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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | en = Mathematical theory |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-23 23:23:34 UTC</tt>.<br>
| | | de = |
| : The original revision id was <tt>347567134</tt>.<br>
| | | es = Teoría Profunda |
| : The revision comment was: <tt></tt><br>
| | | ja = |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | }} |
| <h4>Original Wikitext content:</h4>
| | 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.
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| [[Periodic scale]] | | It is recommended to read the pages listed on [[general theory]] first before exploring this page, as they lay the groundwork. |
| [[Mathematics of MOS|MOS scales]] | | |
| <span class="PageTitle">[[Mathematics of MOS]]</span>
| | == Intervals == |
| [[MODMOS scales]] | | === Interval metrics === |
| [[Monzos and Interval Space]] | | * [[Height]] |
| [[Vals and Tuning Space]] | | * [[Benedetti height]] |
| [[Smonzos and Svals]] | | * [[Tenney norm]] |
| [[Wedgies and Multivals]] | | * [[Kees seminorm]] |
| [[The wedgie]] | | * [[Wilson norm]] |
| [[Interior product]] | | * [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space|Weil norm and Tenney–Weil norm]] |
| [[The dual]] | | |
| [[TOP tuning]] | | === Chords === |
| [[Lp tuning]] | | * [[Chordal space]] |
| [[Tenney-Euclidean tuning]] | | * [[Chord complexity]] |
| [[Tenney-Euclidean temperament measures]] | | * [[Chord matrices]] |
| [[Tenney-Euclidean metrics]] | | * [[Permutation product set]] |
| [[Cangwu badness]] | | * [[Tablet]] |
| [[Generator complexity]] | | |
| [[The Riemann Zeta Function and Tuning]] | | === Musical information theory === |
| [[Fractional monzos]] | | * [[Categorical entropy, mutual information, and channel capacity]] |
| [[Saturation]] | | * [[Harmonic entropy]] |
| [[Abstract regular temperament]] | | * [[The Riemann zeta function and tuning]] |
| [[Target tunings]] | | * [[Maximal dissonance tuning]] |
| [[Normal lists]] | | |
| [[Planar Temperament]] | | === Interval classification === |
| [[The Seven Limit Symmetrical Lattices]] | | * [[Delta-N ratio|Delta-''N'' ratio]] |
| [[Tablets]] | | * [[Non radical intervals with musical significance]] |
| [[Modulatory space]] | | * [[Abc, high quality commas, and epimericity|''abc'', high quality commas, and epimericity]] |
| [[Chordal space]] | | * [[Don Page comma]] |
| [[Hahn distance]] | | |
| [[Transversal]] | | == Regular temperaments == |
| [[Transversal generators]] | | === Foundational theory === |
| [[Gencom]] | | * [[Mathematical theory of regular temperaments]] |
| [[Minkowski blocks]] | | * [[Monzos and interval space]] |
| [[k*N subgroups]] | | ** [[Radical interval]] |
| [[Don Page comma]]</pre></div> | | * [[Vals and tuning space]] |
| <h4>Original HTML content:</h4> | | * [[Temperament mapping matrix]] |
| <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 /> | | * [[Dual list]] |
| <br />
| | * [[Mathematical theory of saturation]] |
| <a class="wiki_link" href="/Periodic%20scale">Periodic scale</a><br />
| | * [[Temperament merging]] |
| <a class="wiki_link" href="/Mathematics%20of%20MOS">MOS scales</a><br />
| | * [[Temperament addition]] |
| <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 />
| | === Subgroup temperaments === |
| <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">Monzos and Interval Space</a><br />
| | * [[Subgroup temperament families, relationships, and genes]] |
| <a class="wiki_link" href="/Vals%20and%20Tuning%20Space">Vals and Tuning Space</a><br />
| | * [[Subgroup monzos and vals]] |
| <a class="wiki_link" href="/Smonzos%20and%20Svals">Smonzos and Svals</a><br />
| | * [[Tempered monzos and vals]] |
| <a class="wiki_link" href="/Wedgies%20and%20Multivals">Wedgies and Multivals</a><br />
| | * [[Subgroup basis matrix]] |
| <a class="wiki_link" href="/The%20wedgie">The wedgie</a><br />
| | * [[Meet and join]] |
| <a class="wiki_link" href="/Interior%20product">Interior product</a><br />
| | * [[k*N subgroups]] |
| <a class="wiki_link" href="/The%20dual">The dual</a><br />
| | |
| <a class="wiki_link" href="/TOP%20tuning">TOP tuning</a><br />
| | === Exterior algebra === |
| <a class="wiki_link" href="/Lp%20tuning">Lp tuning</a><br />
| | * [[Exterior algebra]] |
