Mathematical theory: Difference between revisions
| (53 intermediate revisions by 10 users not shown) | |||
| Line 1: | Line 1: | ||
{{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. | |||
== | 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]] | |||
* [[The Riemann zeta function and tuning]] | |||
* [[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 | == Regular temperaments == | ||
=== | === Foundational theory === | ||
* [[Monzos and | * [[Mathematical theory of regular temperaments]] | ||
* [[Vals and | * [[Monzos and interval space]] | ||
* [[Temperament | ** [[Radical interval]] | ||
* [[Vals and tuning space]] | |||
* [[Temperament mapping matrix]] | |||
* [[Dual list]] | * [[Dual list]] | ||
* [[Mathematical theory of | * [[Mathematical theory of saturation]] | ||
* [[ | * [[Temperament merging]] | ||
* [[Temperament addition]] | |||
=== Subgroup | === Subgroup temperaments === | ||
* [[Subgroup | * [[Subgroup temperament families, relationships, and genes]] | ||
* [[ | * [[Subgroup monzos and vals]] | ||
* [[ | * [[Tempered monzos and vals]] | ||
* [[Subgroup | * [[Subgroup basis matrix]] | ||
* [[Meet and | * [[Meet and join]] | ||
* [[k*N subgroups]] | * [[k*N subgroups]] | ||
=== | === Exterior algebra === | ||
* [[ | * [[Exterior algebra]] | ||
* [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT]] | |||
* [[Wedgie]] and [[Plücker coordinates]] | |||
* [[Recoverability]] | * [[Recoverability]] | ||
* [[ | * [[Hodge dual]] | ||
* [[Interior product]] | * [[Interior product]] | ||
=== Temperament | === Temperament measures and optimization === | ||
* [[Optimization]] | |||
* [[Target tuning]] | |||
* [[Cangwu badness]] | |||
* [[Generator complexity]] | |||
* [[TOP tuning]] | * [[TOP tuning]] | ||
* [[BOP tuning]] | * [[BOP tuning]] | ||
* [[Generalized Tenney | * [[Tenney–Euclidean tuning]] | ||
* [[Generalized Tenney | * [[Tenney–Euclidean temperament measures]] | ||
* [[Tp tuning]] | * [[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]] | |||
* [[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]] | * [[Hahn distance]] | ||
=== | === Lattices and scale shapes === | ||
* [[ | * [[Projection pair]] | ||
* [[Modulatory space]] | * [[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: | [[Category:Math]] | ||
[[Category: | [[Category:Theory]] | ||