This work introduces the Prime Interval Music Equation (PIME), a deterministic and bijective framework that establishes a direct mapping between intervals of consecutive prime numbers and structured musical material. Unlike traditional compositional systems, the proposed model derives pitch, rhythm, density, tonal gravity, and formal continuity exclusively from prime number intervals, without relying on external musical parameters or stylistic rules. The theory demonstrates that each prime interval generates a complete musical block, and that transitions between intervals produce seamless musical continuity through inherited pitch relations. Musical tonality emerges statistically from the distribution of pitch classes rather than being imposed a priori. The model is fully reversible, allowing musical structures to be decoded back into their corresponding prime intervals, establishing a one-to-one correspondence between number theory and musical form. A structural comparison with classical Western musical scores reveals strong correspondence in visual density, melodic contour, rhythmic stability, and tonal anchoring. These results suggest that music may exist as a latent mathematical structure, discoverable through formal numerical systems rather than purely invented through artistic choice. This preprint aims to contribute to interdisciplinary research at the intersection of mathematics, music theory, computational music, and the philosophy of form, proposing a minimal and universal mathematical foundation for musical structure.
Pablo Garcia (Thu,) studied this question.