The calendar described in the Mishnah and Tosefta (early third century c.e.) is purely empirical, both in its intercalation procedure and in its determination of the new moon. But in the Amoraic period (third–fifth centuries), as attested in the Talmud, calendrical rules were introduced, which eventually led to the transformation of the rabbinic calendar into a fixed, calculated scheme. A fixed rabbinic calendar is unlikely to have been formally instituted, e.g. in 359 c.e. by Hillel, as is commonly believed. Rabbinic sources indicate that, even in the Geonic period, the calculated calendar had not reached its final form; this only came about in the ninth century.
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