Euler in 1739 wrote about a way to visualise harmonic relationships in music thus creating what is now called `Euler’s Tonnetz’. This talk is about Euler’s tonnetz from a modern point of view, and how to generalise it. Our ‘Tonnetze’ will take place on triangulated surfaces. We will, in particular, consider a set of examples that live on triangulations of tori and are related to crystallographic reflection groups, and a diatonic example related to a famous finite geometry.