We have measured the inelastic neutron scattering spectrum of solid parahydrogen (at low pressure and T=13.3 K) using the thermal original spectrometer with cylindrical analyzers spectrometer at the ISIS pulsed neutron source (UK). From the experimental spectrum we have obtained the parahydrogen density of phonon states which has been compared with the estimates available in the literature. The present determination improves substantially the previous experimental scenario from the point of view of both statistics and accuracy. The comparison with the most recent estimate obtained from a quantum mechanical simulation of the molecular dynamics calls for an improvement of the computational methods. (C) 2004 American Institute of Physics.