Graph theory tools applied to the harmonic analysis of J. S. Bach: towards an integration of network models and conventional analytical approaches

• Juan Felipe Vásquez R. Unicamp
• Hanner Cajar C. Universidad Distrital Francisco José de Caldas / Universidad Nacional de Colombia

DOI: https://doi.org/10.5753/sbcm.2025.13073

Resumo

This paper applies network analysis methodologies— specifically graph theory and associated centrality measures—to the study of two compositions by Johann Sebastian Bach from the Baroque period (17th–18th centuries). Each composition is segmented into discrete harmonic events, which are then modeled as nodes within a graph, with edges representing their functional or temporal relationships. The structural roles of individual events are assessed through centrality metrics (such as degree, closeness, and betweenness), revealing the presence of hierarchical or functionally pivotal elements within the harmonic network. Results indicate that network-derived centralities can align with, and potentially enrich, traditional music-theoretical interpretations, offering an alternative yet complementary analytical framework.

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