The description of oscillations in inhomogeneous magnetohydrodynamic plasmas in terms of spatial Fourier modes is extended beyond the previous analyses of the incompressible case to a fully compressible plasma in a rigid box. Attention is focused upon the cusp and Alfvén continua and the discrete fast-mode spectrum. As well as providing a convenient method of numerical solution, the modal approach yields novel insights; in particular, the energy ultimately ‘absorbed’ resonantly is just that initially (and always) residing in the continua, and is readily calculated.