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
- Mathematical theory of saturation
Interval Metrics
Chords
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
Exterior algebra
- Wedgies and multivals
- Recoverability
- The dual
- Interior product
- Dave Keenan & Douglas Blumeyer's guide to EA for RTT
- Mike's note: Douglas and Dave, having their own interpretation of RTT, sometimes use different terminology than the rest of the stuff here, but this page still has some very good insights and is a worthwhile read.
Temperament Measures and Optimization
- 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
- Weil norm, Tenney-Weil norm, and TWp interval and tuning space
- Tp tuning
- Constrained tuning
- Target tuning
- 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
Other
- The Riemann zeta function and tuning
- Modulatory space
- Chordal space
- Logarithmic approximants
- Don Page comma
- abc, high quality commas, and epimericity
- Planar temperament
- Projection pair
- Temperament addition