Many people are vaguely aware of connections between mathematics and music, but efforts of specific interdisciplinary research and pedagogy oriented toward such connections often appear as isolated examples or intellectual side-trips. The effects of such efforts are often limited by an unfortunate disciplinary divide between “science and mathematics” and “arts and humanities” that limits communication, understanding, and inquiry. The CISP project “Connections between Mathematics and Music” initiates a more comprehensive approach to the interaction between mathematics and music, with the hope of mitigating the disciplinary divide. Overall goals of the project are to introduce students to the rich connections between mathematics and music, to contribute to the body of scholarly and pedagogical literature on these connections, and to increase scholarly communication between mathematicians and musicians.

The three participants spent much of the summer of 2007 compiling a large (>300 items) annotated bibliography of published items (books and articles) having to do with mathematics and music. The effort was complicated by the fact that the “disciplinary divide” mentioned above is reflected in the indexing of items in bibliographic databases and catalogues; hence, “mathematical” searches are often blind to items published in the “arts and humanities” literature, and vice versa. A broad-based search for published items was a necessary first step, providing a foundation for all other aspects of the project. A version of the bibliography in spreadsheet form is available via a link on the Hughes website at users.etown.edu/h/hughesjr/JRH.htm.

Through communication with music colleagues at other institutions, Hughes learned of some emerging venues specifically devoted to math/music interaction, resulting in his attendance at two conferences. In May 2007 he attended the First International Conference of the Society for Mathematics and Computation in Music, held at the Musical Instrument Museum at the heart of the rebuilt Potsdamer Platz in Berlin, Germany. At that conference he was able to converse with and attend presentations given by many of the researchers at the forefront of current scholarly work involving mathematics and music. Being present at the conference provided more nuanced insight into the state of such interdisciplinary inquiry than reading alone could provide (e.g., on the existence of a distinct “European School” and “American School” with differing goals and approaches, a situation that is rarely, if ever, mentioned in print). In November 2007, Hughes attended the annual meeting of the Society for Music Theory, held in Baltimore, Maryland, at which several special sessions were completely devoted to mathematical music theory. In Baltimore, Hughes was again able to interact with influential researchers, some of whom had been at the Berlin conference, and others who had not.

During the fall of 2007 and early spring of 2008, Hughes completed the design of a new interdisciplinary Honors course, “Mathematics in Music,” which was subsequently approved by Core and Honors committees, and will be offered as HMA275 for the first time in spring 2009. The course will fulfill the Creative Expression Core requirement, reflecting a fundamental epistemological grounding in music. The overall goal of the course is to deepen and enrich the creative experience of music by developing mathematical ways of understanding, analyzing, and synthesizing the elements of music (including, but not limited to, acoustics, tuning, theory, composition, and performance) on various levels. A secondary goal is to instill appreciation for the idea that the emotive and intellectual aspects of creative expression are intertwined parts of a related whole. In recognition of the pedagogical aspect of interdisciplinary inquiry the course will include participation in a “Mathematics in Music” event at a local elementary or middle school.

Guided by the content of the annotated bibliography, his observations at the conferences, and the experience of designing the new course, Hughes constructed a taxonomy for organizing scholarly work involving mathematics and music. A description of this taxonomy can be found via a link on the Hughes website at users.etown.edu/h/hughesjr/JRH.htm.

Hughes will give presentation on the interdisciplinary Honors course “Mathematics in Music” at the MAA Mathfest in August 2008.

The CISP-funded efforts over the past year were only the beginning of what is envisioned to be a much longer-term project. Future plans for the project include the following aspects. Hughes is currently working on a survey paper to present the math/music interdisciplinary area as a whole to the larger academic community. The new course “Mathematics in Music” will be offered for the first time in spring 2009, and in subsequent years in accordance with demand and staffing resources. Summer 2007 participant Michael Tschop will give a presentation on a math/music topic (probably on intonation systems), either at the 2009 Scholarship Day, or at a venue outside of Elizabethtown College (he had plans to do so in spring 2008, but his role as one of the lead singers in the opera “Las Madres de la Plaza” (another CISP project) intervened). As the course progresses, Hughes plans to develop enough original material to produce a publishable textbook. Continued development of the bibliography and taxonomy will be ongoing, and will likely involve the participation of a large set of interdisciplinary colleagues, either via a “wiki” site, or another online collaboration scheme.