Mathematical theory: Difference between revisions

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Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.
== == 
=Scale Basics= 
[[Periodic scale]]
[[Mathematics of MOS|MOS scales]]
<span class="PageTitle">[[Mathematics of MOS]]</span>
[[MODMOS scales]]

=Regular Temperaments= 
**Basics:**
[[Monzos and Interval Space]]
[[Vals and Tuning Space]]
[[Regular Temperaments]]
[[Saturation]]

**Exterior algebra:**
[[Wedgies and Multivals]]
[[The wedgie]]
[[The dual]]
[[Interior product]]

**Linear algebra:**
[[Temperament Mapping Matrices (M-maps)]]
[[xenharmonic/Tmonzos and Tvals|Tmonzos and Tvals]]
[[Subgroup Mapping Matrices (V-maps)]]
[[Smonzos and Svals]]

**Temperament representations:**
[[Abstract regular temperament]]
[[Normal lists]]
[[Gencom]]

**Other:**
[[Planar Temperament]]
[[Transversal generators]]

==Temperament Measures and Optimization== 
[[Target tunings]]
[[TOP tuning]]
[[Lp tuning]]
[[Tenney-Euclidean tuning]]
[[Tenney-Euclidean temperament measures]]
[[Tenney-Euclidean metrics]]
[[Cangwu badness]]
[[Fractional monzos]]
[[Generator complexity]]

==Lattices and Scales== 
[[Transversal]]
[[Fokker blocks]]
[[Weak Fokker blocks|Weak Fokker Blocks]]
[[Minkowski reduced bases for Fokker groups of certain vals]]
[[Minkowski blocks]]
[[The Seven Limit Symmetrical Lattices]]
[[Tablets]]
[[Hahn distance]]

==Other== 
[[The Riemann Zeta Function and Tuning]]
[[Modulatory space]]
[[Chordal space]]
[[k*N subgroups]]
[[Don Page comma]]

Original HTML content:

<html><head><title>Mathematical Theory</title></head><body>Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h2>
 <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Scale Basics"></a><!-- ws:end:WikiTextHeadingRule:2 -->Scale Basics</h1>
 <a class="wiki_link" href="/Periodic%20scale">Periodic scale</a><br />
<a class="wiki_link" href="/Mathematics%20of%20MOS">MOS scales</a><br />
<span class="PageTitle"><a class="wiki_link" href="/Mathematics%20of%20MOS">Mathematics of MOS</a></span><br />
<a class="wiki_link" href="/MODMOS%20scales">MODMOS scales</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Regular Temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Regular Temperaments</h1>
 <strong>Basics:</strong><br />
<a class="wiki_link" href="/Monzos%20and%20Interval%20Space">Monzos and Interval Space</a><br />
<a class="wiki_link" href="/Vals%20and%20Tuning%20Space">Vals and Tuning Space</a><br />
<a class="wiki_link" href="/Regular%20Temperaments">Regular Temperaments</a><br />
<a class="wiki_link" href="/Saturation">Saturation</a><br />
<br />
<strong>Exterior algebra:</strong><br />
<a class="wiki_link" href="/Wedgies%20and%20Multivals">Wedgies and Multivals</a><br />
<a class="wiki_link" href="/The%20wedgie">The wedgie</a><br />
<a class="wiki_link" href="/The%20dual">The dual</a><br />
<a class="wiki_link" href="/Interior%20product">Interior product</a><br />
<br />
<strong>Linear algebra:</strong><br />
<a class="wiki_link" href="/Temperament%20Mapping%20Matrices%20%28M-maps%29">Temperament Mapping Matrices (M-maps)</a><br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tmonzos%20and%20Tvals">Tmonzos and Tvals</a><br />
<a class="wiki_link" href="/Subgroup%20Mapping%20Matrices%20%28V-maps%29">Subgroup Mapping Matrices (V-maps)</a><br />
<a class="wiki_link" href="/Smonzos%20and%20Svals">Smonzos and Svals</a><br />
<br />
<strong>Temperament representations:</strong><br />
<a class="wiki_link" href="/Abstract%20regular%20temperament">Abstract regular temperament</a><br />
<a class="wiki_link" href="/Normal%20lists">Normal lists</a><br />
<a class="wiki_link" href="/Gencom">Gencom</a><br />
<br />
<strong>Other:</strong><br />
<a class="wiki_link" href="/Planar%20Temperament">Planar Temperament</a><br />
<a class="wiki_link" href="/Transversal%20generators">Transversal generators</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Regular Temperaments-Temperament Measures and Optimization"></a><!-- ws:end:WikiTextHeadingRule:6 -->Temperament Measures and Optimization</h2>
 <a class="wiki_link" href="/Target%20tunings">Target tunings</a><br />
<a class="wiki_link" href="/TOP%20tuning">TOP tuning</a><br />
<a class="wiki_link" href="/Lp%20tuning">Lp tuning</a><br />
<a class="wiki_link" href="/Tenney-Euclidean%20tuning">Tenney-Euclidean tuning</a><br />
<a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures">Tenney-Euclidean temperament measures</a><br />
<a class="wiki_link" href="/Tenney-Euclidean%20metrics">Tenney-Euclidean metrics</a><br />
<a class="wiki_link" href="/Cangwu%20badness">Cangwu badness</a><br />
<a class="wiki_link" href="/Fractional%20monzos">Fractional monzos</a><br />
<a class="wiki_link" href="/Generator%20complexity">Generator complexity</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Regular Temperaments-Lattices and Scales"></a><!-- ws:end:WikiTextHeadingRule:8 -->Lattices and Scales</h2>
 <a class="wiki_link" href="/Transversal">Transversal</a><br />
<a class="wiki_link" href="/Fokker%20blocks">Fokker blocks</a><br />
<a class="wiki_link" href="/Weak%20Fokker%20blocks">Weak Fokker Blocks</a><br />
<a class="wiki_link" href="/Minkowski%20reduced%20bases%20for%20Fokker%20groups%20of%20certain%20vals">Minkowski reduced bases for Fokker groups of certain vals</a><br />
<a class="wiki_link" href="/Minkowski%20blocks">Minkowski blocks</a><br />
<a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">The Seven Limit Symmetrical Lattices</a><br />
<a class="wiki_link" href="/Tablets">Tablets</a><br />
<a class="wiki_link" href="/Hahn%20distance">Hahn distance</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Regular Temperaments-Other"></a><!-- ws:end:WikiTextHeadingRule:10 -->Other</h2>
 <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning">The Riemann Zeta Function and Tuning</a><br />
<a class="wiki_link" href="/Modulatory%20space">Modulatory space</a><br />
<a class="wiki_link" href="/Chordal%20space">Chordal space</a><br />
<a class="wiki_link" href="/k%2AN%20subgroups">k*N subgroups</a><br />
<a class="wiki_link" href="/Don%20Page%20comma">Don Page comma</a></body></html>

