A Universal Mathematical Framework for Resonance Structure Analysis in Complex Signals

This paper introduces an interpretable physical–mathematical framework for the analysis of resonance structures in complex signals. The proposed approach focuses on identifying and distinguishing simultaneously present resonant sources whose spectral components partially overlap. While musical audio is used as a demonstrative and well-formalized test environment, the method itself is not music-specific and is applicable to a wide class of resonant systems. The core contribution consists of a formalized radix-12 representation of resonant frequencies combined with algorithmic criteria for resolving harmonic ambiguities (octave, fifth, third). A working software implementation is provided to demonstrate feasibility and reproducibility.