The Riemann zeta function and tuning: 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:

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-15 22:06:59 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-15 22:19:51 UTC</tt>.

: The original revision id was <tt>~~353274506~~</tt>.

: The original revision id was <tt>353276314</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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Using the [[http://functions.wolfram.com/webMathematica/FunctionPlotting.jsp?name=RiemannSiegelZ|online plotter]] we can plot Z in the regions corresponding to scale divisions, using the conversion factor t = 2pi/ln(2) x, for x a number near or at an edo number. Hence, for instance, to plot 12 plot around 108.777, to plot 31 plot around 281.006, and so forth. An alternative plotter is the applet [[http://web.viu.ca/pughg/RiemannZeta/RiemannZetaLong.html|here]].

If you have access to [[http://en.wikipedia.org/wiki/Mathematica|Mathematica]], which has Z, zeta and theta as a part of its suite of initially defined functions, you can do even better. Below is a Mathematicia-generated plot of Z(~~2 pi x~~ /ln(2)) in the region around 12edo:

If you have access to [[http://en.wikipedia.org/wiki/Mathematica|Mathematica]], which has Z, zeta and theta as a part of its suite of initially defined functions, you can do even better. Below is a Mathematicia-generated plot of Z(2πx/ln(2)) in the region around 12edo:

[[image:plot12.png]]

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Using the <a class="wiki_link_ext" href="http://functions.wolfram.com/webMathematica/FunctionPlotting.jsp?name=RiemannSiegelZ" rel="nofollow">online plotter</a> we can plot Z in the regions corresponding to scale divisions, using the conversion factor t = 2pi/ln(2) x, for x a number near or at an edo number. Hence, for instance, to plot 12 plot around 108.777, to plot 31 plot around 281.006, and so forth. An alternative plotter is the applet <a class="wiki_link_ext" href="http://web.viu.ca/pughg/RiemannZeta/RiemannZetaLong.html" rel="nofollow">here</a>.

If you have access to <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Mathematica" rel="nofollow">Mathematica</a>, which has Z, zeta and theta as a part of its suite of initially defined functions, you can do even better. Below is a Mathematicia-generated plot of Z(~~2 pi x~~ /ln(2)) in the region around 12edo:

If you have access to <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Mathematica" rel="nofollow">Mathematica</a>, which has Z, zeta and theta as a part of its suite of initially defined functions, you can do even better. Below is a Mathematicia-generated plot of Z(2πx/ln(2)) in the region around 12edo:

<img src="/file/view/plot12.png/219376858/plot12.png" alt="plot12.png" title="plot12.png" />

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2012-07-15 22:06:59 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-15 22:19:51 UTC</tt>.<br>
-: The original revision id was <tt>353274506</tt>.<br>
+: The original revision id was <tt>353276314</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 100: / Line 100: @@
 Using the [[http://functions.wolfram.com/webMathematica/FunctionPlotting.jsp?name=RiemannSiegelZ|online plotter]] we can plot Z in the regions corresponding to scale divisions, using the conversion factor t = 2pi/ln(2) x, for x a number near or at an edo number. Hence, for instance, to plot 12 plot around 108.777, to plot 31 plot around 281.006, and so forth. An alternative plotter is the applet [[http://web.viu.ca/pughg/RiemannZeta/RiemannZetaLong.html|here]].
-If you have access to [[http://en.wikipedia.org/wiki/Mathematica|Mathematica]], which has Z, zeta and theta as a part of its suite of initially defined functions, you can do even better. Below is a Mathematicia-generated plot of Z(2 pi x /ln(2)) in the region around 12edo:
+If you have access to [[http://en.wikipedia.org/wiki/Mathematica|Mathematica]], which has Z, zeta and theta as a part of its suite of initially defined functions, you can do even better. Below is a Mathematicia-generated plot of Z(2πx/ln(2)) in the region around 12edo:
 [[image:plot12.png]]
@@ Line 261: / Line 261: @@
 Using the &lt;a class="wiki_link_ext" href="http://functions.wolfram.com/webMathematica/FunctionPlotting.jsp?name=RiemannSiegelZ" rel="nofollow"&gt;online plotter&lt;/a&gt; we can plot Z in the regions corresponding to scale divisions, using the conversion factor t = 2pi/ln(2) x, for x a number near or at an edo number. Hence, for instance, to plot 12 plot around 108.777, to plot 31 plot around 281.006, and so forth. An alternative plotter is the applet &lt;a class="wiki_link_ext" href="http://web.viu.ca/pughg/RiemannZeta/RiemannZetaLong.html" rel="nofollow"&gt;here&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-If you have access to &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Mathematica" rel="nofollow"&gt;Mathematica&lt;/a&gt;, which has Z, zeta and theta as a part of its suite of initially defined functions, you can do even better. Below is a Mathematicia-generated plot of Z(2 pi x /ln(2)) in the region around 12edo:&lt;br /&gt;
+If you have access to &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Mathematica" rel="nofollow"&gt;Mathematica&lt;/a&gt;, which has Z, zeta and theta as a part of its suite of initially defined functions, you can do even better. Below is a Mathematicia-generated plot of Z(2πx/ln(2)) in the region around 12edo:&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextLocalImageRule:37:&amp;lt;img src=&amp;quot;/file/view/plot12.png/219376858/plot12.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/plot12.png/219376858/plot12.png" alt="plot12.png" title="plot12.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:37 --&gt;&lt;br /&gt;