Mathematical theory: Difference between revisions
Wikispaces>genewardsmith **Imported revision 347567134 - Original comment: ** |
Wikispaces>guest **Imported revision 355644894 - 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: | : This revision was by author [[User:guest|guest]] and made on <tt>2012-07-31 02:47:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>355644894</tt>.<br> | ||
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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.<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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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters. | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters. | ||
==Tuning Foundations== | |||
[[Monzos and Interval Space]] | |||
[[Vals and Tuning Space]] | |||
[[Smonzos and Svals]] | |||
==Scale Foundations== | |||
[[Periodic scale]] | [[Periodic scale]] | ||
[[Mathematics of MOS|MOS scales]] | [[Mathematics of MOS|MOS scales]] | ||
<span class="PageTitle">[[Mathematics of MOS]]</span> | <span class="PageTitle">[[Mathematics of MOS]]</span> | ||
[[MODMOS scales]] | [[MODMOS scales]] | ||
==Regular Temperaments== | |||
[[ | [[Abstract regular temperament]] | ||
[[Wedgies and Multivals]] | [[Wedgies and Multivals]] | ||
[[The wedgie]] | [[The wedgie]] | ||
[[Interior product]] | [[Interior product]] | ||
[[The dual]] | [[The dual]] | ||
[[Saturation]] | |||
[[Normal lists]] | |||
[[Generator complexity]] | |||
[[Planar Temperament]] | |||
[[Transversal generators]] | |||
[[Gencom]] | |||
==Tuning Optimization== | |||
[[Target tunings]] | |||
[[TOP tuning]] | [[TOP tuning]] | ||
[[Lp tuning]] | [[Lp tuning]] | ||
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[[Tenney-Euclidean metrics]] | [[Tenney-Euclidean metrics]] | ||
[[Cangwu badness]] | [[Cangwu badness]] | ||
[[Fractional monzos]] | [[Fractional monzos]] | ||
==Lattices and Scales== | |||
[[Minkowski blocks]] | |||
[[ | [[Transversal]] | ||
[[ | |||
[[The Seven Limit Symmetrical Lattices]] | [[The Seven Limit Symmetrical Lattices]] | ||
[[Tablets]] | [[Tablets]] | ||
[[Hahn distance]] | |||
==Other== | |||
[[The Riemann Zeta Function and Tuning]] | |||
[[Modulatory space]] | [[Modulatory space]] | ||
[[Chordal space]] | [[Chordal space]] | ||
[[k*N subgroups]] | [[k*N subgroups]] | ||
[[Don Page comma]]</pre></div> | [[Don Page comma]]</pre></div> | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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 /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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 /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Periodic%20scale">Periodic scale</a><br /> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Tuning Foundations"></a><!-- ws:end:WikiTextHeadingRule:0 -->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 /> | |||
<a class="wiki_link" href="/Smonzos%20and%20Svals">Smonzos and Svals</a><br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><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 /> | <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 /> | <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="/MODMOS%20scales">MODMOS scales</a><br /> | ||
< | <br /> | ||
<a | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Regular Temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Regular Temperaments</h2> | ||
<a class="wiki_link" href="/ | <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="/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="/Interior%20product">Interior product</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="/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:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Tuning Optimization"></a><!-- ws:end:WikiTextHeadingRule:6 -->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="/TOP%20tuning">TOP tuning</a><br /> | ||
<a class="wiki_link" href="/Lp%20tuning">Lp tuning</a><br /> | <a class="wiki_link" href="/Lp%20tuning">Lp tuning</a><br /> | ||
| Line 64: | Line 90: | ||
<a class="wiki_link" href="/Tenney-Euclidean%20metrics">Tenney-Euclidean metrics</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="/Cangwu%20badness">Cangwu badness</a><br /> | ||
<a class="wiki_link" href="/Fractional%20monzos">Fractional monzos</a><br /> | <a class="wiki_link" href="/Fractional%20monzos">Fractional monzos</a><br /> | ||
< | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Lattices and Scales"></a><!-- ws:end:WikiTextHeadingRule:8 -->Lattices and Scales</h2> | ||
<a class="wiki_link" href="/Minkowski%20blocks">Minkowski blocks</a><br /> | |||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/Transversal">Transversal</a><br /> | ||
<a class="wiki_link" href="/ | |||
<a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">The Seven Limit Symmetrical Lattices</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="/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="x-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="/Modulatory%20space">Modulatory space</a><br /> | ||
<a class="wiki_link" href="/Chordal%20space">Chordal 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="/k%2AN%20subgroups">k*N subgroups</a><br /> | ||
<a class="wiki_link" href="/Don%20Page%20comma">Don Page comma</a></body></html></pre></div> | <a class="wiki_link" href="/Don%20Page%20comma">Don Page comma</a></body></html></pre></div> | ||