3 papers
math.GM2026
Mathematical Principles of a Generalized Tonal Practice
Drew Flieder
We develop mathematical principles for a generalized tonal practice. We begin with an algebraic theory of modes and scales, formalized as groups and torsors over cyclic groups, res…
math.GM2026
A Theory of Scales and Orbit Covers
Drew Flieder
This paper develops a formal theory of musical scales and their harmonic coverings and introduces orbit covers: coverings obtained by translating a fixed subset across a scale via…
math.CT2025
Type Theory for the Working Mathematical Music Theorist
Drew Flieder
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple f…