Hebrew calendar

Introduction

The Hebrew calendar or Jewish calendar is the annual calendar used in Judaism. It determines the dates of the Jewish holidays, the appropriate Torah portions for public reading, Yahrzeits (the date to commemorate the death of a relative), and the specific daily Psalms which some customarily read. Two major forms of the calendar have been used: an observational form used prior to the destruction of the Second Temple in 70, and based on witnesses observing the phase of the moon, and a rule-based form first fully described by Maimonides in 1178, which was adopted over a transition period between 70 and 1178.

The "modern" form is a rule-based lunisolar calendar, akin to the Chinese calendar, measuring months defined in lunar cycles as well as years measured in solar cycles, and distinct from the purely lunar Islamic calendar and the almost entirely solar Gregorian calendar. Because of the roughly 11 day difference between twelve lunar months and one solar year, the calendar repeats in a Metonic 19-year cycle of 235 lunar months, with an extra lunar month added once every two or three years, for a total of seven times every nineteen years. As the Hebrew calendar was developed in the region east of the Mediterranean Sea, references to seasons reflect the times and climate of the Northern Hemisphere.

History

Biblical period

Jews have been using a lunisolar calendar since Biblical times, but originally referred to the months by number rather than name. Only four pre-exilic month names appear in the Tanakh (the Hebrew Bible): Abib (first, literally "Spring"), Ziv (second), Ethanim (seventh), and Bul (eighth), and all are Canaanite names, and at least two are also Phoenician. It is possible that all of the months were initially identifiable by native Jewish numbers or foreign Canaanite/Phoenician names, but other names do not appear in the Bible.

Furthermore, because solar years cannot be divided evenly into lunar months, an extra "embolismic" month must be added to prevent the starting date of the lunar cycles from "drifting" away from the Spring, although there is no mention of this in the Bible.

Babylonian exile

During the Babylonian exile, immediately after 586 BCE, Jews adopted Babylonian names for the months, and some sects, such as the Essenes, used a solar calendar during the last two centuries BCE. The Babylonian calendar was the direct descendent of the Sumerian calendar.

Names and lengths of the months

The Hebrew names of the months, with their Babylonian analogues, are

Number	Hebrew name	Length	Babylonian analog
1	Nisan	30 days	Nisanu
2	Iyar	29 days	Ayaru
3	Sivan	30 days	Simanu
4	Tammuz	29 days	Du`uzu
5	Av	30 days	Abu
6	Elul	29 days	Ululu
7	Tishrei	30 days	Tashritu
8	Cheshvan, also spelled Heshvan or Marcheshvan	29 or 30 days	Arakhsamna
9	Kislev	30 or 29 days	Kislimu
10	Tevet	29 days	Tebetu
11	Shevat	30 days	Shabatu
12	Adar	29 days	Adaru

Second Temple era

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 or not 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.

Once decided, the beginning of each Hebrew month was first announced to other communities by signal fires lit on mountaintops, but after the Samaritans and Boethusaeans began to light false fires, special messengers were used. The inability of the messengers to reach communities outside Israel within one day, led outlying communities to celebrate scriptural festivals for two days rather than for one, observing the "second feast-day of the Jewish diaspora."

From the times of the Amoraim (third to fifth centuries), calculations were increasingly used, for example by Samuel the astronomer, who stated during the first half of the third century that the year contained 365 ¼ days, and by "calculators of the calendar" circa 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 nor a Monday, lest 10 Tishri (Yom Kippur) 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.

Roman Era

The Jewish-Roman 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.

Alexandrian Jewish calendar

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 Kitos 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 Hellenist 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.

Transition Period

The period between 70 and 1178 was 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. The modern Hebrew calendar cannot be used to calculate 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 the irregular intercalation (adding of extra months) that was performed in three successive years in the early second century, according to the Talmud.

Evidence for adoption of the modern rules

A popular tradition, first mentioned by Hai Gaon (d.1038), holds that the modern continuous calendar was formerly a secret known only to a council of sages or "calendar committee," and that Patriarch Hillel II revealed it in 359 due to Christian persecution. However, the Talmud, which did not reach its final form until c. 500, does not mention the continuous calendar or even anything as mundane as either 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, and all evidence points to the development of the arithmetic rules of the modern calendar in Babylonia during the times of the Geonim (seventh to eighth centuries), with most of the modern rules in place by about 820, according to the Muslim astronomer al-Khwarizmi. One notable difference was the date of the epoch (the fixed reference point at the beginning of year 1), which at that time was identified as one year later than the epoch of the modern calendar.

