English

Motivic Rhythms

Number Theory 2020-08-28 v2

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 H1H^1 of the reduction modulo a prime pp of an hyperelliptic curve (defined over Q\mathbb Q). 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.

Cite

@article{arxiv.1812.09946,
  title  = {Motivic Rhythms},
  author = {Alain Connes},
  journal= {arXiv preprint arXiv:1812.09946},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-23T06:55:26.031Z