Review of Godfried Toussaint, The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good? (CRC Press, 2013)

Abstract

[1] The Geometry of Musical Rhythm is Godfried Toussaint's first monograph offering to the musicological community. Mathematician-cum-musicologists are increasingly common in theory, but Toussaint is a singular case. With expertise covering information theory, electrical engineering, and computer science, and interests spanning everything from African drumming to evolutionary biology, his stated aim to create an interdisciplinary academic bridge between these fields amounts to a considerable undertaking.[2] Toussaint has found an eminently suitable subject for that goal in the mathematical modelling of musical rhythm as expressed in symbolic form. In turn, the musicological community will discover in Toussaint's work an array of current and historical thought on geometric models, and a substantial contribution to a field that still lags behind the more developed theoretical literature on pitch, notwithstanding a vigorous revival of interest in rhythm and meter during the later twentieth century.(1)[3] Toussaint's list of personal acknowledgments provides general insight into the position of the book within the musicological landscape,(2) while for many readers, the modelling will most readily bring to mind the work of other mathematicians to have graced the field. Jeff Pressing ticks both boxes. His iconic 1983 article on isomorphisms between scales and rhythms from around the world is perhaps the most direct precursor to Toussaint's volume in both tone and for its combination of mathematical relations with ethnographic enquiry. Mathematical formalizations of musical space, such as those in Lewin 1987(3) and Polansky 1996 are relevant precedents, though Toussaint's project differs in its aims and target audiences. Some of the relationships between rhythmic patterns have been explored in recent subfields of theory (such as beat-class modulation in Roeder 2003 and Cohn 1992 after Babbitt 1962), and others parallel models from the pitch literature (such as Clough and Douthett's 1991 formalization of maximal evenness).[4] In many senses, this is a timely book. It is interdisciplinary (a quality openly promoted by the academy today), is concerned with an under-represented musical parameter (Toussaint is suitably condemnatory of the long-standing bias against rhythm as the fundamental property of music (305)), and concomitantly focuses on under-represented repertoires. It is also made available to a wide readership, as Toussaint balances the range of technical content with a writing style that remains suitable to lay readers. No knowledge of or mathematics is assumed, although italicized terms are occasionally introduced without definition and others are used in questionable ways.(4)[5] The disposition of the book reflects aspects of its background. Partly owing to the range of fields and topics drawn upon, the 363-page book is divided into many short chapters. Each introduces a different perspective on the same recurring questions (including the eponymous What makes a 'good' rhythm good), and the same illustrious rhythms, democratically taken to be good on the strength of their preponderant use throughout the world and its history.(5) Chapter 37 reprises many of the relations used, though it serves more as a summary than as the climax of an argument.[6] In short, this book does not read as a work of traditional musicology. That is as true of the content and language as it is of the shape and organization. Tellingly, the publisher focuses on scientific, technical, and medical content, and lists this work under General and Introductory Mathematics. However, General and Introductory Mathematics is exactly what certain branches of musicology need, especially when that introduction includes relevant findings from such a wide range of unfamiliar disciplines. For instance, a principal motivation for Toussaint in writing this book has been to evangelize the merits and utility of phylogenetic analysis, a topic which originated in the field of evolutionary biology: hardly the most immediate cousin of musicology. …