The inelastic neutron cross section is calculated for a modulated spring chain, which models an incommensurate composite system. The authors obtain a difference equation for the neutron cross section which has an exact and analytic solution for a periodic modulation. The structure of the neutron spectrum is studied as functions of wavevector and energy transfers for a wide range of model parameters. In general the spectra consist of bands of intensity, except at special wavevectors where bands collapse to a singular structure characteristic of normal modes of vibration.