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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…