-03 21:05:14 UTC</tt>.<br>
-: The original revision id was <tt>250535182</tt>.<br>
+: The original revision id was <tt>250549286</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 136: / Line 136: @@
 Multiplying the Z-function by this factor of adjustment gives a Z-function with the prime p removed from consideration. Zeta peak and zeta integral tunings may then be found as before.
+Removing 2 leads to increasing adjusted peak values corresponding to the division of 3 (the "tritave") into 4, 7, 9, 13, 15, 17, 26, 32, 39, 45, 52, 56, 71, 75, 88, 131, 245, 316 ... parts. A striking feature of this list is the appearance not only of [[13edt]], the [[Bohlen-Pierce]] division of thr tritave, but the multiples 26, 39 and 52 also.
 =Computing zeta=
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 &lt;br /&gt;
 Multiplying the Z-function by this factor of adjustment gives a Z-function with the prime p removed from consideration. Zeta peak and zeta integral tunings may then be found as before.&lt;br /&gt;
+&lt;br /&gt;
+Removing 2 leads to increasing adjusted peak values corresponding to the division of 3 (the &amp;quot;tritave&amp;quot;) into 4, 7, 9, 13, 15, 17, 26, 32, 39, 45, 52, 56, 71, 75, 88, 131, 245, 316 ... parts. A striking feature of this list is the appearance not only of &lt;a class="wiki_link" href="/13edt"&gt;13edt&lt;/a&gt;, the &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; division of thr tritave, but the multiples 26, 39 and 52 also.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Computing zeta"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Computing zeta&lt;/h1&gt;