We present an analytical treatment of the acoustics of liquid-filled wine glasses, or "glass harps." The solution is generalized such that under certain assumptions it reduces to previous glass harp models, but also leads to a proposed musical instrument, the "inverted glass harp," in which an empty glass is submerged in a liquid-filled basin. The versatility of the solution demonstrates that all glass harps are governed by a family of solutions to Laplace's equation around a vibrating disk. Tonal analyses of recordings for a sample glass are offered as confirmation of the scaling predictions.