Mathematical theory: Difference between revisions

Inthar (talk | contribs)
m Regular Temperaments: merged the article into Wedgies and Multivals ("Wedgie" may be a better title)
Mike Battaglia (talk | contribs)
Added some new stuff and better organized the links
Line 8: Line 8:
* [[MODMOS scales]]
* [[MODMOS scales]]
* [[Graph-theoretic properties of scales]]
* [[Graph-theoretic properties of scales]]


== Regular Temperaments ==
== Regular Temperaments ==
'''Basics:'''
=== 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]]
* [[Dual list]]
* [[Meet and Join]]


'''Linear algebra:'''
=== Subgroup Temperaments ===
 
* [[Subgroup Temperament Families, Relationships, and Genes]]
* [[Temperament Mapping Matrices (M-maps)]]
* [[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 Mapping Matrices (V-maps)]]
* [[Subgroup Basis Matrices (V-maps)]]
* [[Smonzos and Svals|Subgroup Monzos ("smonzos") and Subgroup Vals ("svals")]]
* [[Meet and Join]]
* [[Generalized Tenney Norms and Tp Interval Space]]
* [[Sane and Insane Temperaments]]
* [[Generalized Tenney Dual Norms and Tp Tuning Space]]
* [[k*N subgroups]]
 
'''Exterior algebra:'''


=== Exterior algebra ===
* [[Wedgies and Multivals]]
* [[Wedgies and Multivals]]
* [[Recoverability]]
* [[Recoverability]]
Line 36: Line 32:
* [[Interior product]]
* [[Interior product]]


'''Temperament representations:'''
=== Temperament representations ===
 
* [[Abstract regular temperament]]
* [[Abstract regular temperament]]
* [[Normal lists]]
* [[Normal lists]]
* [[Gencom]]
* [[Gencom]]
 
* [[Dual list]]
'''Other:'''
 
* [[Planar Temperament]]
* [[Transversal generators]]


=== Temperament Measures and Optimization ===
=== Temperament Measures and Optimization ===
* [[Target tunings]]
* [[TOP tuning]]
* [[TOP tuning]]
* [[Tp 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]]
Line 60: Line 53:
=== Lattices and Scales ===
=== Lattices and Scales ===
* [[Transversal]]
* [[Transversal]]
* [[Transversal generators]]
* [[Fokker blocks]]
* [[Fokker blocks]]
* [[Weak Fokker blocks]]
* [[Weak Fokker blocks]]
Line 68: Line 62:
* [[Hahn distance]]
* [[Hahn distance]]
* [[Comma-based lattices]]
* [[Comma-based lattices]]
=== Information Theory ===
* [[Harmonic Entropy]]
* [[Categorical Entropy, Mutual Information, and Channel Capacity]]


=== Other ===
=== Other ===
Line 77: Line 67:
* [[Modulatory space]]
* [[Modulatory space]]
* [[Chordal space]]
* [[Chordal space]]
* [[k*N subgroups]]
* [[Logarithmic approximants]]
* [[Logarithmic approximants]]
* [[Don Page comma]]
* [[Don Page comma]]
* [[Sane and Insane Temperaments]]
* [[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]]