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TES: The largest network of teachers in the world

Portions not contributed by visitors are Copyright 2018 Tangient LLC

TES: The largest network of teachers in the world

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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 scaleMOS 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 tuningsTOP tuning

Tp tuning

Tenney-Euclidean tuning

Tenney-Euclidean temperament measures

Tenney-Euclidean metrics

Cangwu badness

Fractional monzos

Generator complexity

## Lattices and Scales

TransversalFokker 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 TuningModulatory space

Chordal space

k*N subgroups

Logarithmic approximants

Don Page comma

ABC, High Quality Commas, and Epimericity