Controversy over the Passover of 4682 AM

The Babylonian rules required the delay of 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. An alternative explanation for the 642 parts is that if Creation occurred in the Autumn, to coincide with the observance of Rosh Hashana, (which marks the changing of the calendar year), the calculated time of New Moon during the six days of creation was on Friday at 14 hours exactly (counting from the day starting at 6pm the previous evening). However, if Creation actually occurred six months earlier, in the Spring, the new moon would have occurred at 9 hours and 642 parts on Wednesday.

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. 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; alternatively, he may have been asserting that the calendar should be run according to Jerusalem time, not Babylonian.

In any event he was opposed by Saadiah Gaon. Only a few Jewish communities accepted ben Meir's opinion, and even these soon rejected it. Accounts of the controversy show that all of the rules of the modern calendar (except for the epoch) 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.

When does the year begin?

According to the Mishnah, there are four new years, in Nisan for civil purposes, Elul for certain matters connected with agriculture and the Temple, Tishri for religious purposes and Shevat for trees. The last of these is marked by a minor festival, Tu Bishvat, named after the day it occurs on, the 15th Shevat (ט"ו בשבט). Months are numbered from Nisan (reflecting the injunction in Exodus "This month shall be to you the beginning of months". However, the New Year is the first of Tishri, when the year number increases by 1 and the formal new year festival Rosh Hashana is celebrated. There may be an echo here of a controversy in the Talmud about whether the world was created in Tishri or Nisan; it was decided that the answer is Tishri.

Modern calendar

Epoch

The epoch of the modern Hebrew calendar is 1 Tishri AM 1 (AM = anno mundi = in the year of the world), which in the proleptic Julian calendar is Monday, October 7, 3761 BCE, the equivalent tabular date (same daylight period). This date is about one year before the traditional Jewish date of Creation on 25 Elul AM 1. A minority place Creation on 25 Adar AM 1, six months earlier, or six months after the modern epoch. Thus adding 3760 to any Julian/Gregorian year number after 1178 will yield the Hebrew year number beginning in autumn (add 3759 for that ending in autumn). Due to the slow drift of the Jewish calendar relative to the Gregorian calendar, this will be true for about another 20,000 years.

Measurement of the month

The Hebrew month is tied to an excellent measurement of the average time taken by the Moon to cycle from lunar conjunction to lunar conjunction. Twelve lunar months are about 354 days while the solar year is about 365 days so an extra lunar month is added every two or three years in accordance with a 19-year cycle of 235 lunar months (12 regular months every year plus 7 extra or embolismic months every 19 years). The average Hebrew year length is about 365.2468 days, about 7 minutes longer than the average tropical solar year which is about 365.2422 days. Approximately every 216 years, those minutes add up so that the Hebrew year is "slower" than the average solar year by a full day. Because the average Gregorian year is 365.2425 days, the average Hebrew year is slower by a day every 231 Gregorian years. During the last century a number of Jewish scholars suggested that the chief rabbinate in Jerusalem consider modifying this rule to avoid this effect.

Pattern of calendar years

There are exactly 14 different patterns that Hebrew calendar years may take. Each of these patterns is called a "keviyah" (Hebrew for "species"), and is distinguished by the day of the week for Rosh Hashanah of that particular year and by that particular year's length.

A chaserah year (Hebrew for "deficient" or "incomplete") is 353 or 383 days long because a day is taken away from the month of Kislev. The Hebrew letter ח "het", and the letter for the weekday denotes this pattern.
A kesidrah year ("regular" or "in-order") is 354 or 384 days long. The Hebrew letter כ "kaf", and the letter for the week-day denotes this pattern.
A shlemah year ("abundant" or "complete") is 355 or 385 days long because a day is added to the month of Heshvan. The Hebrew letter ש "shin", and the letter for the week-day denotes this pattern.

A variant of this pattern of naming includes another letter which specifies the day of the week for the first day of Pesach (Passover) in the year.

Measurement of hours

Every hour is divided into 1080 halakim or parts. A part is 3¹/₃ seconds or ¹/₁₈ minute. The ultimate ancestor of the helek was a small Babylonian time period called a barleycorn, itself equal to ¹/₇₂ of a Babylonian time degree (1° of celestial rotation). Actually, the barleycorn or she was the name applied to the smallest units of all Babylonian measurements, whether of length, area, volume, weight, angle, or time. But by the twelfth century that source had been forgotten, causing Maimonides to speculate that there were 1080 parts in an hour because that number was evenly divisible by all numbers from 1 to 10 except 7. But the same statement can be made regarding 360. The weekdays start with Sunday (day 1) and proceed to Saturday (day 7). Since some calculations use division, a remainder of 0 signifies Saturday.

