The MHD spectrum associated with small perturbations about an analytic equilibrium is determined for a configuration with magnetic flux surfaces which are nested similar elliptic cylinders generated by a uniform axial current. Since the system is periodic, it models the essential features of a toroid. Both analytic and numerical techniques are used to investigate many properties of the modes, including the continuous shear Alfvén and slow acoustic spectra as well as the discrete modes associated with fast magnetosonic waves, kinks, and instabilities where the interchange criterion is violated. In particular, the relationship between discrete and continuum modes is described both qualitatively and quantitatively, and it is shown how the unstable interchange modes emerge from the shear-Alfvén branch of the spectrum.