Hebrew calendar

The Hebrew calendar (Hebrew: הלוח העברי‎ ha'luach ha'ivri) or Jewish calendar is a lunisolar calendar used by Jews, now for predominantly religious purposes. It is used to reckon the Jewish New Year and dates for Jewish holidays, and also to determine appropriate public reading of Torah portions, Yahrzeits (dates to commemorate the death of a relative), and daily Psalm reading, among many ceremonial uses. Originally the Hebrew calendar was used by Jews for all daily purposes. During the era of the Roman occupation (1st century BCE), Jews began additionally following the imperial civil calendar for civic matters such as the payment of taxes and dealings with government officials.

The principles of the Hebrew calendar are found in the Torah, which contains several calendar-related commandments, including God's commandment during the Exodus from Egypt to fix the month of Nisan as the first month of the year.^[1] The Babylonian exile in the 6th century BCE influenced the calendar, including the adoption of Babylonian names for the months.^[2]

Tradition holds that before the destruction of the Second Temple in 70 CE, the calendar was observational, with the beginning of each month determined by the testimony of witnesses who had observed a new crescent moon. Between 70 and 1178 CE a rule-based fixed-arithmetic lunisolar calendar system was adopted to achieve the same effect . The principles and rules of the current calendar were fully described by Maimonides in 1178 CE in the Mishneh Torah.

Because of the roughly eleven-day difference between twelve lunar months and one solar year, the year lengths of the Hebrew calendar vary in a repeating 19-year Metonic cycle of 235 lunar months, with an intercalary lunar month added according to defined rules every two or three years, for a total of 7 times per 19 years. Seasonal references in the Hebrew calendar reflect its development in the region east of the Mediterranean Sea and the times and climate of the Northern Hemisphere. The Hebrew calendar's year is longer by about 6 minutes and 25+²⁵/₅₇ seconds than the present-day mean solar year, so that every 224 years, the Hebrew calendar will fall a full day behind the modern fixed solar year, and about every 231 years it will fall a full day behind the Gregorian calendar year.

Years in the Hebrew calendar are labeled with the era designation Anno Mundi (English: in the year of the world, abbreviated AM or A.M.) and are numbered from the epoch approximately a year before Creation. The Hebrew calendar year in late 2008 is 5769.

Structure

The Jewish calendar is a lunisolar calendar, or "fixed lunar year," based on twelve lunar months of twenty-nine or thirty days, with an intercalary lunar month added seven times every nineteen years (once every two to three years) to synchronize the twelve lunar cycles with the slightly longer solar year. Each Jewish lunar month starts with the new moon. Although originally the new lunar crescent had to be observed and certified by witnesses, the timing of the new moon is now determined mathematically.

Concurrently there is a weekly cycle of seven days, mirroring the seven-day period of the Book of Genesis in which the world is created. The names for the days of the week, like those in the Creation story, are simply the day number within the week, with Shabbat being the seventh day. The Jewish day always runs from sunset to the next sunset; the formal adjustments used to specify a standard time and time zones are not relevant to the Jewish calendar.

The twelve regular months are: Nisan (30 days), Iyar (29 days), Sivan (30 days), Tammuz (29 days), Av (30 days), Elul (29 days), Tishrei (30 days), Cheshvan (29 or 30 days), Kislev (29 or 30 days), Tevet (29 days), Shevat (30 days), and Adar (29 days). In the leap years an additional month, Adar I (30 days) is added after Shevat, and the regular Adar is referred to as "Adar II".

The first month of the festival year is Nisan. The 15th of Nisan is the start of the festival of Pesach, corresponding to the full moon of Nisan. Pesach is a spring festival associated with the barley harvest.^[3] Since at least the 12th century, intercalations in the Hebrew calendar have been mathematically determined. Tradition holds that prior to the adoption of the fixed calendar, the intercalation was determined empirically:

The year may be intercalated on three grounds: 'aviv [i.e.the ripeness of barley], fruits of trees, and the equinox. On two of these grounds it should be intercalated, but not on one of them alone.^[4]

The Bible designates Nisan, which it calls Aviv (Exodus 13:4), as the first month of the year (Exodus 12:2). At the same time, the season of the fall Festival of Booths (Sukkoth), is called "the end of the year" (Exodus 23:16). The Sabbatical year in which the land was to lie fallow, if it was ever observed at all, necessarily began at the time the winter barley and winter wheat would have been sown, in the fall. The Gezer calendar, an Israelite or Canaanite inscription ca. 900 BCE, also begins in the fall. And Josephus, in the first century CE, states that while