Measurement of lunar conjunctions/molads

The calendar is based on mean lunar conjunctions called "molads" spaced precisely 29 days, 12 hours, and 793 parts apart. Actual conjunctions vary from the molads by up to 7 hours in each direction due to the nonuniform velocity of the moon. This value for the interval between molads (the mean synodic month) was measured by Babylonians before 300 BCE and was adopted by the Greek astronomer Hipparchus and the Alexandrian astronomer Ptolemy. Its remarkable accuracy was achieved using records of lunar eclipses from the eighth to fifth centuries BCE. Measured on a strictly uniform time scale, such as that provided by an atomic clock, the mean synodic month is becoming gradually longer, but since the rotation of the earth is slowing even more the mean synodic month is becoming gradually shorter in terms of the day-night cycle. The value 29-12-793 was almost exactly correct at the time of Hillell II and is now about 0.6 s per month too great. However it is still the most correct value possible as long as only whole numbers of parts are used. Especially, it is far more accurate than the average solar year due to the 19-years-235-months equality described above — the total accumulated error of 29-12-793 from its Babylonian measurement until the present amounts to only about five hours.

Metonic cycle

The 19 year cycle has 12 common and 7 leap years. There are 235 lunar months in each cycle. This gives a total of 6939 days, 16 hours and 595 parts for each cycle. Due to the vagaries of the Hebrew calendar, 19 Hebrew years can be either 6939, 6940, 6941, or 6942 days each. To start on the same day of the week, the days in the cycle must be divisible by 7, but none of these values can be so divided. This keeps the Hebrew calendar from repeating itself too often. The calendar almost repeats every 247 years, except for an excess of 50 minutes (905 parts). So the calendar actually repeats every 36,288 cycles (every 689,472 Hebrew years).

Leap years of 13 months are the 3rd, 6th, 8th, 11th, 14th, 17th, and the 19th years beginning at the epoch of the modern calendar. Dividing the Hebrew year number by 19, and looking at the remainder will tell you if the year is a leap year (for the 19th year, the remainder is zero). A Hebrew leap year is one that has 13 months in it, a common year has 12 months. A mnemonic word in Hebrew is GUCHADZaT (the Hebrew letters gimel-vav-het aleph-dalet-zayin-tet, i.e. 3, 6, 8, 1, 4, 7, 9. See Hebrew numerals). Another mnemonic is that the intervals of the major scale follow the same pattern as do Hebrew leap years: a whole step in the scale corresponds to two common years between consecutive leap years, and a half step to one common between two leap years.

A Hebrew common year will only have 353, 354, or 355 days. A leap year will have 383, 384, or 385 days.

Special holiday rules

Although simple math would calculate 21 patterns for calendar years, there are other limitations which mean that Rosh Hashanah may only occur on Mondays, Tuesdays, Thursdays, and Saturdays (the "four gates"), according to the following table:

Day of Week	Number of Days
Monday	353	355	383	385
Tuesday	354			384
Thursday	354	355	383	385
Saturday	353	355	383	385

The lengths are described in the section Names and lengths of the months.

In leap years, a 30 day month called Adar I is inserted immediately after the month of Shevat, and the regular 29 day month of Adar is called Adar II. This is done to ensure that the months of the Jewish calendar always fall in roughly the same seasons of the solar year, and in particular that Nissan is always in spring. Whether either Chesvan or Kislev both have 29 days, or both have 30 days, or one has 29 days and the other 30 days depends upon the number of days needed in each year. Thus a leap year of 13 months has an average length of 383½ days, so for this reason alone sometimes a leap year needs 383 and sometimes 384 days. Additionally, adjustments are needed to ensure certain holy days and festivals do or do not fall on certain days of the week in the coming year. For example, Yom Kippur, on which no work can be done, can never fall on Friday because the high fast could not be broken at sunset — because the end of Yom Kippur would be the start of the Sabbath, on which no work can be done. Thus some flexibility has been built in.

The 265 days from the first day of the 29 day month of Adar (i.e. the twelfth month, but the thirteenth month, Adar II, in leap years) and ending with the 29th day of Heshvan forms a fixed length period that has all of the festivals specified in the Bible, such as Pesach (Nissan 15), Shavuot (Sivan 6), Rosh Hashana (Tishri 1), Yom Kippur (Tishri 10), Sukkot (Tishri 15), and Shemini Atzeret (Tishri 22).

The festival period from Pesach up to and including Shemini Atzeret is exactly 185 days long. The time from the traditional day of the vernal equinox up to and including the traditional day of the autumnal equinox is also exactly 185 days long. This has caused some unfounded speculation that Pesach should be March 21, and Shemini Atzeret should be September 21, which are the traditional days for the equinoxes. Just as the Hebrew day starts at sunset, the Hebrew year starts in the Autumn (Rosh Hashanah), although the mismatch of solar and lunar years will eventually move it to another season if the calendar isn't reformed (this will not happen for thousands of years).

