In the next two chapters, I shall examine specific aspects of the Jewish lunar calendars that prevailed in the first century ce and beyond, restricting myself to non-rabbinic sources, including Jewish literature, Jewish inscriptions, as well as early Christian sources. Rabbinic sources will be left to Chs. 4-5 . For the sake of clarity, I shall examine separately the two essential features of lunar calendar reckoning: intercalation (Ch. 2), and the determination of new months (Ch. 3).
An essential feature of Jewish and other ancient lunar calendars is the intercalation of an additional month (a 13th month) every second or third year. This intercalation is necessary in order to remain in line with the solar year. Twelve lunar months, indeed, amount to approximately 354⅓ days (each month being on average slightly over 29½ days), whereas the solar (tropical) year is just under 365¼ days; hence a discrepancy of almost 11 days. In order for the lunar year to keep up with the solar year, i.e. for lunar months to recur in or around the same seasons, this discrepancy must be compensated every three (and sometimes two) years with the intercalation of an additional lunar month. Because of this solar element, the Jewish calendar is sometimes called 'lunisolar'.
There are two ways of making intercalations. The first is purely empirical. An assessment is made every year—or at most, one or two years in advance—of the discrepancy that has accumulated between the lunar and the solar year. On that basis, the decision is taken whether to intercalate an additional month. In some cases, account is also taken of extraneous considerations, e.g. social, political or economic. The incidence of intercalated years is thus irregular and largely unpredictable.