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.

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