A new interpretation is presented of the vibrational band shapes of the proton disordered ice Ih and Ic in the OH and OD stretch region. The vibrationally excited states are shown to be related to those of a periodic system, whose unit cell is composed of four oscillating dipoles in a tetrahedral arrangement around an O-atom. Analysis of the excitations in this periodic system and of the perturbation induced by disorder is used to provide a detailed assignment of the band shapes of the measured spectra.