Journal of Mathematics and Music (review)

The relationship between mathematics and music has fascinated philosophers and musicians for millennia. Pythagoras's mythical discovery that music was "sounding number," and thus a sensible manifestation of the underlying numeric reality of the Pythagorean universe, cast a shadow over centuries of musical thought. Neo-Platonic philosophers like Boethius, operating within the Pythagorean tradition, considered musica nothing less than a branch of mathematics itself (that branch concerned with compared quantities, i.e., whole-number ratios). The math-music relationship has persisted in various forms since then, waxing and waning with the intellectual tenor of the age. We currently appear to be in a waxing phase: since World War II, many prominent composers and music theorists have turned to mathematics as a means of stimulating musical creation and modeling musical thought. While mathematics may not play as central a role in musical composition today as it did in the postwar heyday of Darmstadt, mathematical music theory has rarely been more active. In the United States, the visionary work of David Lewin has captured the imaginations of many scholars, spawning the music-theoretic subfield of "transformational theory." In Europe, the work of Guerino Mazzola has had a similarly galvanizing effect, stimulating a growing number of European scholars to pursue connections between mathematical category theory and an astonishingly diverse range of musical phenomena.

The present journal arrives perched atop the crest of this wave of burgeoning music-mathematical thought. As the editors make clear in their introduction to this inaugural issue, the journal seeks not only to ride that wave but to channel and focus its considerable energy, funneling the many disparate strands of mathematical music theory into a shared discursive space, one in which connections can be drawn between subfields that have previously remained separate. Most notably, the journal aims to integrate American and European traditions of mathematical music theory, areas of inquiry that have thus far remained largely independent from one another due not only to geography, but also, one suspects, to differences in intellectual style. This commitment to trans-Atlantic dialogue is made clear by the international pair of co-editors: the German Thomas Noll and the American Robert Peck, both eminent scholars in their own right. Noll and Peck stress that they wish the journal to be not only a meeting place for American and European music theorists, but also a site for mathematical dialogue between theorists, composers, performers, cognitive scientists, and even those outside of the "ivory tower"—for example, working musicians involved in such fields as computer music and sound processing. This emphasis on "boundary crossing," as the editors put it, is one of the most attractive and exciting aspects of the journal.

For musicians not involved in any of these fields, and especially for those with some degree of math phobia, the idea of mathematical thought about music likely conjures up images of an arid, mechanical, "hard science" approach to the subject, one unresponsive—or even anathema—to the poetic and expressive immediacies of musical experience. This impression, though understandable, is in fact far from the truth. Much work in mathematical music theory is highly poetic and interpretive, ranging from issues of musical semiosis and hermeneutics, to mappings of embodied musical experience, to models of musical phenomenology. This broadly humanistic angle is amply in evidence in John Rahn's article in this issue. Rahn asserts that Lewin's transformational networks do not so much constitute a theory of music as a "poetic language" in which one can express a variety of musical insights and intuitions. Rahn's virtuosic and delightful essay takes...