Jewish Talmudic Calendar
The Jewish Talmudic Calendar is a lunisolar calendar using Tishri-years, observed by the Jewish people since the Late Antiquity (AD 300-700). While it is based on Nisan-years, which began from the prebiblical Babylonian times (c. 2000 BC), and the Tishri-years was formed in the time of David (c. 1000 BC), the full formation of the Jewish Talmudic Calendar was during the time of the writing of Talmud (c. AD 300-600), usually attributed to Hillel II.
The ancient Israelite Calendar, no matter Nisan-years or Tishri-years, was determined by the astronomical observation of the New Moon, and the agricultural observation of the growth of Abib (the spikes on the Barley) in late Winter and early Spring. After the second (Roman) Diaspora, in order for the Jewish people away from the Land of Israel to be able to observe their Spring Feasts and Fall Feasts in the same calendar, the Jewish Talmudic Calendar was formed, based on mathematical algorithms, and free from the required observations.
The Jewish Talmudic Calendar, in agreement with the Almagest and the writings of Kidinnu, assumes that a month is uniformly of the length of an average synodic month, taken as exactly 29 13753⁄25920 days (about 29.530594 days, which is less than half a second from the modern scientific estimate); it also assumes that a tropical year is exactly 12 7⁄19 times that, i.e. about 365.2468 days. Thus it overestimates the length of the tropical year (365.2422 days) by 0.0046 days (about 7 minutes) per year, or about one day in 216 years. This error is less than the Julian years (365.2500 days) make (0.0078 days/year, or one day in 128 years), but much more than what the Gregorian years (365.2425 days/year) make (0.0003 days/year, or one day in 3333 years).
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