# Mathematics Across the Curriculum

## Introducing mathematics into an elementary music theory course

In the spring of 1997, Timothy Johnson introduced some mathematical
concepts into the elementary music theory course at Mount Holyoke
College. He was assisted by Alan Durfee of the mathematics department.
The project started in the spring of 1996, when Durfee attended the course in
its usual form. In the spring of 1997, Johnson introduced the mathematical
material over the first several weeks of the course. The initial topic
concerned the arrangement of the black keys among the white keys on the piano
keyboard, and the fact that both the white keys and the black keys had a
property of "being spread out as much as possible", with respect to the total
available chromatic notes within an octave. This concept comes from fairly
recent scholarship in music theory and is called "maximally even". The same
property applies to various scales, triads and so forth. Other concepts from
the same body of scholarship subsequentially were introduced, concerning
various ways to arrange musical patterns, given certain restrictions. The
musical goal of all of this special material was to familiarize the student
with some of the basic foundations of music theory. Johnson felt that this
goal was better attained through this new approach than in previous years.
Johnson is now at Ithaca College. A complete description of this
project, in the form of a miniature textbook, is expected to be
published by Dartmouth College as part of their Mathematics Across the Curriculum
project.

- Article intended for a general
audience about the project.
- Short description of the project
from a mathematical point of view.
- Evaluation of the project by Harriet Pollatsek (Department of
Mathematics and Statistics, Mount Holyoke College).
- Bibliography of articles, both from
the music theory and mathematical point of view.

Current author addresses:
- Alan H. Durfee
- Department of Mathematics and Statistics, Mount Holyoke College,
South Hadley MA 01075.
- email: adurfee@mtholyoke.edu

- Timothy A. Johnson
- School of Music, Ithaca College, Ithaca NY 14850
- email: tjohnson@ithaca.edu

Click here for information about the other projects in the Mathematics Across the
Curriculum project at Mount Holyoke College.