Hebrew Calendar

The Hebrew calendar is a lunisolar system: its months are set by the moon, each beginning near the new moon, while the year is kept in step with the sun by adding a thirteenth month in seven years out of every nineteen. An ordinary year runs twelve lunar months of 353 to 355 days; a leap year, with its added month of Adar, runs 383 to 385. Its era, Anno Mundi, counts from the traditional date of creation, placed at 3761 BCE, so its years run in the fifty-eight hundreds and beyond. The intercalated month holds Passover in the spring as the Torah requires, and the whole is governed by fixed arithmetical rules settled in the early medieval period. These are the features of the Jewish calendar tradition, which orders the festivals and the religious year of Judaism.

The nineteen-year leap cycle follows the Metonic cycle, the same nineteen-solar-year period in which 235 lunar months closely match 235 lunations, independently identified by the Athenian astronomer Meton in the fifth century BCE and adopted into the fixed Hebrew calendar attributed to the Nasi Hillel II around 358 to 359 CE. Years 3, 6, 8, 11, 14, 17 and 19 of the cycle carry the extra month, Adar I, with the regular Adar becoming Adar II in those years. Before Hillel II's fixed arithmetic, the calendar had been set by direct observation, witnesses testifying to the Sanhedrin that they had seen the new crescent moon, supplemented by messengers who carried word of the sighting to Jewish communities outside the Land of Israel; the shift to a calculated calendar removed the need for that observational and communication network. The calendar also applies four dechiyot, postponement rules, that can shift the start of Rosh Hashanah by a day or two to keep certain festivals off inconvenient weekdays.

Every calendar in the world solves the same arithmetic problem, and there are only three solutions. A lunation is about 29.53 days and a tropical year about 365.2422 days, and the second is not a whole multiple of the first. A calendar can therefore follow the Moon and let its year drift against the sun, follow the sun and let its months lose contact with the Moon, or follow both and insert an extra month at intervals to keep them together.

The Jewish calendar takes the third path. Twelve lunar months of 29 or 30 days give 354, eleven short of the solar year, and a thirteenth month is added in seven years out of every nineteen on a fixed cycle, which keeps Passover in the spring as the Torah requires. The nineteen-year relation is the same one Greek astronomy knew as the Metonic cycle, since 235 lunations come to within a couple of hours of nineteen solar years.

What distinguishes it from other lunisolar calendars is that it is calculated rather than observed. The present fixed calendar, with its rules of postponement that prevent certain holy days from falling on certain weekdays, replaced a system of monthly observation and proclamation by the court, and the transition is generally placed in the first millennium of the common era though its stages are debated. The result is a calendar that can be computed centuries ahead, which is unusual among lunisolar systems.

The era counts from a calculated date of creation, so the year number is far larger than in the civil calendar, and the year begins in the autumn at Rosh Hashanah while the months are numbered from the spring, which is a genuine double convention rather than an inconsistency.

The Hebrew calendar's leap months follow a rhythm older than the calendar's fixed form: the nineteen year lunisolar cycle. The underlying fact is astronomical. Nineteen solar years and two hundred thirty five lunar months agree with each other to within about two hours, so a calendar that adds a thirteenth month in seven years out of every nineteen keeps its months on the moon and its festivals in their seasons at the same time. Babylonian astronomers standardised intercalation on this cycle by the fifth century BCE, and the Athenian astronomer Meton published it in 432 BCE, which is why the West calls it the Metonic cycle.

The fixed Hebrew calendar embeds it directly: years three, six, eight, eleven, fourteen, seventeen and nineteen of each cycle receive the added month of Adar, and the pattern repeats without observation or decree. The same nineteen year rhythm reached Christian timekeeping through the computus, where the golden number, a year's position in the cycle, located the paschal moon for the date of Easter. Babylonian astronomy yielded a second great period relation, the saros of two hundred twenty three months, after which eclipses repeat; it governs eclipse prediction rather than any calendar, and the two cycles together are the deep arithmetic under this part of the atlas. Neither has an entry of its own by design: they are rhythms, and they live where they are used.