Diachronic Modeling of Tonal Coherence on the Tonnetz Across Classical and Popular Repertoires

TL;DR

This paper introduces a multi-dimensional model based on the Tonnetz to analyze tonal coherence across classical and popular music, revealing distinct patterns in their tonal focus and connection.

Contribution

It presents a novel two-measure model for tonal coherence, applying it to large datasets to differentiate musical traditions quantitatively.

Findings

Popular music has higher tonal focus.

Classical music exhibits higher tonal connection.

The measures provide interpretable dimensions for analysis and generation.

Abstract

How do different musical traditions achieve tonal coherence? Most computational measures to date have analysed tonal coherence in terms of a single dimension, whereas a multi-dimensional analyses have not been sufficiently explored. We propose a new model drawing on the concept of the Tonnetz -- we define two partially independent measures: \emph{tonal focus}, the concentration of pitch content near a tonal center; and \emph{tonal connection}, the degree to which pitch content reflects structured intervallic pathways back to that center. Analyzing over 2,800 pieces from Western classical and popular traditions, we find that these traditions occupy overlapping yet distinguishable regions of the two-dimensional space. Popular music shows higher tonal focus, while classical music exhibits higher tonal connection. Our complementary measures ground the differences between different tonal styles in quantitative evidence, and offer interpretable dimensions for computational music analysis and controllable generation.