Mathematical theory: Difference between revisions
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== Regular Temperaments == | == Regular Temperaments == | ||
=== Basics === | === Basics === | ||
* [[Monzos and | * [[Monzos and interval space]] | ||
* [[Vals and | * [[Vals and tuning space]] | ||
* [[Temperament | * [[Temperament mapping matrices]] | ||
* [[Dual list]] | * [[Dual list]] | ||
* [[Mathematical theory of regular temperaments]] | * [[Mathematical theory of regular temperaments]] | ||
* [[Mathematical theory of saturation | * [[Mathematical theory of saturation]] | ||
=== Subgroup Temperaments === | === Subgroup Temperaments === | ||
* [[Subgroup Temperament Families, Relationships, and Genes]] | * [[Subgroup Temperament Families, Relationships, and Genes]] | ||
* [[Smonzos and | * [[Smonzos and svals|Subgroup monzos ("smonzos") and subgroup vals ("svals")]] | ||
* [[Tmonzos and | * [[Tmonzos and tvals|Tempered monzos ("tmonzos") and tempered vals ("tvals")]] | ||
* [[Subgroup | * [[Subgroup basis matrices]] | ||
* [[Meet and | * [[Meet and join]] | ||
* [[Sane and | * [[Sane and insane temperaments]] | ||
* [[k*N subgroups]] | * [[k*N subgroups]] | ||
=== | === Exterior algebra === | ||
* [[Wedgies and | * [[Wedgies and multivals]] | ||
* [[Recoverability]] | * [[Recoverability]] | ||
* [[The dual]] | * [[The dual]] | ||
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=== Temperament Measures and Optimization === | === Temperament Measures and Optimization === | ||
* [[TOP tuning]] | * [[TOP tuning]] | ||
* [[Tenney-Euclidean | * [[Tenney-Euclidean tuning]] | ||
* [[Tenney-Euclidean temperament measures]] | * [[Tenney-Euclidean temperament measures]] | ||
* [[Tenney-Euclidean metrics]] | * [[Tenney-Euclidean metrics]] | ||
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=== Other === | === Other === | ||
* [[The Riemann | * [[The Riemann zeta function and tuning]] | ||
* [[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 | * [[Planar temperament]] | ||
* [[Wilson height]] | * [[Wilson height]] | ||
== Musical Information Theory == | == Musical Information Theory == | ||
* [[Harmonic | * [[Harmonic entropy]] | ||
* [[Categorical Entropy, Mutual Information, and Channel Capacity]] | * [[Categorical Entropy, Mutual Information, and Channel Capacity]] | ||
Revision as of 22:55, 19 November 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
- Dual list
- Mathematical theory of regular temperaments
- Mathematical theory of 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
- Meet and join
- Sane and insane temperaments
- k*N subgroups
Exterior algebra
- Wedgies and multivals
- Recoverability
- The dual
- Interior product
- Douglas Blumeyer and Dave Keenan's Intro to exterior algebra for RTT
- Mike's note: Douglas and Dave, having their own interpretation of RTT, sometimes use different terminology than the rest of the stuff here, but this page still has some very good insights and is a worthwhile read.
Temperament Measures and Optimization
- TOP tuning
- Tenney-Euclidean tuning
- Tenney-Euclidean temperament measures
- Tenney-Euclidean metrics
- BOP tuning
- 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
- Wilson height