Mathematical theory: Difference between revisions
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m →Regular Temperaments: merged the article into Wedgies and Multivals ("Wedgie" may be a better title) |
Added some new stuff and better organized the links |
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* [[MODMOS scales]] | * [[MODMOS scales]] | ||
* [[Graph-theoretic properties of scales]] | * [[Graph-theoretic properties of scales]] | ||
== Regular Temperaments == | == Regular Temperaments == | ||
=== Basics === | |||
* [[Monzos and Interval Space]] | * [[Monzos and Interval Space]] | ||
* [[Vals and Tuning Space]] | * [[Vals and Tuning Space]] | ||
* [[Temperament Mapping Matrices]] | |||
* [[Regular Temperaments]] | * [[Regular Temperaments]] | ||
* [[Saturation]] | * [[Saturation]] | ||
=== Subgroup Temperaments === | |||
* [[Subgroup Temperament Families, Relationships, and Genes]] | |||
* [[ | * [[Smonzos and Svals|Subgroup Monzos ("smonzos") and Subgroup Vals ("svals")]] | ||
* [[Tmonzos and Tvals|Tempered Monzos ("tmonzos") and Tempered Vals ("tvals")]] | * [[Tmonzos and Tvals|Tempered Monzos ("tmonzos") and Tempered Vals ("tvals")]] | ||
* [[Subgroup | * [[Subgroup Basis Matrices (V-maps)]] | ||
* [[ | * [[Meet and Join]] | ||
* [[ | * [[Sane and Insane Temperaments]] | ||
* [[ | * [[k*N subgroups]] | ||
=== Exterior algebra === | |||
* [[Wedgies and Multivals]] | * [[Wedgies and Multivals]] | ||
* [[Recoverability]] | * [[Recoverability]] | ||
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* [[Interior product]] | * [[Interior product]] | ||
=== Temperament representations === | |||
* [[Abstract regular temperament]] | * [[Abstract regular temperament]] | ||
* [[Normal lists]] | * [[Normal lists]] | ||
* [[Gencom]] | * [[Gencom]] | ||
* [[Dual list]] | |||
* [[ | |||
=== Temperament Measures and Optimization === | === Temperament Measures and Optimization === | ||
* [[TOP tuning]] | * [[TOP tuning]] | ||
* [[Tenney-Euclidean Tuning]] | * [[Tenney-Euclidean Tuning]] | ||
* [[Tenney-Euclidean temperament measures]] | * [[Tenney-Euclidean temperament measures]] | ||
* [[Tenney-Euclidean metrics]] | * [[Tenney-Euclidean metrics]] | ||
* [[Generalized Tenney Norms and Tp Interval Space]] | |||
* [[Generalized Tenney Dual Norms and Tp Tuning Space]] | |||
* [[Tp tuning]] | |||
* [[Target tunings]] | |||
* [[Cangwu badness]] | * [[Cangwu badness]] | ||
* [[Fractional monzos]] | * [[Fractional monzos]] | ||
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=== Lattices and Scales === | === Lattices and Scales === | ||
* [[Transversal]] | * [[Transversal]] | ||
* [[Transversal generators]] | |||
* [[Fokker blocks]] | * [[Fokker blocks]] | ||
* [[Weak Fokker blocks]] | * [[Weak Fokker blocks]] | ||
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* [[Hahn distance]] | * [[Hahn distance]] | ||
* [[Comma-based lattices]] | * [[Comma-based lattices]] | ||
=== Other === | === Other === | ||
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* [[Modulatory space]] | * [[Modulatory space]] | ||
* [[Chordal space]] | * [[Chordal space]] | ||
* [[Logarithmic approximants]] | * [[Logarithmic approximants]] | ||
* [[Don Page comma]] | * [[Don Page comma]] | ||
* [[ABC, High Quality Commas, and Epimericity]] | * [[ABC, High Quality Commas, and Epimericity]] | ||
* [[Planar Temperament]] | |||
== Musical Information Theory == | |||
* [[Harmonic Entropy]] | |||
* [[Categorical Entropy, Mutual Information, and Channel Capacity]] | |||
[[Category:links]] | [[Category:links]] | ||
Revision as of 17:44, 8 May 2021
Español Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.
Scale Basics
Regular Temperaments
Basics
- Monzos and Interval Space
- Vals and Tuning Space
- Temperament Mapping Matrices
- Regular Temperaments
- Saturation
Subgroup Temperaments
- Subgroup Temperament Families, Relationships, and Genes
- Subgroup Monzos ("smonzos") and Subgroup Vals ("svals")
- Tempered Monzos ("tmonzos") and Tempered Vals ("tvals")
- Subgroup Basis Matrices (V-maps)
- Meet and Join
- Sane and Insane Temperaments
- k*N subgroups
Exterior algebra
Temperament representations
Temperament Measures and Optimization
- TOP tuning
- Tenney-Euclidean Tuning
- Tenney-Euclidean temperament measures
- Tenney-Euclidean metrics
- Generalized Tenney Norms and Tp Interval Space
- Generalized Tenney Dual Norms and Tp Tuning Space
- Tp tuning
- Target tunings
- Cangwu badness
- Fractional monzos
- Generator complexity
Lattices and Scales
- Transversal
- Transversal generators
- Fokker blocks
- Weak Fokker blocks
- Minkowski reduced bases for Fokker groups of certain vals
- Minkowski blocks
- The Seven Limit Symmetrical Lattices
- Tablets
- Hahn distance
- Comma-based lattices
Other
- The Riemann Zeta Function and Tuning
- Modulatory space
- Chordal space
- Logarithmic approximants
- Don Page comma
- ABC, High Quality Commas, and Epimericity
- Planar Temperament