A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (review)

There exist first-rate theoretical treatises and articles that seek to explore the known byways of the history of music theory, and there are others that try to define new ways of thinking about the field. Tymoczko’s Geometry of Music belongs to the latter category. No matter what his publisher or he himself says, this book is not easygoing, not even for those experienced in the field, and it is anything but “accessible.” It requires a willingness to set aside generations of thinkers about music theory (from Rameau to Schenker and everyone in between and after, including Schönberg, Forte, and Cohn). Tymoczko wants no less than to include in his system the entire history of music, ranging from medieval contrapuntalists, through Josquin in the fifteenth and sixteenth centuries, through the “common practice” period (Bach, Mozart, Beethoven, Chopin), through the later nineteenth and early twentieth centuries (Wagner, Chopin, Debussy, Schönberg), through jazz and contemporary idioms.

His effort reminds me of no one so much as one of his erstwhile colleagues at Princeton University, Peter Westergaard, who was my counterpoint teacher when I was an undergraduate. That counterpoint class was the finest class I ever took in any field, bar none. A few years later, though, Westergaard wrote up his course as a textbook. I gather it was a commercial disaster, and one can easily understand why. The success of the system depended on the teacher, who was utterly brilliant. I am sure that Tymoczko’s students think the same of him, but learning an entirely new way of thinking about music theory depends on the presence of a teacher who is willing to follow the student through the many false turns he or she is bound to take trying to come to grips with this system and deal with statements like “the rate of pitch-class circulation is independent of the degree of emphasis on particular macroharmonies.” I am not, let it be clear, commenting negatively on Tymoczko’s systemization of music theory; among other things, he shows a remarkable knowledge of contemporary theory, including the works of Lehrdahl, studies of octatonic scales, and Xenakis, even if he chooses to define his terms differently. I am simply questioning whether this intriguing book can aspire to having the impact he clearly wishes it to have.