The method of receptance analysis is used to set up a frequency equation for the free vibration modes of a one-dimensional periodic lattice (mass-spring system) containing a disorder which is itself a one-dimensional periodic lattice. The concepts of the propagation constant and wave-receptance function are used to determine the receptances of the component systems, and these are used to set up a simple frequency equation. An accurate root-searching computer programme has been used to find the natural frequencies and corresponding modes of particle displacement. Some computed results are shown to demonstrate the capability of the method and programme. Special attention is given to modes which occur in the frequency "forbidden" zone, and receptance methods are used to derive formulae for the frequencies of systems with a single-mass disorder. The wider usefulness of the method is briefly discussed.