It is reasonably well attested that Jewish communities, all over the Roman empire, observed the Sabbath and the Jewish or Biblical festivals.1 If so, they must have had ways of reckoning their dates. In some cases, it may have been sufficient for them to establish the individual dates of annual festivals: for instance, that Passover would occur on the first full moon in the spring. But the celebration of new months, noumeniae, is also well attested in a number of Diaspora communities, and this implies a continuous calendar, running from month to month through the whole year. This suggests that Jewish communities reckoned their own calendars, of which the main function was to determine the dates of Jewish noumeniae, fasts, and festivals.