The spectrum of frequencies and growth rates of the linearized magnetohydrodynamic motion about rotating straight theta pinch equilibria is investigated. A qualitative picture is obtained of the distribution of eigenvalues in the complex plane, and of their dependence on equilibrium parameters and the three mode numbers. A numerical procedure is described which uses this picture for computing the eigenvalue with any given triple of mode numbers. It is shown that rigidly rotating equilibria are unstable unless the mass density is an increasing function of radius; computations indicate that rotation shear (within practical limits) cannot stabilize confined equilibria.