Information about local and dynamic atomic correlations can be obtained from inelastic neutron-scattering measurements by Fourier transform of the Q-dependent intensity oscillations at a particular frequency. A local dynamic structure function, S(r, ω), is defined from the dynamic scattering function, S(Q, ω), such that the elastic and frequency-integrated limits correspond to the average and instantaneous pair-distribution functions, respectively. As an example, S(r, ω) is calculated for polycrystalline aluminum in a model where atomic motions are entirely due to harmonic phonons.