Moses...appointed Nisan...as the first month for the festivals...the commencement of the year for everything relating to divine worship, but for selling and buying and other ordinary affairs he preserved the ancient order [i. e. the year beginning with Tishrei]."^[5]

So a multiplicity of new years for different purposes has long been in use. By the time of the redaction of the Mishnah (ca. 200 CE), jurists had identified four new-year dates

The 1st of Nisan is the new year for kings and feasts; the 1st of Elul is the new year for the tithe of cattle... the 1st of Tishri is the new year for years, of the years of release and jubilee years, for the planting and for vegetables; and the 1st of Shevat is the new year for trees-so the school of Shammai; and the school of Hillel say: On the 15th thereof.^[6]

Modern practice follows the scheme described in the Mishnah: Rosh Hashanah, which means "the head of the year", and is celebrated in the month of Tishrei, is "the new year for years." This is when the numbered year changes, and most Jews today view Tishrei as the de facto beginning of the year. The 15th of Shevat, the New Year of the Trees, has become a popular minor holiday in recent decades.

Sources and history

The Torah contains several commandments related to the keeping of the calendar and the lunar cycle.

Day

For smaller units of time, see Measurement of hours below.

The Jewish day is of no fixed length. The Jewish day is modeled on the reference to "...there was evening and there was morning..."^[7] in the Creation story. Accordingly, it runs from sunset (start of "the evening") to the next sunset. However, some apply special rules in the arctic and antarctic regions, where the period between sunsets is twelve solar months.

There is no clock in the Jewish scheme, so that a civil clock is used. Though the civil clock incorporates local adoptions of various conventions such as time zones, standard times and daylight saving, these have no place in the Jewish scheme. The civil clock is used only as a reference point - in expressions such as: "Shabbat starts at ...". The steady progression of sunset around the world and seasonal changes results in gradual civil time changes from one day to the next based on observable astronomical phenomena (the sunset) and not on man-made laws and conventions. Instead of the international date line convention, the antimeridian of Jerusalem is used. (Jerusalem is 35°13’ east of the prime meridian).

Weeks

A bronze Shabbat candlestick holder made in Israel in the 1940s.

The Hebrew calendar follows a seven-day weekly cycle, which runs concurrently but independently of the monthly and annual cycles. The names for the days of the week are simply the day number within the week. In Hebrew, these names may be abbreviated using the numerical value of the Hebrew letters, for example יום א׳ (Day 1, or Yom Rishon (Hebrew: יום ראשון‎):

Yom Rishon (Hebrew: יום ראשון‎), abbreviated יום א׳ = "first day" = Sunday

Yom Sheni (יום שני), abbr. יום ב׳ = "second day" = Monday

Yom Shlishi (יום שלישי), abbr. יום ג׳ = "third day" = Tuesday

Yom Reviʻi (יום רבעי), abbr. יום ד׳ = "fourth day" = Wednesday

Yom Chamishi (יום חמישי), abbr. יום ה׳ = "fifth day" = Thursday

Yom Shishi (יום ששי), abbr. יום ו׳ = "sixth day" = Friday

Yom Shabbat (יום שבת or more usually שבת - Shabbat), abbr. יום ש׳ = "Sabbath day (Rest day)" = Saturday

The names of the days of the week are modeled on the seven days mentioned in the Creation story. For example, Genesis 1:5 "... And there was evening and there was morning, one day". "One day" also translates to "first day" or "day one". Similarly, see Genesis 1:8, 1:13, 1:19, 1:23, 1:31 and 2.2.

The Jewish Shabbat has a special place in the Jewish weekly cycle. There are many special rules which relate to the Shabbat, discussed more fully in the Talmudic tractate "Shabbat".

In Hebrew, the word "Shabbat" (שַׁבָּת) can also mean "(Talmudic) week",^[8] so that in ritual liturgy a phrase like "Yom Reviʻi bəShabbat" means "the fourth day in the week".^[9]

Importance of Lunar Months

Num 10:10 stresses the importance of the new moon and consequently lunar months, "... in your new moons, ye shall blow with the trumpets over your burnt-offerings,"^[10]. Similarly in Num 28:11.