| <a class="wiki_link" href="/Tenney-Euclidean%20tuning">Tenney-Euclidean tuning</a><br />
| | * [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT]] |
| <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures">Tenney-Euclidean temperament measures</a><br />
| | * [[Wedgie]] and [[Plücker coordinates]] |
| <a class="wiki_link" href="/Tenney-Euclidean%20metrics">Tenney-Euclidean metrics</a><br />
| | * [[Recoverability]] |
| <a class="wiki_link" href="/Cangwu%20badness">Cangwu badness</a><br />
| | * [[Hodge dual]] |
| <a class="wiki_link" href="/Generator%20complexity">Generator complexity</a><br />
| | * [[Interior product]] |
| <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning">The Riemann Zeta Function and Tuning</a><br />
| | |
| <a class="wiki_link" href="/Fractional%20monzos">Fractional monzos</a><br />
| | === Temperament measures and optimization === |
| <a class="wiki_link" href="/Saturation">Saturation</a><br />
| | * [[Optimization]] |
| <a class="wiki_link" href="/Abstract%20regular%20temperament">Abstract regular temperament</a><br />
| | * [[Target tuning]] |
| <a class="wiki_link" href="/Target%20tunings">Target tunings</a><br />
| | * [[Cangwu badness]] |
| <a class="wiki_link" href="/Normal%20lists">Normal lists</a><br />
| | * [[Generator complexity]] |
| <a class="wiki_link" href="/Planar%20Temperament">Planar Temperament</a><br />
| | * [[TOP tuning]] |
| <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">The Seven Limit Symmetrical Lattices</a><br />
| | * [[BOP tuning]] |
| <a class="wiki_link" href="/Tablets">Tablets</a><br />
| | * [[Tenney–Euclidean tuning]] |
| <a class="wiki_link" href="/Modulatory%20space">Modulatory space</a><br />
| | * [[Tenney–Euclidean temperament measures]] |
| <a class="wiki_link" href="/Chordal%20space">Chordal space</a><br />
| | * [[Tenney–Euclidean metrics]] |
| <a class="wiki_link" href="/Hahn%20distance">Hahn distance</a><br />
| | * [[Generalized Tenney norms and Tp interval space|Generalized Tenney norms and T<sub>''p''</sub> interval space]] |
| <a class="wiki_link" href="/Transversal">Transversal</a><br />
| | * [[Generalized Tenney dual norms and Tp tuning space|Generalized Tenney dual norms and T<sub>''p''</sub> tuning space]] |
| <a class="wiki_link" href="/Transversal%20generators">Transversal generators</a><br />
| | * [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space|Weil norm, Tenney–Weil norm, and TW<sub>''p''</sub> interval and tuning space]] |
| <a class="wiki_link" href="/Gencom">Gencom</a><br />
| | * [[Tp tuning|T<sub>''p''</sub> tuning]] |
| <a class="wiki_link" href="/Minkowski%20blocks">Minkowski blocks</a><br />
| | * [[Constrained tuning]] |
| <a class="wiki_link" href="/k%2AN%20subgroups">k*N subgroups</a><br />
| | * [[Logarithmic approximants]] |
| <a class="wiki_link" href="/Don%20Page%20comma">Don Page comma</a></body></html></pre></div>
| | |
| | === Temperament classification === |
| | * [[Rank-2 temperament]] (include linear temperaments) |
| | * [[Rank-3 temperament]] (include planar temperaments) |
| | (''Rank-1 temperaments are [[equal-step tuning]]s''.) |
| | * [[Temperament families and clans]] |
| | * [[Cluster temperament]] |
| | * [[Associated temperament]] |
| | * [[Microtemperament]] and [[exotemperament]] |
| | * [[Trivial temperament]] |
| | * [[Sane and insane temperaments]] |
| | |
| | == Scales == |
| | === MOS scales === |
| | * [[Periodic scale]] |
| | * [[MOS scale]] |
| | * [[Mathematics of MOS]] |
| | * [[MODMOS scale]] |
| | * [[Modal UDP Notation]] |
| | * [[Graph-theoretic properties of scales]] |
| | |
| | === Scale measurements === |
| | * [[Consonant class scale]] |
| | * [[Distributional evenness]] |
| | * [[Maximum variety]] |
| | * [[Lumma stability]] |
| | * [[Structure metric]] |
| | * [[Hahn distance]] |
| | |
| | === Lattices and scale shapes === |
| | * [[Projection pair]] |
| | * [[Modulatory space]] |
| | * [[Detempering]] |
| | * [[Generator preimage]] |
| | * [[Fokker block]] |
| | * [[Minkowski block]] |
| | * [[Minkowski reduced bases for Fokker groups of certain vals]] |
| | * [[7-limit symmetrical lattices]] |
| | * [[Comma-based lattices]] |
| | === Combinatorics on words === |
| | * [[Ternary scale theorems]] |
| | |
| | == More pages == |
| | * [[:Category: Theory]] |
| | * [[:Category: Math]] |
| | |
| | [[Category:Math]] |
| | [[Category:Theory]] |