# The harmony of mathematics and music

Two IB teachers reveal how an innovative interdisciplinary unit sparked curiosity in their students

Middle Years Programme (MYP) students at La Côte International School in Aubonne in Switzerland, explored how mathematics can help explain our reactions to music. Here, Francesco Banchini, who was the school’s Director of Performing Arts, and Lynda Thompson, mathematics teacher and former IB Diploma Programme (DP) coordinator at La Côte International School, share their interdisciplinary approach:

It all started with a conversation one evening between the two of us, a mathematics teacher and a music teacher. Why, we wondered, does some music make us sad and reflective, while other music makes us want to party?

That question inspired us to create an MYP interdisciplinary unit aimed at understanding to what extent our emotions can be described as mathematical. We focused on pattern and repetition, which is used in a variety of ways in both disciplines.

Since the music our students listen to and share is a meaningful part of their lives, they were intrigued at the prospect of finding out why they like the music they like. There was great appeal in using the ‘objective’ tool of mathematics to understand a ‘subjective’ reaction.

From Mayan temples to Arabian souks, we drew upon a range of different cultural traditions to illustrate how students can make meaningful use of skills developed within these two disciplines. While studying the Ancient Greeks, students made their own mono-chord instruments and used them to discover that as the length of the chord is halved, the frequency doubles. This doubling continues as an exponential function. We examined how the Greeks used different musical modes for different social purposes, and how these were associated with different emotions.

We looked at the relationship between the frequencies of notes that ‘sound good together’ (consonance) and those that do not (dissonance) using mathematical methods.

Students also enjoyed discovering that Lorde, Maroon 5, the Beatles and the Ramones all make use of modes from the Greek and Arabic traditions, and we found examples of songs by Guns N’ Roses, Madonna, the Rolling Stones, Gorillaz, Coldplay and Radiohead in the Greek Mixolydian mode. We considered whether this was a conscious decision on the part of the musicians.

One of the discussions that will stay with us was about how much our culture ‘trains’ our ears to find certain sounds consonant. We explored whether members of an isolated tribe, who had only ever heard forest sounds and their own instruments, would have the same ideas about consonance and dissonance as we do. What are the implications of living in a globally connected world where music is shared in every corner of the earth?

When delivering the unit we were able to team-teach certain sessions, which we felt served as strong role models to our students, who enjoyed sharing subject knowledge with the other teacher. In many ways, the most valuable lesson students gained was the understanding that what they learn in school subjects can be fused to become relevant to their interests and passions outside school.

The spark for this interdisciplinary unit was a genuine interest of our own, but it was just as meaningful for the students, and thus gave responsibility and ownership to them. While it required a time and energy commitment from us outside the school day as well as inside, it has left us thirsty to explore the link between music and maths more fully. In the words of Guns N’ Roses (in the Greek Mixolydian form), “Where do we go, where do we go now, where do we go”?

This article is part of a series of stories from IB World magazine that bring to life the wonderful initiatives undertaken by IB students and educators from around the globe. Follow these stories on Twitter @iborganization #IBcommunitystories. Share your great stories and experiences: email editor@ibo.org