The problem of how musical scales should sound has a long history and has had many different solutions over different times and cultures. We will discuss the close connection of the problem to mathematics, and using simple facts about numbers we will explore the tuning system commonly attributed to Pythagoras, the origin of the current Western system of tuning, and explain why it is impossible to tune a piano perfectly. We will also relate different tuning systems to ideas of more modern mathematics, and use the fundamental concept of synchronisation to create new nonlinear musical scales.
No prior knowledge of musical tuning is required to enjoy this talk - all musical and mathematical concepts will be explained as they occur.