Review of Godfried Toussaint, The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good? (CRC Press, 2013)
Mark Gotham · Music Theory Online · 2013
The Geometry of Musical Rhythm is Godfried Toussaint's first monograph offering to the musicological community.Mathematician-cum-musicologists are increasingly common in music 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.[3] Toussaint's list of personal acknowledgments provides general insight into the position of the book within the musicological landscape, 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 content, for its combination of mathematical relations with ethnographic enquiry.Mathematical formalizations of musical space, such as those in Lewin 1987 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 music 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