Inelastic incoherent neutron scattering (IINS) cross sections have been measured for the recovered high-pressure phases of ice, ices II, V, VI, and IX (H2O) and ices II and IX (D2O) in the energy range from 2 to 150 meV at 20 K using the TFXA (time-focused crystal analyzer) neutron spectrometer on the ISIS pulsed neutron source at the Rutherford-Appleton Laboratory. The excellent resolution of the TFXA (less than 2%) covers the whole range of translational and librational modes for the ices investigated and enables us to identify the fine structures in their spectra. Hence a direct comparison between the amplitude-weighted phonon density of states derived from the experimental spectrum and from a lattice dynamic calculation is possible [E. Whalley and J. E. Bertie, J. Chem. Phys. 46, 1271 (1967); J. E. Bertie and E. Whalley, ibid. 40, 1646 (1964)]. The spectra from these polymorphic ices show many new features in the translational region, which are not visible using infared and Raman techniques. In the librational band region, the general features vary remarkably between phases. Thus, for instance, ice II, in which the protons are ordered, shows more structure in this region and has a sharper low-energy cutoff than do the other phases examined. The most significant observation is that the low-energy cutoff is characteristic of the phase. Relative to ice Ih, there is a shift of 4.3 meV for ice IX, of 8.8 meV for ice II, 8.6 meV for ice V, and 12.2 meV for ice VI.