Mathematical theory
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
- Monzos and Interval Space
- Vals and Tuning Space
- Temperament Mapping Matrices
- Dual list
- Mathematical theory of regular temperaments
- Saturation
Subgroup Temperaments
- Subgroup Temperament Families, Relationships, and Genes
- Subgroup Monzos ("smonzos") and Subgroup Vals ("svals")
- Tempered Monzos ("tmonzos") and Tempered Vals ("tvals")
- Subgroup Basis Matrices
- Meet and Join
- Sane and Insane Temperaments
- k*N subgroups
The Exterior algebra
Temperament Measures and Optimization
- TOP tuning
- Tenney-Euclidean Tuning
- Tenney-Euclidean temperament measures
- Tenney-Euclidean metrics
- BOP tuning
- Generalized Tenney Norms and Tp Interval Space
- Generalized Tenney Dual Norms and Tp Tuning Space
- Tp tuning
- Target tunings
- Cangwu badness
- Fractional monzos
- Generator complexity
Lattices and Scales
- 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