Mathematical theory: Difference between revisions
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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]] | ||
* [[MOS scales]] | * [[MOS scales]] | ||
| Line 9: | Line 9: | ||
* [[Graph-theoretic properties of scales]] | * [[Graph-theoretic properties of scales]] | ||
=Regular Temperaments= | == Regular Temperaments == | ||
'''Basics:''' | '''Basics:''' | ||
| Line 51: | Line 51: | ||
* [[Transversal generators]] | * [[Transversal generators]] | ||
==Temperament Measures and Optimization== | === Temperament Measures and Optimization === | ||
* [[Target tunings]] | * [[Target tunings]] | ||
* [[TOP tuning]] | * [[TOP tuning]] | ||
| Line 62: | Line 62: | ||
* [[Generator complexity]] | * [[Generator complexity]] | ||
==Lattices and Scales== | === Lattices and Scales === | ||
* [[Transversal]] | * [[Transversal]] | ||
* [[Fokker blocks]] | * [[Fokker blocks]] | ||
| Line 73: | Line 73: | ||
* [[Comma-based lattices]] | * [[Comma-based lattices]] | ||
==Other== | === Other === | ||
* [[The Riemann Zeta Function and Tuning]] | * [[The Riemann Zeta Function and Tuning]] | ||
* [[Modulatory space]] | * [[Modulatory space]] | ||
Revision as of 10:45, 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:
- 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:
Abstract algebra:
Temperament representations:
Other:
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