June 22, 2017
Julian Hook, Jacobs School of Music, Indiana University
Music unfolds on a vast playing field whose complex mathematical structure has never been well understood. This talk will illustrate applications of several different branches of mathematics in describing musical phenomena. Emphasis will be on applications of graph theory, particularly in describing various versions of a diagram called a Tonnetz in which certain musical pitch relationships can be graphed and certain kinds of chord progressions can be traced. Some Tonnetz graphs are embedded in a torus; one version, for example, illustrates a toroidal embedding of the complete graph K7. In some cases relationships between musical structures may be described algebraically using transformation groups, which range from familiar small cyclic groups to complex constructions such as wreath products. Other ways of conceiving of chordal relationships lead to topological descriptions in which, for example, all possible two-note chords define a Möbius strip while larger chords lie in more complex spaces (orbifolds) in higher dimensions.
Julian Hook holds graduate degrees in mathematics, architecture, piano performance, and music theory. He is Associate Professor of Music Theory at the Indiana University Jacobs School of Music, where he has taught since 2003. His research on mathematical approaches to the study of music engages branches of mathematics from combinatorics, graph theory, and group theory to geometry and topology; it has appeared primarily in music theory journals but also at conferences of the American Mathematical Society and in the pages of Science. He is a former chair of the music theory department at Indiana University, a past president of Music Theory Midwest, and the founding Reviews Editor of the Journal of Mathematics and Music. He is a past winner of a publication award from the Society for Music Theory and a Sabbatical Fellowship from the American Philosophical Society. As a pianist, he has performed chamber music with members of the Chicago Symphony Orchestra. He is currently writing a book titled Exploring Musical Spaces.
Following the presentation, Professor Hook and Ms. Sun Huh will perform in a concert for piano and violin.
A native of South Korea, Sun Huh began her study of the violin at the age of eight. She studied at the Hanns Eisler Hochschule für Musik in Berlin and the Robert Schumann Musikhochschule in Düsseldorf. She has won several national competitions in South Korea as well as many prizes as soloist and chamber musician in Germany; performed as soloist with several German orchestras; and performed chamber music with many internationally known musicians. She came to Indiana University in 2009 as the recipient of a prestigious Barbara and David Jacobs Scholarship. At IU she earned a Performer Diploma as a student of Ik-Hwan Bae and a Master of Music degree as a student of Mark Kaplan, while holding the position of concertmaster in an IU orchestra. She is currently pursuing the Doctor of Music degree, studying with Mark Kaplan.