  Let $S$ be the union of finitely many disjoint intervals on the real line.
Suppose that there are two real numbers $\alpha, \beta$ such that the length of
each interval belongs to $Z \alpha + Z \beta$. We use quasicrystals to
construct a discrete set of real frequencies such that the corresponding system
of exponentials is a Riesz basis in the space $L^2(S)$.
