Computational Strategies for Measuring and Visualizing Tonal Structures: Towards a Large-Scale Analysis of Wagner’s Ring Cycle

Within Western classical music, Richard Wagner’s Der Ring des Nibelungen stands out as a monumental work, comprising nearly 22,000 measures and 15 hours of music with a continuous dramatic narrative. Structuring such a large-scale work comprises an enormous challenge, which particularly affects the work’s tonal organization. While other compositional techniques such as Wagner’s use of leitmotifs have been extensively studied, his approach to structuring the tonal framework of the Ring remains subject to musicological debate. In this paper, we present a computer-assisted approach for exploring the tonal organization of the Ring combining two traditional analytical perspectives based on sheet music with a novel computational strategy based on audio recordings. The first traditional perspective is the idealized tonal analysis by Alfred Lorenz from the 1920s, the second perspective examines key signature regions derived from Wagner’s original score. We complement and compare these two views with a third, computational perspective: an audio-based strategy for measuring diatonic scale content over time, which is based on deep-learning techniques introduced in our previous work. To integrate these three perspectives, we propose a visual overlay technique using a dedicated color scheme, which offers a comprehensive and comparative view of Wagner’s tonal conception. This integrated approach not only provides new insights into the Ring ’s large-scale tonal organization but also demonstrates the broader potential of computational methods for musicological research regarding their ability to address challenges such as scalability, reproducibility, and objectivity of analysis. Audio-based strategies, in particular, offer a promising alternative to using symbolic (machine-readable) scores, which are often unavailable for large-scale works and tedious to create. Overall, we demonstrate that by providing automated measurements of tonal structures, computational tools can significantly enhance and expedite the tonal analysis of large-scale musical compositions such as Wagner’s Ring .