MUS-T 658, section 8889, Spring 2005
Seminar in Music Theory: Musical Spaces and Transformations
Instructor: Julian Hook
11:15-12:30 TR, MA 004

It has long been recognized that mathematical principles underlie
many musical phenomena. Within the last two decades, a variety of
sophisticated techniques from group theory and other areas of
mathematics have been applied to the study of music. Students in this
seminar will explore some of these exciting developments.

The concepts fundamental to this exploration are the spaces in which
musical objects reside, and transformations defining relationships
among objects in those spaces. Familiar examples of musical spaces
include pitch space and pitch-class space; there are also chordal
spaces, rhythmic spaces, and many others. Spaces can be finite or
infinite, discrete or continuous, chromatic or diatonic. Many musical
spaces have appealing geometric representations, which we will study
early in the semester. Transformations are mappings defined on spaces
(what mathematicians call “functions”); examples include the familiar
transposition and inversion operators. As David Lewin has shown,
transformations are intimately related to a general notion of the
interval between two musical objects.

Our study will cover essential concepts in the areas generally known
as transformation theory and neo-Riemannian theory; there will also
be some intersections with topics in pitch-class set theory,
including diatonic set theory (which explores the remarkably subtle
and complex relationships between diatonic and chromatic spaces). The
subject matter is more theoretical than analytical in nature, but our
readings will include analytical applications to a variety of
repertoires, both tonal and atonal, and individual projects will
offer an opportunity for students to pursue further analytical work.
Theorists whose work we will read are likely to include David Lewin,
Richard Cohn, John Clough, Robert Morris, Fred Lerdahl, and the
instructor.

Requirements: assigned readings and discussion; additional individual
readings and class presentations; one or two short papers or other
written assignments; one major paper and final presentation.

Prerequisites: Students enrolling in T658 should be familiar with the
fundamentals of pitch-class set theory as covered, for instance, in
T556, Analysis of Music Since 1900. There are no specific
mathematical prerequisites; mathematical concepts will be introduced
as needed during the semester.