Mathematical theory: Difference between revisions

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<span style="display: block; text-align: right;">[[Teoría_Profunda|Español]]</span>
<span style="display: block; text-align: right;">[[Teoría_Profunda|Español]]</span>
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.


=Scale Basics=
=Scale Basics=
[[Periodic_scale|Periodic scale]]
* [[Periodic scale]]
 
* [[MOS scales]]
[[Mathematics_of_MOS|MOS scales]]
* [[Mathematics of MOS]]
 
* [[MODMOS scales]]
<span style="">[[Mathematics_of_MOS|Mathematics of MOS]]</span>
* [[Graph-theoretic properties of scales]]
 
[[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]]
* [[Monzos and Interval Space]]
 
* [[Vals and Tuning Space]]
[[Vals_and_Tuning_Space|Vals and Tuning Space]]
* [[Regular Temperaments]]
 
* [[Saturation]]
[[Regular_Temperaments|Regular Temperaments]]
* [[Dual list]]
 
* [[Meet and Join]]
[[Saturation|Saturation]]
 
[[dual_list|Dual List]]
 
[[Meet_and_Join|Meet and Join]]
 


'''Linear algebra:'''
'''Linear algebra:'''


[[Temperament_Mapping_Matrices_(M-maps)|Temperament Mapping Matrices (M-maps)]]
* [[Temperament Mapping Matrices (M-maps)]]
 
* [[Tmonzos and Tvals]]
[[Tmonzos_and_Tvals|Tmonzos and Tvals]]
* [[Subgroup Mapping Matrices (V-maps)]]
 
* [[Smonzos and Svals]]
[[Subgroup_Mapping_Matrices_(V-maps)|Subgroup Mapping Matrices (V-maps)]]
* [[Generalized Tenney Norms and Tp Interval Space]]
 
* [[Generalized Tenney Dual Norms and Tp Tuning Space]]
[[Smonzos_and_Svals|Smonzos and Svals]]
 
[[Generalized_Tenney_Norms_and_Tp_Interval_Space|Generalized Tenney Norms and Tp Interval Space]]
 
[[Generalized_Tenney_Dual_Norms_and_Tp_Tuning_Space|Generalized Tenney Dual Norms and Tp Tuning Space]]
 


'''Exterior algebra:'''
'''Exterior algebra:'''


[[Wedgies_and_Multivals|Wedgies and Multivals]]
* [[Wedgies and Multivals]]
 
* [[The wedgie]]
[[The_wedgie|The wedgie]]
* [[Recoverability]]
 
* [[The dual]]
[[Recoverability|Recoverability]]
* [[Interior product]]
 
[[The_dual|The dual]]
 
[[Interior_product|Interior product]]
 


'''Abstract algebra:'''
'''Abstract algebra:'''


[[Groups,_Lattices,_Z-modules,_and_Vector_Spaces|Groups, Lattices, Z-modules and Vector spaces]]
* [[Groups, Lattices, Z-modules and Vector spaces]]
 


'''Temperament representations:'''
'''Temperament representations:'''


[[Abstract_regular_temperament|Abstract regular temperament]]
* [[Abstract regular temperament]]
 
* [[Normal lists]]
[[Normal_lists|Normal lists]]
* [[Gencom]]
 
[[Gencom|Gencom]]
 


'''Other:'''
'''Other:'''


[[Planar_Temperament|Planar Temperament]]
* [[Planar Temperament]]
 
* [[Transversal generators]]
[[Transversal_generators|Transversal generators]]


==Temperament Measures and Optimization==
==Temperament Measures and Optimization==
[[Target_tunings|Target tunings]]
* [[Target tunings]]
 
* [[TOP tuning]]
[[TOP_tuning|TOP tuning]]
* [[Tp tuning]]
 
* [[Tenney-Euclidean Tuning]]
[[Tp_tuning|Tp tuning]]
* [[Tenney-Euclidean temperament measures]]
 
* [[Tenney-Euclidean metrics]]
[[Tenney-Euclidean_Tuning|Tenney-Euclidean tuning]]
* [[Cangwu badness]]
 
* [[Fractional monzos]]
[[Tenney-Euclidean_temperament_measures|Tenney-Euclidean temperament measures]]
* [[Generator complexity]]
 
[[Tenney-Euclidean_metrics|Tenney-Euclidean metrics]]
 
[[Cangwu_badness|Cangwu badness]]
 
[[Fractional_monzos|Fractional monzos]]
 
[[Generator_complexity|Generator complexity]]


==Lattices and Scales==
==Lattices and Scales==
[[Transversal|Transversal]]
* [[Transversal]]
 
* [[Fokker blocks]]
[[Fokker_blocks|Fokker blocks]]
* [[Weak Fokker blocks]]
 
* [[Minkowski reduced bases for Fokker groups of certain vals]]
[[Weak_Fokker_blocks|Weak Fokker Blocks]]
* [[Minkowski blocks]]
 
* [[The Seven Limit Symmetrical Lattices]]
[[Minkowski_reduced_bases_for_Fokker_groups_of_certain_vals|Minkowski reduced bases for Fokker groups of certain vals]]
* [[Tablets]]
 
* [[Hahn distance]]
[[Minkowski_blocks|Minkowski blocks]]
* [[Comma-based lattices]]
 
[[The_Seven_Limit_Symmetrical_Lattices|The Seven Limit Symmetrical Lattices]]
 
[[Tablets|Tablets]]
 
[[Hahn_distance|Hahn distance]]
 
[[Comma-based_lattices|Comma-based lattices]]


==Other==
==Other==
[[The_Riemann_Zeta_Function_and_Tuning|The Riemann Zeta Function and Tuning]]
* [[The Riemann Zeta Function and Tuning]]
 
* [[Modulatory space]]
[[Modulatory_space|Modulatory space]]
* [[Chordal space]]
 
* [[k*N subgroups]]
[[Chordal_space|Chordal space]]
* [[Logarithmic approximants]]
 
* [[Don Page comma]]
[[k*N_subgroups|k*N subgroups]]
* [[Sane and Insane Temperaments]]
 
* [[ABC, High Quality Commas, and Epimericity]]
[[Logarithmic_approximants|Logarithmic approximants]]
 
[[Don_Page_comma|Don Page comma]]
 
[[Sane_and_Insane_Temperaments|Sane and Insane Temperaments]]


[[ABC,_High_Quality_Commas,_and_Epimericity|ABC, High Quality Commas, and Epimericity]]      [[Category:links]]
[[Category:links]]
[[Category:math]]
[[Category:math]]
[[Category:overview]]
[[Category:overview]]
[[Category:theory]]
[[Category:theory]]

Revision as of 01:30, 1 October 2018

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:

Linear algebra:

Exterior algebra:

Abstract algebra:

Temperament representations:

Other:

Temperament Measures and Optimization

Lattices and Scales

Other

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