In generative metrics, a meter is taken to be an abstract periodic template with a set of constraints mapping linguistic material onto it. Such templates, constrained by periodicity and line length, are usually limited in number. The repertoire of Classical Sanskrit verse meters is characterized by three features which contradict each of the above properties – (a) templates constituted by arbitrary syllable sequences without any overtly discernible periodic repetition: APERIODICITY, (b) absolute faithfulness of linguistic material to a given metrical template: INVARIANCE, and (c) a vast number of templates, ranging between 600–700: RICH REPERTOIRE. In this paper, I claim that in spite of apparent incompatibility, Sanskrit meters are based on the same principles of temporal organization as other versification traditions, and can be accounted for without significant alterations to existing assumptions about metrical structure. I demonstrate that a majority of aperiodic meters are, in fact, surface instantiations of a small set of underlying quantity-based periodic templates and that aperiodicity emerges from the complex mappings of linguistic material to these templates. Further, I argue that the appearance of a rich repertoire is an effect of nomenclatural choices and poetic convention and not variation at the level of underlying structure.