In his work Mishneh Torah, of 1178, Maimonides included a chapter "Sanctification of the New Moon," in which he discusses the calendrical rules and their scriptural basis. He notes,

"By how much does the solar year exceed the lunar year? By approximately 11 days. Therefore, whenever this excess accumulates to about 30 days, or a little more or less, one month is added and the particular year is made to consist of 13 months, and this is the so-called embolismic (intercalated) year. For the year could not consist of twelve months plus so-and-so many days, since it is said: throughout the months of the year (Num 28:14), which implies that we should count the year by months and not by days."^[11]

Months

Mosaic pavement of a zodiac in the 6th century synagogue at Beit Alpha, Israel.

Biblical references to the pre-Jewish calendar include ten months identified by number rather than by name. In parts of the Torah portion Noach (Noah) (specifically, Gen 7:11, Gen 8:4-5, Gen 8:13-14) it is implied that the months are thirty days long.^[12] There is no indication as to the total number of months in the annual cycle.

In the parts of the Tanakh (the Hebrew Bible) prior to the Babylonian exile, only four months are named: Aviv (first; literally "spring", which originally probably meant "the ripening of barley"), Ziv (second; literally "light"), Ethanim (literally "strong" in plural, perhaps referring to strong rains) I Kings 6:38: seventh month; and Bul I Kings 6:38: eighth month. All of these are Canaanite names, and at least two are Phoenician (Northern Canaanite).

According to the Book of Exodus, the first commandment the Jewish people received as a nation was to determine the new moon: Exodus 12:2 states, "This month [Nisan] is for you the first of months." Deut 16:1 refers to a specific month: "Observe the month of Aviv (HE: spring), and keep the passover unto the LORD thy God; for in the month of Aviv the LORD thy God brought thee forth out of Egypt by night."

During the Babylonian exile, which started in 586 BCE, Jews adopted Babylonian names for the months, which are still in use. The Babylonian calendar also used a lunisolar calendar, derived from the Sumerian calendar.

Hebrew names and romanized transliteration may somewhat differ, as they do for כסלו / Kislev or חשוון / Marheshvan: the Hebrew words shown here are those commonly indicated e.g. in newspapers. The Syrian calendar used in the Levant countries shares many of the same names for months as the Hebrew calendar, such as Nisan, Iyyar, Tammuz, Ab, Elul, Tishreen, and Adar.

In a short (chaser) year, both Kislev and Cheshvan have 29 days. In a regular (kesidran) year, Kislev has 29 days and Cheshvan has 30 days. In a full (maleh) year, both Kislev and Cheshvan have 30 days.

The calendar rules have been designed to ensure that Rosh Hashanah does not fall on a Sunday, Wednesday or Friday. This is to ensure that Yom Kippur does not directly precede or follow Shabbat, which would create practical difficulties, and that Hoshana Rabbah is not on a Shabbat, in which case certain ceremonies would be lost for a year.

Leap months

The solar year is about eleven days longer than twelve lunar months. The Bible does not directly mention the addition of "embolismic" or intercalary months. However, without the insertion of embolismic months, Jewish festivals would gradual shift outside of the seasons required by the Torah. This has been ruled as implying a requirement for the insertion of embolismic months to reconcile the lunar cycles to the seasons, which are integral to solar yearly cycles.

When the observational form of the calendar was in use, whether or not an embolismic month was announced after the "last month" (Adar) depended on whether "the barley was ripe". It may be noted that in the Bible the name of the first month, Aviv, literally means "spring" but originally it probably meant "the ripening of barley". Thus, if Adar was over and the barley was not yet ripe, an additional month was observed. However, according to some traditions, the announcement of the month of Aviv could also be postponed depending on the condition of roads used by families to come to Jerusalem for Passover, adequate numbers of lambs to be sacrificed at the Temple, and on the ripeness of the barley that was needed for the first fruits ceremony.

Under the codified rules, the Jewish calendar is based on the Metonic cycle of 19 years, of which 12 are common years (12 months) and 7 leap years (13 months). The leap years are years 3, 6, 8, 11, 14, 17, and 19 of the Metonic cycle. Year 19 (there is no year 0) of the Metonic cycle is a year exactly divisible by 19 (when the Jewish year number, when divided by 19, has no remainder). In the same manner, the remainder of the division indicates the year in the Metonic cycle (years 1 to 18) the year is in.

