2016/02/09 by Susannah Wixey, Wixey, Susannah, Rob Sturman +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #History and Overview (math.HO) #Slime Mold and Myxomycetes Research #Topological and Geometric Data Analysis #math.HO
paper · pdf · doi:10.48550/arxiv.1602.04137
15 pages, 5 figures
arxiv created 2016/02/09 · openalex publication_date 2016/02/09 · arxiv updated 2016/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We study the Neo-Riemannian principle of parsimonious voice-leading using tools and techniques from classical graph theory and the modern field of complex networks. We quantify the relative importance of particular chords within this framework. The graph-theoretic notion of eccentricity suggests that when working in a harmonic scheme dictated by any common musical scale, no triad is any more isolated than any other. Complex network theory refines this idea, and in this context provides measures of how important particular triads might be for the flow of chord progressions through the harmonic network. We review and compare several different such measures of centrality and communicability.