Mathematical theory: Difference between revisions
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{{interwiki | |||
| en = Mathematical theory | |||
| de = | |||
| es = Teoría Profunda | |||
| ja = | |||
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Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters. | Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters. | ||
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* [[Height]] | * [[Height]] | ||
* [[Benedetti height]] | * [[Benedetti height]] | ||
* [[Tenney | * [[Tenney norm]] | ||
* [[Kees | * [[Kees seminorm]] | ||
* [[Wilson | * [[Wilson norm]] | ||
* [[Weil | * [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space|Weil norm and Tenney–Weil norm]] | ||
=== Chords === | === Chords === | ||
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=== Musical information theory === | === Musical information theory === | ||
* [[Categorical | * [[Categorical entropy, mutual information, and channel capacity]] | ||
* [[Harmonic entropy]] | * [[Harmonic entropy]] | ||
* [[The Riemann zeta function and tuning]] | * [[The Riemann zeta function and tuning]] | ||
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=== Interval classification === | === Interval classification === | ||
* [[Delta-N ratio]] | * [[Delta-N ratio|Delta-''N'' ratio]] | ||
* [[Non radical intervals with musical significance]] | * [[Non radical intervals with musical significance]] | ||
* [[Abc, high quality commas, and epimericity|''abc'', high quality commas, and epimericity]] | * [[Abc, high quality commas, and epimericity|''abc'', high quality commas, and epimericity]] | ||
* [[Don Page comma]] | * [[Don Page comma]] | ||
== Regular temperaments == | == Regular temperaments == | ||
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* [[Mathematical theory of regular temperaments]] | * [[Mathematical theory of regular temperaments]] | ||
* [[Monzos and interval space]] | * [[Monzos and interval space]] | ||
** [[ | ** [[Radical interval]] | ||
* [[Vals and tuning space]] | * [[Vals and tuning space]] | ||
* [[Temperament mapping | * [[Temperament mapping matrix]] | ||
* [[Dual list]] | * [[Dual list]] | ||
* [[Mathematical theory of saturation]] | * [[Mathematical theory of saturation]] | ||
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=== Subgroup temperaments === | === Subgroup temperaments === | ||
* [[Subgroup | * [[Subgroup temperament families, relationships, and genes]] | ||
* [[ | * [[Subgroup monzos and vals]] | ||
* [[ | * [[Tempered monzos and vals]] | ||
* [[Subgroup basis | * [[Subgroup basis matrix]] | ||
* [[Meet and join]] | * [[Meet and join]] | ||
* [[k*N subgroups]] | * [[k*N subgroups]] | ||
=== Exterior algebra === | === Exterior algebra === | ||
* [[Exterior algebra]] | |||
* [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT]] | * [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT]] | ||
* | * [[Wedgie]] and [[Plücker coordinates]] | ||
* [[Recoverability]] | * [[Recoverability]] | ||
* [[ | * [[Hodge dual]] | ||
* [[Interior product]] | * [[Interior product]] | ||
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* [[TOP tuning]] | * [[TOP tuning]] | ||
* [[BOP tuning]] | * [[BOP tuning]] | ||
* [[ | * [[Tenney–Euclidean tuning]] | ||
* [[ | * [[Tenney–Euclidean temperament measures]] | ||
* [[ | * [[Tenney–Euclidean metrics]] | ||
* [[Generalized Tenney norms and Tp interval space]] | * [[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 Tp tuning space|Generalized Tenney dual norms and T<sub>''p''</sub> tuning space]] | ||
* [[Weil norm, | * [[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]] | * [[Tp tuning|T<sub>''p''</sub> tuning]] | ||
* [[Constrained tuning]] | * [[Constrained tuning]] | ||
* [[Logarithmic approximants]] | * [[Logarithmic approximants]] | ||
=== Temperament classification === | === Temperament classification === | ||
* [[Rank-2 temperament]] | * [[Rank-2 temperament]] (include linear temperaments) | ||
* [[Rank-3 temperament]] | * [[Rank-3 temperament]] (include planar temperaments) | ||
(''Rank-1 temperaments are [[equal-step tuning]]s''.) | (''Rank-1 temperaments are [[equal-step tuning]]s''.) | ||
* [[Temperament families and clans]] | * [[Temperament families and clans]] | ||
* [[Cluster temperament]] | * [[Cluster temperament]] | ||
* [[Associated temperament]] | * [[Associated temperament]] | ||
* [[Microtemperament]] | * [[Microtemperament]] and [[exotemperament]] | ||
* [[Trivial temperament]] | |||
* [[Trivial temperament]] | |||
* [[Sane and insane temperaments]] | * [[Sane and insane temperaments]] | ||
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=== MOS scales === | === MOS scales === | ||
* [[Periodic scale]] | * [[Periodic scale]] | ||
* [[MOS | * [[MOS scale]] | ||
* [[Mathematics of MOS]] | * [[Mathematics of MOS]] | ||
* [[MODMOS | * [[MODMOS scale]] | ||
* [[Modal UDP Notation]] | * [[Modal UDP Notation]] | ||
* [[Graph-theoretic properties of scales]] | * [[Graph-theoretic properties of scales]] | ||
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* [[Projection pair]] | * [[Projection pair]] | ||
* [[Modulatory space]] | * [[Modulatory space]] | ||
* [[ | * [[Detempering]] | ||
* [[ | * [[Generator preimage]] | ||
* [[Fokker | * [[Fokker block]] | ||
* [[Minkowski block]] | |||
* [[Minkowski | |||
* [[Minkowski reduced bases for Fokker groups of certain vals]] | * [[Minkowski reduced bases for Fokker groups of certain vals]] | ||
* [[ | * [[7-limit symmetrical lattices]] | ||
* [[Comma-based lattices]] | * [[Comma-based lattices]] | ||
== More pages == | == More pages == | ||
* [[: | * [[:Category: Theory]] | ||
* [[: | * [[:Category: Math]] | ||
[[Category:Math]] | [[Category:Math]] | ||
[[Category:Theory]] | [[Category:Theory]] | ||