Mathematical theory: Difference between revisions

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[[Meet_and_Join|Meet and Join]]
[[Meet_and_Join|Meet and Join]]


'''Linear algebra:'''
'''Linear algebra:'''
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[[Generalized_Tenney_Dual_Norms_and_Tp_Tuning_Space|Generalized Tenney Dual Norms and Tp Tuning Space]]
[[Generalized_Tenney_Dual_Norms_and_Tp_Tuning_Space|Generalized Tenney Dual Norms and Tp Tuning Space]]


'''Exterior algebra:'''
'''Exterior algebra:'''
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[[Interior_product|Interior product]]
[[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|Groups, Lattices, Z-modules and Vector spaces]]


'''Temperament representations:'''
'''Temperament representations:'''
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[[Gencom|Gencom]]
[[Gencom|Gencom]]


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

Revision as of 19:47, 17 September 2018

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Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.

Scale Basics

Periodic scale

MOS scales

Mathematics of MOS

MODMOS scales

Graph-theoretic properties of scales

Regular Temperaments

Basics:

Monzos and Interval Space

Vals and Tuning Space

Regular Temperaments

Saturation

Dual List

Meet and Join


Linear algebra:

Temperament Mapping Matrices (M-maps)

Tmonzos and Tvals

Subgroup Mapping Matrices (V-maps)

Smonzos and Svals

Generalized Tenney Norms and Tp Interval Space

Generalized Tenney Dual Norms and Tp Tuning Space


Exterior algebra:

Wedgies and Multivals

The wedgie

Recoverability

The dual

Interior product


Abstract algebra:

Groups, Lattices, Z-modules and Vector spaces


Temperament representations:

Abstract regular temperament

Normal lists

Gencom


Other:

Planar Temperament

Transversal generators

Temperament Measures and Optimization

Target tunings

TOP tuning

Tp tuning

Tenney-Euclidean tuning

Tenney-Euclidean temperament measures

Tenney-Euclidean metrics

Cangwu badness

Fractional monzos

Generator complexity

Lattices and Scales

Transversal

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

k*N subgroups

Logarithmic approximants

Don Page comma

ABC, High Quality Commas, and Epimericity