Yale University, New Haven, Connecticut, USA, 19-22 June 2009.

Reviewed by Jonathan Bragg, Cheng-Zhi Anna Huang
Cambridge, Massachusetts, USA

The Second International Conference on Mathematics and Computation in Music (MCM) met in conjunction with the John Clough Memorial Conference 19-22 June 2009 at Yale University in New Haven, Connecticut, USA. MCM is the biennial meeting of the Society for Mathematics and Computation in Music (SMCM), and the John Clough Memorial Conference meets every four years to commemorate the mathematical music theory pioneer. The joining of the two conferences builds on a relationship that began in 2007. The very first volume of the SMCM's flagship publication, Journal of Mathematics and Music, which was published in that year, featured a special issue dedicated to "The legacy of John Clough in mathematical music theory." These two conferences are naturally linked by the traditionally strong affinity between mathematics and music theory. David Cohen highlighted this continuing tradition in his keynote lecture. The conference welcome and the keynote lecture were held at the Beinecke Rare Book and Manuscript Library at Yale University, where a special collection of historic musical and mathematical materials were on display and complemented the lecture.

The four-day conference included 26 paper presentations, grouped into six sessions: "Composition, Voice-leading, Atonality," "Geometry," "Scale," "Perception," "Time," and "New Interdisciplinary Approaches." In accordance with the conference title, "Mathematics and Computation in Music," the talks fell into two categories. The first three sessions centered on topics that are more naturally approached using the concepts and analytical tools in mathematics, while the last three sessions introduced approaches that are more computational and sometimes involving human subjects. In this way, the conference followed a trajectory that nicely parallels the increasing interaction of mathematical music research with applied and empirical research in other fields such as computing, signal processing, and psychology. We feel that more frequent use of audible musical examples would have enriched some of the presentations, especially in the first half of the conference. The titles and abstracts of all the papers can be found at the conference Web site (www.mcm2009.info/papers.html). The proceedings of this conference are also readily available both online (www.springerlink.com/content/ul0p34) and in print from Springer.

Although the title "Mathematics and Computation in Music" implies a primarily scientific approach to music, the tutorials and a panel session at the conference showed how scientific and aesthetic approaches can inspire each other. For example, one of the tutorials introduced OpenMusic, a graphical computer-aided composition environment developed at the Institute de Recherche et Coordination Acoustique/Musique (IRCAM), in which composers can prototype their compositions by leveraging the implemented algorithms to generate musical material that would otherwise be difficult to do by hand. In addition, the panel session featured a screening of a dance performance choreographed in such a way as to embody Fourier's mathematical formula. In the future, we look forward to the conference having a call for scores and performances to further explore how research can enable new stylistic and personal expression.

Forming personal connections is important to the progress of, and one's progress in, any field; it is especially important in the interdisciplinary fields represented at this conference. Researchers at these intersections are sparse and spread across the world, and few institutions exist to bring them together. Even universities are typically partitioned into departments with little intercommunication. In the absence of many central sources of information, personal collaboration and communication enable researchers to build on past and current efforts.

The conference provided an excellent opportunity for networking and for the building of these foundational relationships. The size of the conference was intimate, with enough attendees to modestly fill a small lecture hall, enabling one to get to know a good portion of the attendees. Attendees ranged from professors and leading researchers to graduate students and even a few undergraduate students. The atmosphere was collegiate and friendly, with an emphasis on learning about the material being presented. There was also a poster session for students to present their work in progress and to receive feedback. An overall feeling of equality and a de-emphasis on seniority made possible a host of interactions, not only among professors and among students, but also between professors and students. At local restaurants and in between paper sessions, groups of professors and students would socialize and discuss ideas as fellow researchers.

Unique to this conference among similarly-themed conferences was free registration, room, and board for the first 30 students to register for the conference. In this respect, the conference provided an ideal opportunity for students early in their careers and students from a variety of backgrounds—ranging from music performance and composition to music theory and musicology, and from cognitive science and computer science to statistics and mathematics—to learn about the field and about attending this type of conference. It is important to encourage and enable young interested researchers like ourselves to participate in current research, and for this reason, we applaud the conference committee's decision to cover expenses.

The joint nature of the Second International Conference on Mathematics and Computation in Music and the John Clough Memorial Conference brought together groups of specialists in many interdisciplinary research areas, demonstrating impressive breadth and depth. The conference provided a platform for researchers to speak to a broad audience with a shared passion for music research. We came away from the conference with a feeling of community, and we foresee exciting collaborations resulting from the new professional friendships that were initiated at this conference.