Honors | Mathematical Approaches to Music (MUS)
N399 | 9671 | Julian Hook
Since the time of Pythagoras it has been recognized that
mathematical relationships underlie many musical phenomena, but the
precise nature of these relationships remains elusive to this day.
Scholars in the middle ages grouped music together with arithmetic,
geometry, and astronomy in the quadrivium, the higher division of
the Seven Liberal Arts. More recent generations of music theorists
have tried to codify music according to mathematical rules,
sometimes applying sophisticated mathematical techniques, with
varying degrees of success.
This course will survey some of these mathematical approaches to
music, both historical and contemporary. Specific topics to be
studied include Pythagorean music and mathematics, Johannes Kepler
and the “music of the spheres,” selected topics in acoustics,
geometric representations of musical phenomena, group theory and its
applications to pitch-class set theory and twelve-tone theory, and a
brief introduction to recent research in musical transformation
theory and diatonic set theory.
Course requirements will include regular attendance and
participation, assigned readings, several short homework
assignments, one major paper, and a class presentation. The paper
and presentation will give students an opportunity to explore topics
of their own choosing, depending on individual interests and
Prerequisites: Knowledge of pre-calculus mathematics and junior
standing, or consent of instructor. Non-music majors with some
knowledge of basic music theory are welcome.