The Diverse World of Music Charts
A new publication in Series II of the Swiss Society for Music Research offers insights into the still largely unexplored history of musical diagrams.
The publication series *Publikationen der Schweizerischen Musikforschenden Gesellschaft* serves as a central platform for musicological research in Switzerland and is primarily dedicated to topics with a connection to Switzerland. It includes both major individual studies as well as commemorative volumes and conference proceedings, and illuminates the full breadth of Swiss cultural history.
The richly illustrated volume *The Art of Musical Diagrams – From Boethius to Albersheim and Beyond* (2026), edited by Daniel Muzzulini, features contributions from an international team of authors who demonstrate that visual strategies have shaped musical thinking since time immemorial.
This publication was preceded by the project «Sound Color Space – A Virtual Museum,» funded by the Swiss National Science Foundation, (2015–2016) at the Zurich University of the Arts, which presents a networked collection of diagrams on music and color theory, and an online lecture series by the «Musical Diagrams» Study Group of the International Musicological Society, founded in 2020.
The first two chapters (by Daniel Muzzulini) deal with Pythagorean intervals in historical visualizations. Among other topics, they discuss triangular matrices, which can be used to determine chains of equal intervals, and complete graphs, which were employed in the analysis of complex interval structures.
The third chapter (by John L. Snyder) deals with Theinred of Dover’s *De legitimis ordinibus pentachordorum et tetrachordorum*. The treatise and its innovative diagrams have left no discernible mark on the history of music theory. A comparable circular diagram in René Descartes« »Compendium musicae’ (1619) was likely developed independently of its predecessors.
The fourth chapter (Judith I. Haug) shows that circular diagrams are widespread in Arabic, Persian, and Ottoman-Turkish sources on music theory. Not only octave relationships but also rhythmic periodicity were illustrated using the circle. An example of the diatonic scale with a small gap between the two endpoints of the octave allows for the distinction between fourths and opposing fifths.
The fifth chapter (by Susan Forscher Weiss) focuses on depictions of the musical hand and volvelles (diagrams with rotating parts). The conventional placement of pitches and solfège syllables on the hand guides the teaching and performance of a specific musical repertoire. And the various states of a volvelle lend a two-dimensional diagram an additional dynamic component that can be utilized in a didactic context.
Pie charts and volvelles are also the subject of the sixth chapter (Michael R. Dodds). The focus is on the transition from modal thinking to the modern system of freely transposable keys. The volvelles by António Fernandez (1626) and João Muito Vaz Barradas (1735) are based on a tonal system with 55 steps per octave and interpret transpositions as rotations.
The seventh chapter (by Christoph Reuter) deals with visualizations of timbre. Gerhard Albersheim’s vowel cylinder (1939) and John Grey’s timbre space (1975) are cornerstones of a dynamic approach to a multidimensional phenomenon that is still not fully understood.
