Generalising Euler’s Tonnetz

3 PM, 17 Oct 2025

Konstanze Rietsch explores Euler’s Tonnetz through the lens of modern geometry, revealing new links between music, symmetry and harmony.

In 1739, Euler devised the Tonnetz, a lattice to visualise harmonic relations in music. In this talk, Prof. Konstanze Rietsch revisits Euler’s Tonnetz from a modern point of view, exploring Tonnetze on tiled surfaces. She presents examples on triangulated tori related to crystallographic reflection groups, as well as a diatonic case tied to finite geometry, yielding elegant new visualisations of chord progressions.

Konstanze Rietsch is a professor at King’s College London. She works on the geometry of flag varieties and is also interested in total positivity, a theory that allows many geometric objects occurring in Lie theory to be defined, in some sense, over the positive real numbers.

Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz
Generalising Euler’s Tonnetz