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 Foundations== [[Periodic scale]] [[Mathematics of MOS|MOS scales]] <span class="PageTitle">[[Mathematics of MOS]]</span> [[MODMOS scales]] ==Tuning Foundations== [[Monzos and Interval Space]] [[Vals and Tuning Space]] ==Regular Temperaments== [[Abstract regular temperament]] [[Wedgies and Multivals]] [[The wedgie]] [[Interior product]] [[The dual]] [[Saturation]] [[Normal lists]] [[Generator complexity]] [[Planar Temperament]] [[Transversal generators]] [[Gencom]] =Subgroups= [[Smonzos and Svals]] [[V-maps and M-maps]] ==Tuning Optimization== [[Target tunings]] [[TOP tuning]] [[Lp tuning]] [[Tenney-Euclidean tuning]] [[Tenney-Euclidean temperament measures]] [[Tenney-Euclidean metrics]] [[Cangwu badness]] [[Fractional monzos]] ==Lattices and Scales== [[Minkowski blocks]] [[Transversal]] [[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:<h2> --><h2 id="toc1"><a name="x-Scale Foundations"></a><!-- ws:end:WikiTextHeadingRule:2 -->Scale Foundations</h2> <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:<h2> --><h2 id="toc2"><a name="x-Tuning Foundations"></a><!-- ws:end:WikiTextHeadingRule:4 -->Tuning Foundations</h2> <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 /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-Regular Temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Regular Temperaments</h2> <a class="wiki_link" href="/Abstract%20regular%20temperament">Abstract regular temperament</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="/Interior%20product">Interior product</a><br /> <a class="wiki_link" href="/The%20dual">The dual</a><br /> <a class="wiki_link" href="/Saturation">Saturation</a><br /> <a class="wiki_link" href="/Normal%20lists">Normal lists</a><br /> <a class="wiki_link" href="/Generator%20complexity">Generator complexity</a><br /> <a class="wiki_link" href="/Planar%20Temperament">Planar Temperament</a><br /> <a class="wiki_link" href="/Transversal%20generators">Transversal generators</a><br /> <a class="wiki_link" href="/Gencom">Gencom</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Subgroups"></a><!-- ws:end:WikiTextHeadingRule:8 -->Subgroups</h1> <a class="wiki_link" href="/Smonzos%20and%20Svals">Smonzos and Svals</a><br /> <a class="wiki_link" href="/V-maps%20and%20M-maps">V-maps and M-maps</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Subgroups-Tuning Optimization"></a><!-- ws:end:WikiTextHeadingRule:10 -->Tuning 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 /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Subgroups-Lattices and Scales"></a><!-- ws:end:WikiTextHeadingRule:12 -->Lattices and Scales</h2> <a class="wiki_link" href="/Minkowski%20blocks">Minkowski blocks</a><br /> <a class="wiki_link" href="/Transversal">Transversal</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:14:<h2> --><h2 id="toc7"><a name="Subgroups-Other"></a><!-- ws:end:WikiTextHeadingRule:14 -->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>