View source for 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. 

It is recommended to read the pages listed on [[general theory]] first before exploring this page, as they lay the groundwork.

== Intervals ==
=== 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]]

=== Chords ===
* [[Chordal space]]
* [[Chord complexity]]
* [[Chord matrices]]
* [[Permutation product set]]
* [[Tablet]]

=== Musical information theory ===
* [[Categorical entropy, mutual information, and channel capacity]]
* [[Harmonic entropy]]
* [[Riemann zeta function]]
* [[Maximal dissonance tuning]]

=== Interval classification ===
* [[Delta-N ratio|Delta-''N'' ratio]]
* [[Non radical intervals with musical significance]]
* [[Abc, high quality commas, and epimericity|''abc'', high quality commas, and epimericity]]
* [[Don Page comma]]

== 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]]

=== Subgroup temperaments ===
* [[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]]
* [[Hodge dual]]
* [[Interior product]]

=== 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]]

=== 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]]
* [[Microtemperament]] and [[exotemperament]]
* [[Trivial temperament]]
* [[Sane and insane temperaments]]

== Scales ==
=== MOS scales ===
* [[Periodic scale]]
* [[MOS scale]]
* [[Mathematics of MOS]]
* [[MODMOS scale]]
* [[Cluster MOS]]
* [[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]]