A new theory of lattice vibrations in amorphous silicon dioxide is presented in which the randomness of the solid is treated separately from its chemistry. The theory attributes all measurable properties of phonons in silica to the nearly crystalline nearest-neighbor geometry of the lattice and to the disruptive effects of bondangle disorder. Neutron, infrared, and Raman spectra are calculated and compared with experiment. The theory is an application of the recently developed cluster-Bethe-lattice approach to studying amorphous solids.