Abstraction of Consonance

This study develops a mathematical and harmonic interpretation of consonance, conceived as a phenomenon entirely deduced from the physical-harmonic principle. It stems from the need to eliminate all subjective elements from the traditional conception of consonance and dissonance, and to define them instead through purely numerical and structural relationships among the partials of a single fundamental series. By treating every musical interval as a specific interaction between harmonics—rather than between notes—the study establishes an objective framework for the measurement and classification of consonant and dissonant relationships. Within this formulation, notions such as fundamental, interval, or harmonic center acquire precise physical definitions, allowing a consistent quantification of harmonic systems. The work thus constitutes an abstraction of consonance: a formulation independent of historical, aesthetic, or perceptual contingencies, in which the consonant–dissonant continuum emerges from the intrinsic laws that govern the harmonic series itself. Its application, both in the analytical and compositional fields, may prove highly practical, as it renders measurable many of the concepts that, until now, remained surrounded by a considerable degree of vagueness and uncertainty, largely due to the lack of rigor in the methods traditionally employed for their determination.