General theory: 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:~~akjmicro~~|~~akjmicro~~]] and made on <tt>2012-03-~~18 18~~:10:22 UTC</tt>.<br>

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-03-22 07:53:29 UTC</tt>.<br>

: The original revision id was <tt>~~312185448~~</tt>.<br>

: The original revision id was <tt>313519846</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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[[xenharmonic/Equal Temperaments|Equal Temperaments]]

[[xenharmonic/Periods and Generators|Periods and Generators]]

~~[[xenharmonic/Keenan's explanation of vals|Keenan's explanation of vals]]~~

[[xenharmonic/EDO|EDO]]

[[xenharmonic/EDT|EDT]]

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[[xenharmonic/AID|Arithmetic irrational divisions]]

[[ADO|ADO (Arithmetic rational divisions)]]

~~=Javascript tools=~~

~~[[xenharmonic/Interval calculator|Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too]]~~

~~[[xenharmonic/AnimatedSternBrocotTree|An animated Stern-Brocot tree, courtesy untwelve.org]]~~

~~[[http://www.untwelve.org/javascript_demos/MOSring.html|An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation]]~~

~~[[http://www.toverlamp.org/static/wickisynth/wickisynth.html|An excellent Firefox browser tuning demo synthesizer, 'Wicksynth']]~~

=How it Works=

[[xenharmonic/Monzos|Monzos]]

[[xenharmonic/Vals|Vals]]

[[xenharmonic/Vals|Vals]] (see also [[xenharmonic/Keenan's explanation of vals|Keenan's explanation of vals]])

[[xenharmonic/Mappings|Mappings]]

[[xenharmonic/Patent val|Patent val]]

[[xenharmonic/tempering out|Tempering Out]]

[[xenharmonic/Rank and codimension|Rank and codimension]]

=Javascript tools=

[[xenharmonic/Interval calculator|Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too]]

[[xenharmonic/AnimatedSternBrocotTree|An animated Stern-Brocot tree, courtesy untwelve.org]]

[[http://www.untwelve.org/javascript_demos/MOSring.html|An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation]]

[[http://www.toverlamp.org/static/wickisynth/wickisynth.html|An excellent Firefox browser tuning demo synthesizer, 'Wicksynth']]

=Additional Stuff=

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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Equal%20Temperaments">Equal Temperaments</a><br />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Periods%20and%20Generators">Periods and Generators</a><br />

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Keenan%27s%20explanation%20of%20vals">Keenan's explanation of vals</a><br />~~

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<a class="wiki_link" href="/ADO">ADO (Arithmetic rational divisions)</a><br />

<br />

<h1 id="toc2~~"><a name="Javascript tools"></a>Javascript tools</h1>~~

<h1 id="toc2"><a name="How it Works"></a>How it Works</h1>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Interval%20calculator">Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too</a><br />

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/AnimatedSternBrocotTree">An animated Stern-Brocot tree, courtesy untwelve.org</a><br />~~

<a class="wiki_link_ext" href="http://www.untwelve.org/javascript_demos/MOSring.html" rel="nofollow">An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation</a><br />

~~<a class="wiki_link_ext" href="http://www.toverlamp.org/static/wickisynth/wickisynth.html" rel="nofollow">An excellent Firefox browser tuning demo synthesizer, 'Wicksynth'</a><br />~~

~~<br />~~

~~<h1 id="toc3~~"><a name="How it Works"></a>How it Works</h1>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Monzos">Monzos</a><br />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vals">Vals</a> (see also <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Keenan%27s%20explanation%20of%20vals">Keenan's explanation of vals</a>)<br />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Mappings">Mappings</a><br />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Patent%20val">Patent val</a><br />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">Tempering Out</a><br />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Rank%20and%20codimension">Rank and codimension</a><br />

<br />

<h1 id="toc3"><a name="Javascript tools"></a>Javascript tools</h1>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Interval%20calculator">Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too</a><br />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/AnimatedSternBrocotTree">An animated Stern-Brocot tree, courtesy untwelve.org</a><br />

<a class="wiki_link_ext" href="http://www.untwelve.org/javascript_demos/MOSring.html" rel="nofollow">An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation</a><br />

<a class="wiki_link_ext" href="http://www.toverlamp.org/static/wickisynth/wickisynth.html" rel="nofollow">An excellent Firefox browser tuning demo synthesizer, 'Wicksynth'</a><br />