During leap years a month, Adar II, is added before Nisan. During leap years Adar I (or Adar Aleph — "first Adar") is actually considered to be the extra month, and has 30 days. Adar II (or Adar Bet — "second Adar") is the "real" Adar, and has the usual 29 days. For this reason, during a leap year, holidays such as Purim are observed in Adar II, not Adar I.

New year

A shofar made from a ram's horn is traditionally blown in observance of Rosh Hashana, the beginning of the Jewish civic year.

The Jewish year has four distinct starting points, according to the Mishnah, Rosh Hashanah 1:1:

The day most commonly referred to as the "New Year" is the first of Tishrei, when the formal New Year festival, Rosh Hashanah ("head of the year") is observed. (see Ezekiel 40:1, which uses the phrase "beginning of the year".) This is the beginning of the civil year, and the point at which the year number advances. Certain agricultural practices are also marked from this date.^[13]

However, the first month of the year as prescribed in Exodus 12:2 is Nisan: "This month shall be to you the beginning of months". This means that the civil new year, Rosh Hashanah, actually begins in the seventh month of the year.

The month of Elul is the new year for counting animal tithes (ma'aser). Tu Bishvat ("the 15th of Shevat") marks the new year for trees (and agricultural tithes).

There may be an echo here of a controversy in the Talmud about whether the world was created in Tishrei or Nisan; it was decided that the answer is Tishrei, and this is now reflected in the prayers on Rosh Hashanah.^[14]

The use of multiple starting dates for a year is comparable to different starting dates for civil "calendar years", "tax or fiscal years", "academic years", "religious cycles", etc.

Epoch

The Jewish calendar's reference point is traditionally held to be about one year before the Creation of the world.

The Jewish calendar uses a calendar era anno mundi ("in the year of the world"), abbreviated AM. Interestingly, the beginning of "year 1" is not Creation, but about one year before Creation. This caused the new moon of its first month (Tishrei) to be called molad tohu (the mean new moon of chaos or nothing).

The Jewish calendar's epoch (reference date), 1 Tishrei 1 AM, is equivalent to Monday, October 7 3761 BCE in the proleptic Julian calendar, the equivalent tabular date (same daylight period) and is about one year before the traditional Jewish date of Creation on 25 Elul AM 1, based upon the Seder Olam Rabbah of Rabbi Yossi ben Halafta, a second century CE sage.^[15] Thus, adding 3760 before Rosh Hashana or 3761 after to a Julian or Gregorian year number after 1 CE will yield the Hebrew year. For earlier years there may be a discrepancy (see: "Missing Years" in the Hebrew Calendar).

The Jewish year starting on Rosh Hashanah, 1 Tishrei, 5769 AM is equivalent to 29 September 2008.

Karaite interpretation

For several centuries, many Karaites, especially those outside Israel, followed the calculated Rabbinical calendar used by most Jews for the sake of convenience. However, in recent years most Karaites have chosen to again follow the observational method.

Karaites use the lunar month and the solar year, but the Karaite calendar differs from the Rabbinical calendar in two ways: the determination of the first day of each month (Rosh Chodesh), and the determination of the first month of the year (called aviv), which is the month in which Passover falls.

For Karaites, the beginning of each month, the Rosh Chodesh, can be calculated, but is confirmed by the observation in Israel of the first sightings of the new moon. This may result in an occasional variation of a maximum of one day, depending on the inability to observe the new moon. The day is usually "picked up" in the next month.

The addition of the leap month (Adar II) is determined by observing in Israel the ripening of barley (called abib), rather than using the calculated and fixed calendar of Rabbinic Judaism. The four rules of postponement are not applied, as they are not found in the Tanakh. Occasionally this results in Karaites being one month ahead of Jews using the calculated Rabbinic calendar. The "lost" month would be "picked up" in the next cycle when Karaites would observe a leap month while other Jews would not.

Change to a calculated calendar

Observational principles

A stone (2.43x1 m) with Hebrew inscription "To the Trumpeting Place" is believed to be a part of the Second Temple.

