Mathematical theory: Difference between revisions

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-<span style="display: block; text-align: right;">[[Teoría_Profunda|Español]]</span>
+{{interwiki
-Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.
+| en = Mathematical theory
+| de =
+| es = Teoría Profunda
+| ja =
+}}
+Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.
-== Scale Basics ==
+It is recommended to read the pages listed on [[general theory]] first before exploring this page, as they lay the groundwork.
-* [[Periodic scale]]
-* [[MOS scales]]
-* [[Mathematics of MOS]]
-* [[MODMOS scales]]
-* [[Graph-theoretic properties of scales]]
-== Regular Temperaments ==
+== Intervals ==
-'''Basics:'''
+=== Interval metrics ===
+* [[Height]]
+* [[Benedetti height]]
+* [[Tenney norm]]
+* [[Kees seminorm]]
+* [[Wilson norm]]
+* [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space|Weil norm and Tenney–Weil norm]]
-* [[Monzos and Interval Space]]
+=== Chords ===
-* [[Vals and Tuning Space]]
+* [[Chordal space]]
-* [[Regular Temperaments]]
+* [[Chord complexity]]
-* [[Saturation]]
+* [[Chord matrices]]
-* [[Dual list]]
+* [[Permutation product set]]
-* [[Meet and Join]]
+* [[Tablet]]
-'''Linear algebra:'''
+=== Musical information theory ===
+* [[Categorical entropy, mutual information, and channel capacity]]
+* [[Harmonic entropy]]
+* [[The Riemann zeta function and tuning]]
+* [[Maximal dissonance tuning]]
-* [[Temperament Mapping Matrices (M-maps)]]
+=== Interval classification ===
-* [[Tmonzos and Tvals]]
+* [[Delta-N ratio|Delta-''N'' ratio]]
-* [[Subgroup Mapping Matrices (V-maps)]]
+* [[Non radical intervals with musical significance]]
-* [[Smonzos and Svals]]
+* [[Abc, high quality commas, and epimericity|''abc'', high quality commas, and epimericity]]
-* [[Generalized Tenney Norms and Tp Interval Space]]
+* [[Don Page comma]]
-* [[Generalized Tenney Dual Norms and Tp Tuning Space]]
-'''Exterior algebra:'''
+== Regular temperaments ==
+=== Foundational theory ===
+* [[Mathematical theory of regular temperaments]]
+* [[Monzos and interval space]]
+** [[Radical interval]]
+* [[Vals and tuning space]]
+* [[Temperament mapping matrix]]
+* [[Dual list]]
+* [[Mathematical theory of saturation]]
+* [[Temperament merging]]
+* [[Temperament addition]]
-* [[Wedgies and Multivals]]
+=== Subgroup temperaments ===
-* [[The wedgie]]
+* [[Subgroup temperament families, relationships, and genes]]
+* [[Subgroup monzos and vals]]
+* [[Tempered monzos and vals]]
+* [[Subgroup basis matrix]]
+* [[Meet and join]]
+* [[k*N subgroups]]
+=== Exterior algebra ===
+* [[Exterior algebra]]
+* [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT]]
+* [[Wedgie]] and [[Plücker coordinates]]
 * [[Recoverability]]
-* [[The dual]]
+* [[Hodge dual]]
 * [[Interior product]]
-'''Abstract algebra:'''
+=== Temperament measures and optimization ===
+* [[Optimization]]
+* [[Target tuning]]
+* [[Cangwu badness]]
+* [[Generator complexity]]
+* [[TOP tuning]]
+* [[BOP tuning]]
+* [[Tenney–Euclidean tuning]]
+* [[Tenney–Euclidean temperament measures]]
+* [[Tenney–Euclidean metrics]]
+* [[Generalized Tenney norms and Tp interval space|Generalized Tenney norms and T<sub>''p''</sub> interval space]]
+* [[Generalized Tenney dual norms and Tp tuning space|Generalized Tenney dual norms and T<sub>''p''</sub> tuning space]]
+* [[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]]
+* [[Tp tuning|T<sub>''p''</sub> tuning]]
+* [[Constrained tuning]]
+* [[Logarithmic approximants]]
-* [[Groups, Lattices, Z-modules and Vector spaces]]
+=== 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]]
-'''Temperament representations:'''
+== Scales ==
+=== MOS scales ===
+* [[Periodic scale]]
+* [[MOS scale]]
+* [[Mathematics of MOS]]
+* [[MODMOS scale]]
+* [[Modal UDP Notation]]
+* [[Graph-theoretic properties of scales]]
-* [[Abstract regular temperament]]
+=== Scale measurements ===
-* [[Normal lists]]
+* [[Consonant class scale]]
-* [[Gencom]]
+* [[Distributional evenness]]
+* [[Maximum variety]]
+* [[Lumma stability]]
+* [[Structure metric]]
+* [[Hahn distance]]
-'''Other:'''
+=== Lattices and scale shapes ===
+* [[Projection pair]]
-* [[Planar Temperament]]
+* [[Modulatory space]]
-* [[Transversal generators]]
+* [[Detempering]]
+* [[Generator preimage]]
-=== Temperament Measures and Optimization ===
+* [[Fokker block]]
-* [[Target tunings]]
+* [[Minkowski block]]
-* [[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]]
 * [[Minkowski reduced bases for Fokker groups of certain vals]]
-* [[Minkowski blocks]]
+* [[7-limit symmetrical lattices]]
-* [[The Seven Limit Symmetrical Lattices]]
-* [[Tablets]]
-* [[Hahn distance]]
 * [[Comma-based lattices]]
+=== Combinatorics on words ===
+* [[Ternary scale theorems]]
-=== Other ===
+== More pages ==
-* [[The Riemann Zeta Function and Tuning]]
+* [[:Category: Theory]]
-* [[Modulatory space]]
+* [[:Category: Math]]
-* [[Chordal space]]
-* [[k*N subgroups]]
-* [[Logarithmic approximants]]
-* [[Don Page comma]]
-* [[Sane and Insane Temperaments]]
-* [[ABC, High Quality Commas, and Epimericity]]
-[[Category:links]]
+[[Category:Math]]
-[[Category:math]]
+[[Category:Theory]]
-[[Category:overview]]
-[[Category:theory]]