A Numerical Ontology of Music: Mapping Infinite Numbers to Infinite Musical Structures

This work presents a theoretical framework in which music is understood as an abstract numerical structure that exists independently of its physical realization or human discovery. Inspired by mathematical realism, the paper proposes that musical compositions preexist as trajectories within an infinite multidimensional musical space, analogous to the existence of numbers in mathematics. A master equation is introduced to formalize the mapping between numerical sequences, musical structure, temporal unfolding, and audible manifestation. Within this model, composition is reinterpreted as an act of discovery rather than invention, and listening as a perceptual projection of abstract structures into time. The framework integrates concepts from mathematics, music theory, and philosophy, offering a unified ontological interpretation of music as a non-material yet experiential phenomenon. This approach opens new perspectives for research in mathematical music theory, algorithmic composition, artificial intelligence, and the philosophy of art.