Calendrical evidence for the postexilic Persian period is found in papyri from the Jewish colony at Elephantine, in Egypt. These documents show that the Jewish community of Elephantine used the Egyptian and Babylonian calendars.^[16][17]

In the Maccabean and Herodian periods, according to the (possibly unreliable) evidence of the Mishnah, the Hebrew calendar operated on an observational basis. The beginning of each lunar month was decided on the basis of two eye witnesses testifying to the Sanhedrin to having seen the new lunar crescent at sunset.^[18] Patriarch Gamaliel II (c. 100) would ask the witnesses to select the appearance of the moon from a collection of drawings that depicted the crescent in a variety of orientations, only a few of which could be valid in any given month.^[19] According to tradition, these observations were compared against calculations.^[20] When thirty days elapsed since the last new moon, the witnesses were readily believed.

At first the beginning of each Jewish month was (again, according to the Mishnah) signaled to the communities of Israel and beyond by fires lit on mountaintops, but after the Samaritans began to light false fires, messengers were sent.^[21] The inability of the messengers to reach communities outside Israel before mid-month High Holy Days (Succot and Passover) led outlying communities to celebrate scriptural festivals for two days rather than one, observing the second feast-day of the Jewish diaspora because of uncertainty of whether the previous month ended after 29 or 30 days.^[22]

Transitional period

In Rome the Arch of Titus still stands, depicting the enslaved Judeans and objects from the Temple being brought to Rome.

The period 70 CE to 1178 CE saw a gradual transition from an observation based calendar to a mathematically calculated one.^[23] Except for the epoch year number, the calendar rules reached their current form before 820 or 921, with some uncertainty regarding when.

The evidence of the Mishnah suggests that the Rabbis attempted at first to use an empirical calendar based on observations. The evidence of the Talmuds and other sources suggests that the attempt failed. From the times of the Amoraim (third to fifth centuries), calculations were increasingly used. According to a statement attributed to Yose, an Amora who lived during the second half of the third century, the feast of Purim, 14 Adar, could not fall on a Sabbath nor a Monday, lest 10 Tishrei (Yom Kippur) fall on a Friday or a Sunday.^[24]This indicates that, by the time of the redaction of the Jerusalem Talmud (ca. 400 CE), there were 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. In another passage, a sage is reported to have counseled "those who make computations" not to set the first day of Tishrei or the Day of the Willow on the sabbbath.^[25] This indicates that some who "made computations" were in a position to control, to some extent, the weekday on which Rosh Hashanah would fall.

Outside of Rabbinic circles, the evidence shows a diversity of Jewish practice. The Sardica paschal table shows that the Jewish community of some eastern city, possibly Antioch, used a calendrical scheme that kept Nisan 14 within the limits of the Julian month of March^[26]. Some of the dates in the document are clearly corrupt, but they can be emended to make the sixteen years in the table consistent with a regular intercalation scheme. Peter, the bishop of Alexandria (early 4th century CE), mentions that the Jews of his city "hold their Passover according to the course of the moon in the month of Phamenoth, or according to the intercalary month every third year in the month of Pharmuthi"^[27], suggesting a fairly consistent intercalation scheme that kept Nisan 14 approximately between the Phamenoth 10 and Pharmuthi 10. Jewish funerary inscriptions from Zoar, south of the Dead Sea, dated from the 3rd to the 5th century CE, indicate that when years were intercalated, the intercalary month was at least sometimes a repeated month of Adar. But the inscriptions reveal no clear pattern of regular intercalations, nor do they indicate any consistent rule for determining the start of the lunar month.^[28]

There is a tradition, first mentioned by Hai Gaon (d.1038 CE), that one Hillel b. R. Yehuda "in the year 670 of the Seleucid era" (i.e. 358-359 CE) was responsible for the fixed intercalation cycle. Later writers, such as Nachmanides, interpreted Hai Gaon's words to mean that the entire computed calendar was due to Hillel b. Yehuda. At about the same time, Maimonides stated that the Mishnaic calendar was used "until the days of Abaye and Rava", who flourished ca. 320-350 CE, and that the change came when "the land of Israel was destroyed, and no permanent court was left." Some modern commentators have combined these two traditions to hold that Hillel b. Yehuda (whom they identify with the mid-4th century Jewish patriarch Ioulos, attested in a letter of the Emperor Julian^[29], and the Jewish patriarch Ellel, mentioned by Epiphanius^[30]) instituted the computed Hebrew Calendar because of persecution. H. Graetz attempted^[31] to link the introduction of the computed calendar to the sharp repression following a failed Jewish insurrection that occurred during the rule of Constantius and Gallus. A later writer, S. Lieberman, argued^[32] instead that the introduction of the fixed calendar was due to measures taken by Roman authorities to prevent the Jewish patriarch from sending calendrical messengers.

