  Let $\frak{e}\subset\mathbb{R}$ be a finite union of disjoint closed
intervals. In the study of OPRL with measures whose essential support is
$\frak{e}$, a fundamental role is played by the isospectral torus. In this
paper, we use a covering map formalism to define and study this isospectral
torus. Our goal is to make a coherent presentation of properties and bounds for
this special class as a tool for ourselves and others to study perturbations.
One important result is the expression of Jost functions for the torus in terms
of theta functions.
