User-defined calendars and periodicities are gaining an increasing relevance in AI and DB theory and applications. Thus several representation languages have been introduced to model them. Even focusing the attention on symbolic languages only, several different proposals can be chosen, and the comparisons between them are not trivial at all. In this paper, we propose a lattice of properties about periodicity and use it in order to classify different symbolic approaches in the literature. We then propose a language which covers all the properties in the lattice.