[en] Starting from the augmented space formalism (Mookerjee 1973 a,b), a cluster CPA calculation for the phonon density of states is presented for linear chains as well as three-dimensional lattices. Off-diagonal disorder has been taken into account, and a self-consistent medium has been generated. Unlike earlier work, the Green function does not suffer from analytical difficulties in any concentration range. At the same time, the self-consistent medium gives a superior estimate of the band edges and the structures near them. (author)