The 7 Color Materials Theory

This paper presents the 7 Color Materials (7CM) Theory, an axiomatic system of music theory that models tonality, musical structure, and musical perception through a small set of formal axioms. The theory describes tonality as a weighted superposition of Monotonalities, and decomposes musical space into two independent components: Structure and Radiance. It further introduces a system of gravitational relations between scale degrees from which functional properties can be derived. The paper provides formal definitions, axioms, propositions, and proofs establishing the mathematical structure of the theory. It also discusses the implications of the framework for functional harmony, tonal perception, and musical analysis. This is the English-language mathematical paper presenting the formal formulation of 7CM Theory. A less mathematical version intended for musicians is available separately.