  In this paper we investigate the connection between (non-)geometry and
(non-)commutativity of the closed string. To this end, we solve the classical
string on three T-dual toroidal backgrounds: a torus with H-flux, a twisted
torus and a non-geometric background with Q-flux. In all three situations we
work under the assumption of a dilute flux and consider quantities to linear
order in the flux density. Furthermore, we perform the first steps of a
canonical quantization for the twisted torus, to derive commutators of the
string expansion modes. We use them as well as T-duality to determine, in the
non-geometric background, a commutator of two string coordinates, which turns
out to be non-vanishing. We relate this non-commutativity to the closed string
boundary conditions, and the non-geometric Q-flux.
