Mathematical theory: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 535825750 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 539217136 - Original comment: ** |
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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> | : 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> | : 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> | ||
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[[Wedgies and Multivals]] | [[Wedgies and Multivals]] | ||
[[The wedgie]] | [[The wedgie]] | ||
[[Recoverability]] | |||
[[The dual]] | [[The dual]] | ||
[[Interior product]] | [[Interior product]] | ||
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<a class="wiki_link" href="/Wedgies%20and%20Multivals">Wedgies and Multivals</a><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%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="/The%20dual">The dual</a><br /> | ||
<a class="wiki_link" href="/Interior%20product">Interior product</a><br /> | <a class="wiki_link" href="/Interior%20product">Interior product</a><br /> | ||
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.
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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:<h2> --><h2 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h2> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><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:<h1> --><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:<h2> --><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:<h2> --><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:<h2> --><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>