Creative experiences in an interdisciplinary Honors course on mathematics in music

Abstract

I present six “Creative Experiences” that serve as culminating activities for each of the main units of study in an undergraduate interdisciplinary Honors course of my own design, “Mathematics in Music.” I discuss the rationale and philosophy behind the Creative Experiences, and provide a description and examples of each one. I conclude with some reflections on features that make the Creative Experiences effective learning tools. Supplemental online material for this article can be accessed at http://dx.doi.org/10.1080/17459737.2014.936916.

Keywords:

• education
• undergraduate
• creative process
• interdisciplinary
• curriculum
• pedagogy

Acknowledgements

I am grateful to Elizabethtown College, the CISP program, and my students for supporting the development and delivery of my Mathematics in Music course. I thank the students and staff at Bainbridge Elementary School, St. Peter's parochial school, and Elizabethtown Area Middle School for hosting versions of the school projects developed for Creative Experience 6. Finally, I am especially appreciative of the anonymous reviewers, and of JMM Editors Jason Yust and Thomas Fiore, for their insight regarding the JMM readership, and their many useful suggestions based on that insight.

Supplemental online material

Supplemental online material for this article can be accessed at http://dx.doi.org/10.1080/17459737.2014.936916.

Notes

¹I considered team-teaching the course with a music faculty member, but issues of staffing and teaching loads rendered it impractical. I did, however, consult with music faculty colleagues during the preparation of the course.

²Listed are the “objectives” of the Creative Expression AU as they appeared in College documents in 2007. The language has since been updated to that of “student learning outcomes,” but the essential focus on artistic creation remains unchanged.

³See the beginning of the section Creative Experience 4 for a discussion of my use of the term “analysis.”

⁴Karpinski (2000) distinguishes transcription (which allows for unlimited hearings, and is applied to recordings of musical performances) from dictation (which limits the number of hearings and has a different focus and goal). For my course, with its emphasis on music that students are likely to hear outside the classroom, and the idea that mathematical thinking can provide valuable insight into the creative processes involved in writing and performing music, transcription is the more appropriate exercise.

⁵I specify “whole number of octaves” here rather than simply “octaves” for the sake of mathematical precision. The students learn that musical transposition can be understood as an action of the additive group Z of integers on the set of pitches; in Creative Experience 4 they are being instructed to seek a transposition example that does not belong to the subgroup generated by an octave (i.e. 12Z). Admittedly, “octaves” would probably suffice, but emphasizing the structure of the disallowed set helps reinforce the role of mathematical thinking in the exercise, utilization of which is central to the course.