@@ 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>2012-07-31 10:36:56 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-07-31 10:51:36 UTC</tt>.<br>
-: The original revision id was <tt>355691590</tt>.<br>
+: The original revision id was <tt>355694448</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 28: / Line 28: @@
 **Linear algebra:**
+[[Temperament Mapping Matrices (M-maps)]]
 [[xenharmonic/Tmonzos and Tvals|Tmonzos and Tvals]]
-[[Temperament Mapping Matrices (M-maps)]]
+[[Subgroup Mapping Matrices (V-maps)]]
+[[Smonzos and Svals]]
 **Temperament representations:**
@@ Line 39: / Line 41: @@
 [[Planar Temperament]]
 [[Transversal generators]]
-==Subgroups==
-[[Smonzos and Svals]]
-[[Subgroup Mapping Matrices (V-maps)]]
 ==Temperament Measures and Optimization==
@@ Line 57: / Line 55: @@
 ==Lattices and Scales==
 [[Transversal]]
+[[Fokker blocks]]
+[[Weak Fokker blocks|Weak Fokker Blocks]]
+[[Minkowski reduced bases for Fokker groups of certain vals]]
 [[Minkowski blocks]]
 [[The Seven Limit Symmetrical Lattices]]
@@ Line 91: / Line 92: @@
 &lt;br /&gt;
 &lt;strong&gt;Linear algebra:&lt;/strong&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/Temperament%20Mapping%20Matrices%20%28M-maps%29"&gt;Temperament Mapping Matrices (M-maps)&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tmonzos%20and%20Tvals"&gt;Tmonzos and Tvals&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Temperament%20Mapping%20Matrices%20%28M-maps%29"&gt;Temperament Mapping Matrices (M-maps)&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/Subgroup%20Mapping%20Matrices%20%28V-maps%29"&gt;Subgroup Mapping Matrices (V-maps)&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;strong&gt;Temperament representations:&lt;/strong&gt;&lt;br /&gt;
@@ Line 103: / Line 106: @@
 &lt;a class="wiki_link" href="/Transversal%20generators"&gt;Transversal generators&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="Regular Temperaments-Subgroups"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Subgroups&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Regular Temperaments-Temperament Measures and Optimization"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Temperament Measures and Optimization&lt;/h2&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="/Subgroup%20Mapping%20Matrices%20%28V-maps%29"&gt;Subgroup Mapping Matrices (V-maps)&lt;/a&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="Regular Temperaments-Temperament Measures and Optimization"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Temperament Measures and 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="/TOP%20tuning"&gt;TOP tuning&lt;/a&gt;&lt;br /&gt;
@@ Line 118: / Line 117: @@
 &lt;a class="wiki_link" href="/Generator%20complexity"&gt;Generator complexity&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="Regular Temperaments-Lattices and Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Lattices and Scales&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Regular Temperaments-Lattices and Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Lattices and Scales&lt;/h2&gt;
   &lt;a class="wiki_link" href="/Transversal"&gt;Transversal&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/Fokker%20blocks"&gt;Fokker blocks&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/Weak%20Fokker%20blocks"&gt;Weak Fokker Blocks&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/Minkowski%20reduced%20bases%20for%20Fokker%20groups%20of%20certain%20vals"&gt;Minkowski reduced bases for Fokker groups of certain vals&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="/The%20Seven%20Limit%20Symmetrical%20Lattices"&gt;The Seven Limit Symmetrical Lattices&lt;/a&gt;&lt;br /&gt;
@@ Line 125: / Line 127: @@
 &lt;a class="wiki_link" href="/Hahn%20distance"&gt;Hahn distance&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Regular Temperaments-Other"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Other&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Regular Temperaments-Other"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&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="/Modulatory%20space"&gt;Modulatory space&lt;/a&gt;&lt;br /&gt;

Mathematical theory: Difference between revisions

Revision as of 10:51, 31 July 2012

IMPORTED REVISION FROM WIKISPACES

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