Modulation Graphs in Popular Music

TL;DR

This paper applies graph theory to analyze tonal modulation in popular music, defining modulation graphs based on common scales and examining their properties through Lennon-McCartney songs, offering mathematical insights for composers.

Contribution

It introduces the concept of modulation graphs for popular music scales and analyzes their properties using Beatles songs, bridging music theory and graph theory.

Findings

Modulation graphs effectively model tonal shifts in popular music.

Lennon-McCartney songs exhibit specific modulation graph patterns.

Mathematical properties of these graphs can inform compositional techniques.

Abstract

In this paper, graph theory is used to explore the musical notion of tonal modulation, in theory and application. We define (pivot) modulation graphs based on the common scales used in popular music. Properties and parameters of these graphs are discussed. We also investigate modulation graphs for the canon of Lennon-McCartney songs in the works of The Beatles. Our approach may provide composers with mathematical insights into pivot modulation.