Both the tradition that Hillel b. Yehuda instituted the complete computed calendar, and the theory that the computed calendar was introduced due to repression or persecution, have been questioned.^[33][34][35] It is noted that the Babylonian Talmud, which did not reach its final form until c. 600, 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, suggesting the final form of the modern calendar was fixed subsequent to the sixth century.

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), under the Abbasid Caliphate. The Babylonian rules required the delay of the first day of Tishrei when the new moon occurred after noon.

Nevertheless, as was noted above, the 4th-century CE date stated by Hai Gaon and Maimonides seems consistent with the facts to this extent: By the time of the redaction of the Palestinian Talmud (ca. 400 CE) "computations" of some sort were being used to assist in the regulation of the Jewish calendar in Palestine.

Epoch year

One notable difference between the calendar of that era and the modern form was the date of the epoch (the fixed reference point at the beginning of year 1), which at that time was one year later than the epoch of the modern calendar.

Most of the present rules of the calendar appear to have been in place by about 820, according to a treatise by the Muslim astronomer Muḥammad ibn Mūsā al-Ḵwārizmī (c. 780-850 CE) a Persian polymath noted for his contributions to Islamic mathematics, astronomy, astrology and geography. Al-Khwārizmī's study of the Jewish calendar, Risāla fi istikhrāj taʾrīkh al-yahūd "Extraction of the Jewish Era" describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishrī shall fall, the interval between the Jewish era (creation of Adam) and the Seleucid era, and the rules for determining the mean longitude of the sun and the moon using the Jewish calendar.

In 921, Aaron ben Meir proposed changes to the calendar. Though the proposals were rejected, it indicates that all of the rules of the modern calendar (except for the epoch) were in place before that date. In 1000, the Muslim chronologist al-Biruni described all of the modern rules of the Hebrew calendar, except that he specified three different epochs used by various Jewish communities being one, two, or three years later than the modern epoch.^[36]

Codification of rules

Finally, in 1178, Maimonides, in his work Mishneh Torah, codified the rules and their scriptural basis, including the modern epochal year. Maimonides showed analytically how the scriptural procedure for determining the calendar must be flawed, something he could explain through his faith. He noted that non-Jewish savants had presented mathematically correct methods of calculating the potential visibility of the new crescent, and reasoned that since these methods exist, they must have been used by the Sanhedrin and the record of their use lost.^[37] Whether or not the disagreements on the epoch year had in fact been resolved when he wrote the Mishneh Torah, Maimonides' code has been accepted as the modern position on the matter.

Principles

Measurement of month

Animation of the Moon as it cycles through its phases, as seen from the Northern Hemisphere. The apparent wobbling of the Moon is known as libration.

Synodic month

A synodic month (known in Hebrew as a "molad") is a scientifically defined lunar conjunction based on the position of the moon in the lunar orbit. It equals exactly ⁷⁶⁵⁴³³/₂₅₉₂₀ days, or 29 days, 12 hours, and 793 parts (44+¹/₁₈ minutes) (ie 29.5306 days). This interval matches the mean synodic month determined by the Babylonians before 300 BCE and as adopted by the Greek astronomer Hipparchus and the Alexandrian astronomer Ptolemy. Its remarkable accuracy is thought to have been achieved using records of lunar eclipses from the eighth to fifth centuries BCE, with a reference meridian midway between the Nile River and the end of the Euphrates River, about 4° east of Jerusalem.

Traditional new moon

A "new moon" is the day on which the first visible crescent of the moon is observed. It occurs 29 or 30 days after the preceding visible crescent and traditionally signaled the start of a Jewish lunar month.

Combining the observation method with the scientific lunar month length works as follows. Assume one begins at a particular new month of 29 days. As the mean lunar month is 29.5306 days long, there would be a carry forward into the next month of 0.5306 days (ie 12 hours, 44+¹/₁₈ minutes). Adding that carry forward amount to the next month will make it equal 30.0612 days (30 days, 1 hour and 24+²/₁₈ minutes). So the second month would be 30 days long, and 0.0612 days (or 1 hour 24+²/₁₈ minutes) would be carried forward to be added to the next cycle, and so on. Then every 17 lunar months the carry forward amounts would exceed 24 hours (0.0612 x 17 = 1.0404), which would require an additional day to be added to that month. In summary, the progression becomes: year 1 | 29 – 30 – 29 – 30 – 29 – 30 – 29 – 30 – 29 – 30 – 29 – 30 | year 2 | 29 – 30 – 29 – 30 – 30 – 29 – etc.

