Mathematical theory: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Wikispaces>genewardsmith
**Imported revision 535825750 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 539217136 - Original comment: **
Line 1: Line 1:
<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:genewardsmith|genewardsmith]] and made on <tt>2014-12-22 17:39:27 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-01-31 20:18:08 UTC</tt>.<br>
: The original revision id was <tt>535825750</tt>.<br>
: The original revision id was <tt>539217136</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>
Line 35: Line 35:
[[Wedgies and Multivals]]
[[Wedgies and Multivals]]
[[The wedgie]]
[[The wedgie]]
[[Recoverability]]
[[The dual]]
[[The dual]]
[[Interior product]]
[[Interior product]]
Line 108: Line 109:
&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;
&lt;a class="wiki_link" href="/The%20wedgie"&gt;The wedgie&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/The%20wedgie"&gt;The wedgie&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Recoverability"&gt;Recoverability&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/The%20dual"&gt;The dual&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/The%20dual"&gt;The dual&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Interior%20product"&gt;Interior product&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Interior%20product"&gt;Interior product&lt;/a&gt;&lt;br /&gt;

Revision as of 20:18, 31 January 2015

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2015-01-31 20:18:08 UTC.
The original revision id was 539217136.
The revision comment was:

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

Original Wikitext content:

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]]
[[Graph-theoretic properties of scales]]

=Regular Temperaments= 
**Basics:**
[[Monzos and Interval Space]]
[[Vals and Tuning Space]]
[[Regular Temperaments]]
[[Saturation]]
[[Dual List]]
[[Meet and Join]]

**Linear algebra:**
[[Temperament Mapping Matrices (M-maps)]]
[[xenharmonic/Tmonzos and Tvals|Tmonzos and Tvals]]
[[Subgroup Mapping Matrices (V-maps)]]
[[Smonzos and Svals]]
[[Generalized Tenney Norms and Tp Interval Space]]
[[Generalized Tenney Dual Norms and Tp Tuning Space]]

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

**Abstract algebra:**
[[Groups, Lattices, Z-modules, and Vector Spaces|Groups, Lattices, Z-modules and Vector spaces]]

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

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

==Temperament Measures and Optimization== 
[[Target tunings]]
[[TOP tuning]]
[[Tp 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]]
[[Comma-based lattices]]
==Other== 
[[The Riemann Zeta Function and Tuning]]
[[Modulatory space]]
[[Chordal space]]
[[k*N subgroups]]
[[Don Page comma]]
[[xenharmonic/ABC, High Quality Commas, and Epimericity|ABC, High Quality Commas, and Epimericity]]

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 />
<a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales">Graph-theoretic properties of 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 />
<a class="wiki_link" href="/Dual%20List">Dual List</a><br />
<a class="wiki_link" href="/Meet%20and%20Join">Meet and Join</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 />
<a class="wiki_link" href="/Generalized%20Tenney%20Norms%20and%20Tp%20Interval%20Space">Generalized Tenney Norms and Tp Interval Space</a><br />
<a class="wiki_link" href="/Generalized%20Tenney%20Dual%20Norms%20and%20Tp%20Tuning%20Space">Generalized Tenney Dual Norms and Tp Tuning Space</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="/Recoverability">Recoverability</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>Abstract algebra:</strong><br />
<a class="wiki_link" href="/Groups%2C%20Lattices%2C%20Z-modules%2C%20and%20Vector%20Spaces">Groups, Lattices, Z-modules and Vector spaces</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="/Tp%20tuning">Tp 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 />
<a class="wiki_link" href="/Comma-based%20lattices">Comma-based lattices</a><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><br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/ABC%2C%20High%20Quality%20Commas%2C%20and%20Epimericity">ABC, High Quality Commas, and Epimericity</a></body></html>