Karaite interpretation

Karaites use the lunar month and the solar year, but determine when to add a leap month by observing the ripening of barley in Israel, rather than a fixed calendar. This occasionally puts them a month out of sync with the rest of the Jews. (For several centuries, most Karaites, especially outside Israel, have kept in step with other Jews for the sake of simplicity. However, in recent years many Karaites have reverted to their traditional practice.)

Accuracy

The average length of the month assumed by the calendar is correct within a fraction of a second (although individual months may be a few hours longer or shorter than average). There will thus be no significant errors from this source for a very long time. However, the assumption that 19 tropical years exactly equal 235 months is wrong, so the average length of a 19 year cycle is too long (compared with 19 tropical years) by about 0.088 days or just over 2 hours. Thus on average the calendar gets further out of step with the tropical year by roughly one day in 216 years. If the intention of the calendar is that Pesach should fall on the first full moon after the vernal equinox, this is still the case in most years. However, at present three times in 19 years Pesach is a month late by this criterion (as in 2005). Clearly, this problem will get worse over time and if the calendar is not amended, Pesach and the other festivals will progress through a complete cycle of seasons in about 79,000 years.

As the 19 year cycle (and indeed all aspects of the calendar) is part of codified Jewish law, it would only be possible to amend it if a Sanhedrin could be convened. This will only take place when the rebuilding of the Third Temple has begun, which will mark the salvation of the Hebrews according to Jewish belief. Theoretically, if Jewish law could be modified, one solution would be to replace the 19-year cycle with a 334-year cycle of 4131 lunations. This cycle has an error of only one day in about 11,500 years. However, this would be impossibly cumbersome in practice. Further, no fixed rule could be valid in perpetuity, because the lengths of both the month and tropical year are slowly changing. Another possibility would be to calculate the approximate time of the vernal equinox and have a leap year if and only if Pesach would otherwise start before the vernal equinox. Similar ideas are used in the Chinese calendar and some Indian calendars.

References

The Code of Maimonides (Mishneh Torah), Book Three, Treatise Eight: Sanctification of the New Moon. Translated by Solomon Gandz. Yale Judaica Series Volume XI, Yale University Press, New Haven, Conn., 1956.
Ernest Wiesenberg. "Appendix: Addenda and Corrigenda to Treatise VIII". The Code of Maimonides (Mishneh Torah), Book Three: The Book of Seasons. Yale Judaica Series Volume XIV, Yale University Press, New Haven, Conn., 1961. pp.557-602.
Samuel Poznanski. "Calendar (Jewish)". Encylopædia of Religion and Ethics, 1911.
F.H. Woods. "Calendar (Hebrew)", Encylopædia of Religion and Ethics, 1911.
Sherrard Beaumont Burnaby. Elements of the Jewish and Muhammadan Calendars. George Bell and Sons, London, 1901.
W.H. Feldman. Rabbinical Mathematics and Astronomy,3rd edition, Sepher-Hermon Press, 1978.
Otto Neugebauer. Ethiopic astronomy and computus. Österreichische Akademie der Wissenschaften, philosophisch-historische klasse, sitzungsberichte 347. Vienna, 1979.
Ari Belenkiy. "A Unique Feature of the Jewish Calendar — Dehiyot". Culture and Cosmos 6 (2002) 3-22.
Arthur Spier. The Comprehensive Hebrew Calendar. Feldheim, 1986.
L.A. Resnikoff. "Jewish calendar calculations", Scripta Mathematica 9 (1943) 191-195, 274-277.
Edward M. Reingold and Nachum Dershowitz. Calendrical Calculations: The Millenium Edition. Cambridge University Press; 2 edition (July 1, 2001). ISBN 0521777526

External links

Jewish Calendar Details various Jewish points-of-view about the history of the Jewish calendar/Hebrew calendar. Includes several charts.

Hebrew Calendar Science and Myth gives complete rules of the Hebrew calendar and a lot more.
Sumerian astronomy & calendars
The Molad of the Hebrew calendar
The Jewish Controversy about Calendar Postponements

Date convertors

Jewish Calendar for Outlook - A solution for incorporating Jewish dates and holidays into Microsoft Outlook.
Kaluach - Hebrew/civil calendars
Hebcal Hebrew Date Converter
Jewish Perpetual Calendar
Sample VB.Net and Javascript code to convert the Hebrew Date to the Gregorian Date

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