An Algebraic-Symmetric Analysis of Counterpoint and Modulation in the Music of Claudio Monteverdi

Abstract: We address certain structural innovations in the music of Claudio Monteverdi, which defined the pivotal transition from the Renaissance prima pratica to the Baroque seconda pratica. To formalize this analysis, we employ Mazzola's symmetry-based framework for counterpoint and quantum/duality models for tonal modulation. Our findings demonstrate that these mathematical structures provide a rigorous validation of Monteverdi's compositional choices, revealing an underlying logic to harmonic and contrapuntal treatments that were heavily criticized by contemporaries such as Giovanni Artusi. By quantifying concepts like compositional parsimony and modulations, we aim to provide a precise and analytical lens to the interdisciplinary field of mathematical musicology, bridging the gap between historical interpretation and formal theory.