Motivic Rhythms
arXiv:1812.09946
Abstract
In this article on mathematics and music, we explain how one can "listen to motives" as rhythmic interpreters. In the simplest instance which is the one we shall consider, the motive is simply the of the reduction modulo a prime of an hyperelliptic curve (defined over ). The corresponding { time onsets} are given by the arguments of the complex eigenvalues of the Frobenius. We find a surprising relation between mathematical properties of the motives and the ideas on rhythms developed by the composer Olivier Messiaen.
28 pages, link with the music mp3 at https://www.dropbox.com/s/df3vvuhkvel5eap/musescoremi.mp3?dl=0 and to related video https://www.dropbox.com/s/ld1z64em5u3mxjx/fullvideo.mp4 , accepted by the Journal of Mathematics and Music