Mathematical theory: Difference between revisions

Wikispaces>guest
**Imported revision 355644894 - Original comment: **
Wikispaces>mbattaglia1
**Imported revision 355646312 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:guest|guest]] and made on <tt>2012-07-31 02:47:14 UTC</tt>.<br>
: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-07-31 03:14:57 UTC</tt>.<br>
: The original revision id was <tt>355644894</tt>.<br>
: The original revision id was <tt>355646312</tt>.<br>
: The revision comment was: <tt></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>
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>
<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">Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.
<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">Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.
 
== ==  
==Tuning Foundations==  
[[Monzos and Interval Space]]
[[Vals and Tuning Space]]
[[Smonzos and Svals]]
 
==Scale Foundations==  
==Scale Foundations==  
[[Periodic scale]]
[[Periodic scale]]
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&lt;span class="PageTitle"&gt;[[Mathematics of MOS]]&lt;/span&gt;
&lt;span class="PageTitle"&gt;[[Mathematics of MOS]]&lt;/span&gt;
[[MODMOS scales]]
[[MODMOS scales]]
==Tuning Foundations==
[[Monzos and Interval Space]]
[[Vals and Tuning Space]]


==Regular Temperaments==  
==Regular Temperaments==  
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[[Transversal generators]]
[[Transversal generators]]
[[Gencom]]
[[Gencom]]
=Subgroups=
[[Smonzos and Svals]]
[[M-maps and V-maps]]


==Tuning Optimization==  
==Tuning Optimization==  
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<h4>Original HTML content:</h4>
<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;Mathematical Theory&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.&lt;br /&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;Mathematical Theory&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt; &lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Tuning Foundations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Tuning Foundations&lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Scale Foundations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Scale Foundations&lt;/h2&gt;
  &lt;a class="wiki_link" href="/Monzos%20and%20Interval%20Space"&gt;Monzos and Interval Space&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Vals%20and%20Tuning%20Space"&gt;Vals and Tuning Space&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Smonzos and Svals&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Scale Foundations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Scale Foundations&lt;/h2&gt;
  &lt;a class="wiki_link" href="/Periodic%20scale"&gt;Periodic scale&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/Periodic%20scale"&gt;Periodic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Mathematics%20of%20MOS"&gt;MOS scales&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Mathematics%20of%20MOS"&gt;MOS scales&lt;/a&gt;&lt;br /&gt;
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&lt;a class="wiki_link" href="/MODMOS%20scales"&gt;MODMOS scales&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/MODMOS%20scales"&gt;MODMOS scales&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Regular Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Regular Temperaments&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Tuning Foundations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Tuning Foundations&lt;/h2&gt;
&lt;a class="wiki_link" href="/Monzos%20and%20Interval%20Space"&gt;Monzos and Interval Space&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Vals%20and%20Tuning%20Space"&gt;Vals and Tuning Space&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Regular Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Regular Temperaments&lt;/h2&gt;
  &lt;a class="wiki_link" href="/Abstract%20regular%20temperament"&gt;Abstract regular temperament&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/Abstract%20regular%20temperament"&gt;Abstract regular temperament&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;Wedgies and Multivals&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;Wedgies and Multivals&lt;/a&gt;&lt;br /&gt;
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&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Tuning Optimization"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Tuning Optimization&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Subgroups"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Subgroups&lt;/h1&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Smonzos and Svals&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/M-maps%20and%20V-maps"&gt;M-maps and V-maps&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Subgroups-Tuning Optimization"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Tuning Optimization&lt;/h2&gt;
  &lt;a class="wiki_link" href="/Target%20tunings"&gt;Target tunings&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/Target%20tunings"&gt;Target tunings&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/TOP%20tuning"&gt;TOP tuning&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/TOP%20tuning"&gt;TOP tuning&lt;/a&gt;&lt;br /&gt;
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&lt;a class="wiki_link" href="/Fractional%20monzos"&gt;Fractional monzos&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Fractional%20monzos"&gt;Fractional monzos&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Lattices and Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Lattices and Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Subgroups-Lattices and Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Lattices and Scales&lt;/h2&gt;
  &lt;a class="wiki_link" href="/Minkowski%20blocks"&gt;Minkowski blocks&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/Minkowski%20blocks"&gt;Minkowski blocks&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Transversal"&gt;Transversal&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Transversal"&gt;Transversal&lt;/a&gt;&lt;br /&gt;
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&lt;a class="wiki_link" href="/Hahn%20distance"&gt;Hahn distance&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Hahn%20distance"&gt;Hahn distance&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Other"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Other&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Subgroups-Other"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Other&lt;/h2&gt;
  &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;The Riemann Zeta Function and Tuning&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;The Riemann Zeta Function and Tuning&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Modulatory%20space"&gt;Modulatory space&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Modulatory%20space"&gt;Modulatory space&lt;/a&gt;&lt;br /&gt;