<br />

<h1 id="toc4"><a name="Additional Stuff"></a>Additional Stuff</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:akjmicro|akjmicro]] and made on <tt>2012-03-18 18:10:22 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-03-22 07:53:29 UTC</tt>.<br>
-: The original revision id was <tt>312185448</tt>.<br>
+: The original revision id was <tt>313519846</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 18: / Line 18: @@
 [[xenharmonic/Equal Temperaments|Equal Temperaments]]
 [[xenharmonic/Periods and Generators|Periods and Generators]]
-[[xenharmonic/Keenan's explanation of vals|Keenan's explanation of vals]]
 [[xenharmonic/EDO|EDO]]
 [[xenharmonic/EDT|EDT]]
@@ Line 25: / Line 24: @@
 [[xenharmonic/AID|Arithmetic irrational divisions]]
 [[ADO|ADO (Arithmetic rational divisions)]]
-=Javascript tools=
-[[xenharmonic/Interval calculator|Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too]]
-[[xenharmonic/AnimatedSternBrocotTree|An animated Stern-Brocot tree, courtesy untwelve.org]]
-[[http://www.untwelve.org/javascript_demos/MOSring.html|An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation]]
-[[http://www.toverlamp.org/static/wickisynth/wickisynth.html|An excellent Firefox browser tuning demo synthesizer, 'Wicksynth']]
 =How it Works=
 [[xenharmonic/Monzos|Monzos]]
-[[xenharmonic/Vals|Vals]]
+[[xenharmonic/Vals|Vals]] (see also [[xenharmonic/Keenan's explanation of vals|Keenan's explanation of vals]])
 [[xenharmonic/Mappings|Mappings]]
 [[xenharmonic/Patent val|Patent val]]
 [[xenharmonic/tempering out|Tempering Out]]
 [[xenharmonic/Rank and codimension|Rank and codimension]]
+=Javascript tools=
+[[xenharmonic/Interval calculator|Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too]]
+[[xenharmonic/AnimatedSternBrocotTree|An animated Stern-Brocot tree, courtesy untwelve.org]]
+[[http://www.untwelve.org/javascript_demos/MOSring.html|An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation]]
+[[http://www.toverlamp.org/static/wickisynth/wickisynth.html|An excellent Firefox browser tuning demo synthesizer, 'Wicksynth']]
 =Additional Stuff=
@@ Line 68: / Line 67: @@
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Equal%20Temperaments"&gt;Equal Temperaments&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Periods%20and%20Generators"&gt;Periods and Generators&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Keenan%27s%20explanation%20of%20vals"&gt;Keenan's explanation of vals&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/EDO"&gt;EDO&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/EDT"&gt;EDT&lt;/a&gt;&lt;br /&gt;
@@ Line 76: / Line 74: @@
 &lt;a class="wiki_link" href="/ADO"&gt;ADO (Arithmetic rational divisions)&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Javascript tools"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Javascript tools&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="How it Works"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;How it Works&lt;/h1&gt;
- &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Interval%20calculator"&gt;Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/AnimatedSternBrocotTree"&gt;An animated Stern-Brocot tree, courtesy untwelve.org&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.untwelve.org/javascript_demos/MOSring.html" rel="nofollow"&gt;An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.toverlamp.org/static/wickisynth/wickisynth.html" rel="nofollow"&gt;An excellent Firefox browser tuning demo synthesizer, 'Wicksynth'&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="How it Works"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;How it Works&lt;/h1&gt;
   &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Monzos"&gt;Monzos&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vals"&gt;Vals&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vals"&gt;Vals&lt;/a&gt; (see also &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Keenan%27s%20explanation%20of%20vals"&gt;Keenan's explanation of vals&lt;/a&gt;)&lt;br /&gt;
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Mappings"&gt;Mappings&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Patent%20val"&gt;Patent val&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out"&gt;Tempering Out&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Rank%20and%20codimension"&gt;Rank and codimension&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Javascript tools"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Javascript tools&lt;/h1&gt;
+ &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Interval%20calculator"&gt;Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/AnimatedSternBrocotTree"&gt;An animated Stern-Brocot tree, courtesy untwelve.org&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://www.untwelve.org/javascript_demos/MOSring.html" rel="nofollow"&gt;An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://www.toverlamp.org/static/wickisynth/wickisynth.html" rel="nofollow"&gt;An excellent Firefox browser tuning demo synthesizer, 'Wicksynth'&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Additional Stuff"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Additional Stuff&lt;/h1&gt;