Some fascinating Developments in Mathematics and Music

Abstract

The strength of the bonds between music and mathematics goes without saying. This popular belief hides a subtler misconception, that this relationship involves old school mathematics: arithmetics in the Greek School (Pythagoras), diophantine approximations in tuning theory (Euler, Rameau), Fourier series for the decomposi-tion of sound signal, and little else. However, there is much more than that and these two sciences still ad-vance hand in hand as of today. This paper will present by way of example three musical situations involving contemporary mathematical topics: Galois theory in a rhythmic canon problem in the field of minimalist mu-sic; a graph theory question raised by Ludwig van Beethoven which had to wait almost two centuries for an answer; and a neat word theory theorem discovered in a construction originating in combinations of mystical octaves and fifths in Plato’s Timaeus.