Mathematical theory
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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]] [[Dual Transformations]] **Temperament representations:** [[Abstract regular temperament]] [[Normal lists]] [[Gencom]] **Other:** [[Planar Temperament]] [[Transversal generators]] ==Subgroups== [[Smonzos and Svals]] [[Subgroup Mapping Matrices (V-maps)]] ==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]] [[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]]
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<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 /> <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 /> <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="/Dual%20Transformations">Dual Transformations</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-Subgroups"></a><!-- ws:end:WikiTextHeadingRule:6 -->Subgroups</h2> <a class="wiki_link" href="/Smonzos%20and%20Svals">Smonzos and Svals</a><br /> <a class="wiki_link" href="/Subgroup%20Mapping%20Matrices%20%28V-maps%29">Subgroup Mapping Matrices (V-maps)</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Regular Temperaments-Temperament Measures and Optimization"></a><!-- ws:end:WikiTextHeadingRule:8 -->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:10:<h2> --><h2 id="toc5"><a name="Regular Temperaments-Lattices and Scales"></a><!-- ws:end:WikiTextHeadingRule:10 -->Lattices and Scales</h2> <a class="wiki_link" href="/Transversal">Transversal</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:12:<h2> --><h2 id="toc6"><a name="Regular Temperaments-Other"></a><!-- ws:end:WikiTextHeadingRule:12 -->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>