Marissa Numer | 2025 I.S. Symposium

Name: Marissa Numer
Title: A Link Between Mathematics and Music: The Tonnetz
Major: Mathematics
Minor: Music
Advisor: Dr. Cynthia Lester

I was interested in discovering a connection between mathematics and music, two of my seemingly unrelated passions. I discovered the Tonnetz is one link of many that exist between mathematics and music theory. In fact, advancements in mathematical calculations were the core reasons why instruments can be tuned by equal temperament today.

My project aims to understand the historical contexts in which the Tonnetz was developed, describe note- and chord-based graphs, explain the mathematical implications of how the note-based Tonnetz graph is constructed in two dimensions, and briefly mention how the Tonnetz was generalized by Dmitri Tymoczko and Konstanze Rietsch to n-dimensional space. Introductions to relevant music theoretical and mathematical concepts necessary to understand the discussion within this thesis are also included. Some of these topics are set and group theory, vector spaces, introductory Euclidean geometry, and topology.

In the future, I would enjoy developing a deeper understanding of the generalization process as well as the complexities and simplifications of chord space. It is interesting to note that in one paper, Fourier phase space was used to generalize the Tonnetz.
Additionally, I am fascinated by studies that are using machine learning and model building to understand and represent music theoretical concepts. Not only can mathematics be used as a tool to better understand structures within music theory, but data science can be used as well

Posted in Symposium 2025 on May 1, 2025.