Mathematical theory: Difference between revisions

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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.

* [[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]]

* [[Chordal space]]

* [[Chord complexity]]

* [[Chord matrices]]

* [[Permutation product set]]

* [[Tablet]]

* [[Categorical entropy, mutual information, and channel capacity]]

* [[The Riemann zeta function and tuning]]

* [[Maximal dissonance tuning]]

* [[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]]

** [[Radical interval]]

* [[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 ===

* [[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_''p'' interval space]]

* [[Generalized Tenney dual norms and Tp tuning space|Generalized Tenney dual norms and T_''p'' tuning space]]

* [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space|Weil norm, Tenney–Weil norm, and TW_''p'' interval and tuning space]]

* [[Tp tuning|T_''p'' tuning]]

 

=== 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]]

* [[Sane and insane temperaments]]

 

== Scales ==

=== MOS scales ===

* [[Graph-theoretic properties of scales]]

 

=== Scale measurements ===

 

=== Lattices and scale shapes ===

* [[Generator preimage]]

* [[Fokker block]]

* [[Minkowski reduced bases for Fokker groups of certain vals]]

=== Combinatorics on words ===

 

== More pages ==

* [[:Category: Math]]

 

[[Category:Theory]]