A Senior Capstone Experience by Faithlin Hunter

Submitted to the Departments of Mathematics and Music

Advised by Dr. Kyle Wilson and Dr. Jon McCollum

Contributor Biography: Faithlin Hunter is a class of 2023 graduate with a Bachelor of Arts in Mathematics and Music and a minor in Dance. She graduated with first honors summa cum laude and received double departmental honors on her thesis. She was also a member of the John S. Toll Science and Mathematics Fellows, the Libby and Douglass Cater Society of Junior Fellows, and Phi Beta Kappa. Faithlin received the Outstanding Dance Minor Student Award and Department of Music Award for Professional Promise in Research and Creative Achievement. During her time at Washington College, Faithlin served as President of the Sho’Troupe Dance Team and Musicians’ Union for two years, and worked as a Senior Resident Assistant, the Events Officer for the George’s Generals, and a tutor for the Writing Center. Aside from academics, Faithlin loves curling up with a good book, watching cheesy rom-coms, and connecting with new songs for her future choreography!

Description: In Johann Sebastian Bach’s “Canon 1 a 2” from The Musical Offering (1747), the piece begins by playing the original melody line of the canon and then introduces a retrograde of the line by playing the melody backwards, hence the canon’s nickname of the “crab canon.” However, in the transformation into a Möbius strip, the retrograded line is then also inverted and placed on the backside of the strip before twisting and linking the ends together. In topology, one could argue that a true Möbius strip was not created if a split in the strip was utilized before the twist, but scholars highly regard Bach’s Canon as a true Möbius strip. After defining the necessary musical and mathematical terms, we explore the topological phenomenon of Bach’s Crab Canon and whether it is truly a composition on a Möbius strip. Through mathematical concepts such as surfaces and transformations, music visualization can be expanded to aid audiences in understanding the compositional choices of composers. Finally, we gather all of these concepts to analyze a brief self-composed canon to demonstrate musical transformations and surfaces.

Keywords: composition, crab canons, mathematics, Möbius strip, music, symmetry, transformations

Read Faithlin’s SCE below: