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. | Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters. | ||
== | == Intervals == | ||
=== | === Interval metrics === | ||
* [[ | * [[Height]] | ||
* [[ | * [[Benedetti height]] | ||
* [[ | * [[Tenney height]] | ||
* [[ | * [[Kees height]] | ||
* [[ | * [[Wilson height]] | ||
* [[Weil height and Tenney-Weil height]] | |||
* [[Abc, high quality commas, and epimericity]] | |||
=== Chords === | |||
* [[Chord complexity]] | |||
* [[Chord matrices]] | |||
* [[Chordal space]] | |||
=== Musical information theory === | |||
* [[Harmonic entropy]] | |||
* [[Categorical Entropy, Mutual Information, and Channel Capacity]] | |||
* [[The Riemann zeta function and tuning]] | |||
* [[Maximal dissonance tuning]] | |||
=== Interval classification === | |||
* [[Delta-N ratio]] | |||
* [[Non radical intervals with musical significance]] | |||
* [[Abc, high quality commas, and epimericity|''abc'', high quality commas, and epimericity]] | |||
* [[Don Page comma]] | |||
=== | === Lists of factorizations === | ||
* [[ | * [[List of 3-limit factorizations]] | ||
* [[ | * [[List of 5-limit factorizations]] | ||
* [[ | * [[List of 7-limit factorizations]] | ||
* [[ | * [[List of 11-limit factorizations]] | ||
* [[ | * [[List of 13-limit factorizations]] | ||
== Regular temperaments == | == Regular temperaments == | ||
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* [[Cluster temperament]] | * [[Cluster temperament]] | ||
== | == Scales == | ||
=== | === Basics === | ||
* [[ | * [[Periodic scale]] | ||
* [[ | * [[MOS scales]] | ||
* [[ | * [[Mathematics of MOS]] | ||
* [[ | * [[MODMOS scales]] | ||
* [[ | * [[Graph-theoretic properties of scales]] | ||
=== | === Lattices and scale shapes === | ||
* [[ | * [[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]] | |||
* [[Consonant class scale]] | |||
* [[ | * [[Distributional evenness]] | ||
* [[ | * [[Maximum variety]] | ||
* [[ | |||
* [[ | |||
* [[ | |||
* [[ | |||
== Other == | == Other == | ||