The Hebrew calendar or Jewish calendar is the annual calendar used in Judaism. It determines the Jewish holidays, which Torah portions to read, Yahrzeits, and which set of Psalms should be read each day. Originally observational, it is now a rule-based lunisolar calendar, using both lunar months and years defined via a solar cycle. This is in contrast to the Gregorian calendar, which is based solely upon a solar cycle, or the Islamic calendar, which is purely lunar. Although the Chinese calendar is also a lunisolar calendar, its rules are totally different. All seasons mentioned here are Northern Hemisphere seasons because the Hebrew calendar developed in the region east of the Mediterranean Sea.

History

Two major forms of the calendar have been used: an observational form used before the destruction of the Second Temple in 70 and a rule-based form first fully described by Maimonides in 1178. The period between 70 and 1178 is a transition period between the two forms, with the gradual adoption of more and more of the rules characteristic of the modern form. Except for the modern year number, the modern rules reached their final form before 820 or 921, with some uncertainty regarding when (see below). The modern Hebrew calendar cannot be used for Biblical dates because new moon dates may be in error by up to four days and months may be in error by up to four months. The latter accounts for irregular intercalation such as the three successive years which were given extra months during the early second century according to the Talmud.

Jews have been using a lunisolar calendar since Biblical times, but originally referred to the months by number rather than name. Although the Bible never mentions an embolismic (extra) month, it must have existed in order to keep the first month in spring. Only four pre-exilic month names appear in the Tanakh (the Old Testament), Abib (first), Ziv (second), Ethanim (seventh), and Bul (eighth). All are Canaanite and at least two are Phoenician names. Indeed, all of the months may have been identifiable via either native Jewish numbers or foreign Canaanite/Phoenician names, but the other names were simply not recorded in the Bible. During the Babylonian exile, immediately after 586 BCE, Jews adopted Babylonian names for the months. The Babylonian calendar was the direct descendent of the Sumerian calendar. Some sects, such as the Essenes, used a solar calendar during the last two centuries BCE.

In Second Temple times, the beginning of each lunar month was decided by two eyewitnesses testifying to having seen the new crescent moon. Patriarch Gamaliel II (c. 100) compared these accounts to drawings of the lunar phases. According to tradition, these observations were compared against calculations made by the main Jewish court, the Sanhedrin. Whether an embolismic month (a second Adar) was needed depended on the condition of roads used by families to come to Jerusalem for Passover, on an adequate number of lambs which were to be sacrificed at the temple, and on the earing of barley needed for first fruits. The beginning of each Hebrew month, once decided, was first announced to other communities by signal fires lit on mountaintops, but the Samaritans and Boethusaeans lit false fires, leading to the use of special messengers. But they could not reach the communities outside Israel within one day, so the outlying communities opted to celebrate scriptural festivals a second day as well, the "second feast-day of the Diaspora". During the time of the Amoraim (third to fifth centuries) calculations were increasingly used, e.g. by Samuel the astronomer during the first half of the third century who stated that the year contained 365 ¼ days, and by "calculators of the calendar" about 300. Jose, an Amora who lived during the second half of the fourth century, stated that the feast of Purim, 14 Adar, could not fall on a Sabbath or a Monday, lest 10 Tishri fall on a Friday or a Sunday. This indicates a fixed number of days in all months from Adar to Elul, also implying that the extra month was already a second Adar added before the regular Adar.

The Roman-Jewish wars of 66.74, 115.117, and 132.135 caused major disruptions in Jewish life, also disrupting the calendar. During the third and fourth centuries, Christian sources describe the use of eight, nineteen, and 84 year lunisolar cycles by Jews, all linked to the civil calendars used by various communities of Diaspora Jews, which were effectively isolated from Levant Jews and their calendar. Some assigned major Jewish festivals to fixed solar calendar dates, whereas others used epacts to specify how many days before major civil solar dates Jewish lunar months were to begin.

The Ethiopic Christian computus (used to calculate Easter) describes in detail a Jewish calendar which must have been used by Alexandrian Jews near the end of the third century. These Jews formed a relatively new community in the aftermath of the annihilation (by murder or enslavement) of all Alexandrian Jews by Emperor Trajan at the end of the 115.117 war. Their calendar used the same epacts in nineteen year cycles that were to become canonical in the Easter computus used by almost all medieval Christians, both those in the Latin West and the Greek East. Only those churches beyond the eastern border of the Byzantine Empire differed, changing one epact every nineteen years, causing four Easters every 532 years to differ.

A popular tradition holds that Patriarch Hillel II revealed the continuous calendar in 359 due to Christian persecution, formerly a secret known only to the 'calendar committee', a council of sages. This tradition was first mentioned quite late by Hai Gaon (died 1038). But the Talmud, which did not reach its final form until c. 500, does not mention it or even anything as mundane as the nineteen year cycle or the length of any month, despite discussing the characteristics of earlier calendars. Furthermore, Jewish dates during post-Talmudic times (specifically in 506 and 776) are impossible using modern rules. Instead, all evidence points to the arithmetic rules of the modern calendar being developed in Babylonia during the times of the Geonim (seventh to eighth centuries). Most of the modern rules were in place by about 820 as described by the Muslim astronomer al-Khwarizmi. A notable exception was the epoch (the beginning of year 1), which was placed one year later than that of the modern calendar.

In 921, Aaron ben Meir, a person otherwise unknown, sought to return the authority for the calendar to Palestine by asserting that the first day of Tishri should be the day of the new moon unless the new moon occurred more than 642 parts after noon, when it should be delayed by one or two days. The Babylonian rules delayed the first day of Tishri when the new moon occurred after noon. One possible explanation is that local time on the Babylonian meridian is 642 parts later than on the meridian of Jerusalem, so ben Meir was asserting that the calendar should be run from Jerusalem, not Babylon. An alternative explanation for the 642 parts is as follows: The calculated time of New Moon during the six days of creation was on Friday at 14 hours exactly (day starting at 6pm the previous evening), assuming that creation occurred in the Autumn to coincide with Rosh Hashana. However, it was at 9 hours and 642 parts on Wednesday if creation actually took place six months earlier, in Spring. Ben Meir may thus have believed, along with many earlier Jewish scholars, that creation occurred in Spring and the calendar rules had been adjusted by 642 parts to fit in with an Autumn date. In any event he was opposed by Sa'adiah Gaon and in the end all Jewish communities ignored his opinion, but accounts of the controversy show that all of the rules of the modern calendar (except for the year) were in place before 921. In 1000, the Muslim chronologist al-Biruni also described all of the modern rules except that he specified three different epochs used by various Jewish communities being one, two, or three years later than the modern epoch. Finally, in 1178 Maimonides described all of the modern rules, including the modern epochal year.