Some fascinating developments in mathematics and music

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 decomposition of sound signal, and little else. However, there is much more than that and these two sciences still advance 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 music; 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.