Pattern of calendar years

The Jewish calendar is based on the Metonic cycle of 19 years, of which 12 are common years (12 months) and 7 leap years (13 months). A Metonic cycle equates to 235 lunar months in each 19-year cycle. This gives an average of 6939 days, 16 hours and 595 parts for each cycle.

But due to the Rosh HaShanah postponement rules (see below), a cycle of 19 Jewish years can be either 6939, 6940, 6941, or 6942 days in duration. Since none of these values is evenly divisible by seven, the Jewish calendar repeats exactly only following 36,288 Metonic cycles, or 689,472 Jewish years. There is a near-repetition every 247 years, except for an excess of 50 minutes (905 parts).

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

A Jewish non-leap year can only have 353, 354, or 355 days. A leap year can have 383, 384, or 385 days (always 30 days longer than the non-leap length).

• A chaserah year (Hebrew for "deficient" or "incomplete") is 353 or 383 days long. Both Kislev and Cheshvan have 29 days. 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. Kislev has 29 days and Cheshvan has 30 days. 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. Both Kislev and Cheshvan have 30 days. The Hebrew letter ש "shin", and the letter for the week-day denotes this pattern.

Determining leap years

The Jewish leap years are years 3, 6, 8, 11, 14, 17, and 19 of the Metonic cycle. To determine whether a year is a leap year, find the remainder when dividing the Jewish year number by 19. If the remainder is 3, 6, 8, 11, 14 or 17, the year is a leap year and an extra month, Adar II, is added. If the remainder is zero, the year is also a leap year since year 19 of the Metonic cycle is a year exactly divisible by 19. Another way to check a specific year is to find the remainder in the following calculation: ( 7 x the Jewish year number + 1 ) / 19. If the remainder is less than 7, the year is a leap year.

A mnemonic word in Hebrew is GUCHADZaT "גוחאדז"ט" (the Hebrew letters gimel-vav-het aleph-dalet-zayin-tet, i.e. 3, 6, 8, 1, 4, 7, 9. See Hebrew numerals). 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.

Another memory aid notes that intervals of the major scale follow the same pattern as do Jewish leap years, with do corresponding to year 19 (or 0): a whole step in the scale corresponds to two common years between consecutive leap years, and a half step to one common year between two leap years.

Special holiday rules

Adjustments are made to ensure certain holy days and festivals do or do not fall on certain days of the week.

Yom Kippur

Adjustments are made to ensure that Yom Kippur, on which no work can be done, does not fall on Friday (the day prior to the Sabbath) to avoid having Yom Kippur's restrictions still going on at the start of Sabbath, or on Sunday (the day after Shabbat) to avoid having the Shabbat restrictions still going on at the start of Yom Kippur.

The Rosh Hashanah postponement rules are the mechanism used to make the adjustments. As Yom Kippur falls on Tishrei 10, and Rosh Hashanah falls on the 1st, the adjustment is made so that Rosh Hashanah does not fall on a Wednesday or Friday.

Rosh Hashanah postponement rules

To ensure that Yom Kippur does not directly precede or follow Shabbat, and that Hoshana Rabbah is not on a Shabbat, in which case certain ceremonies would be lost for a year, the first day of Rosh Hashanah may only occur on Mondays, Tuesdays, Thursdays, and Saturdays (the "four gates"). Adjustments are made to ensure that Rosh Hashanah does not fall on the other three days. To achieve that result the year may be made into a short (chaser) year (both Kislev and Cheshvan have 29 days) or full (maleh) year (both Kislev and Cheshvan have 30 days). (see table)

The day of the week on which Rosh Hashanah falls in any given year will also be the day on which Sukkot and Shmini Atzeret will occur.

Short or full years

A leap year (ie. one which has 13 months) has an average length of 383½ days, so that in discrete numbers a leap year may have either 383 or 384 days.

Also, 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.

The period from Adar 29 (or Adar II, in leap years) to Heshvan 29 contains all of the festivals specified in the Bible - Pesach (Nisan 15), Shavuot (Sivan 6), Rosh Hashana (Tishrei 1), Yom Kippur (Tishrei 10), Sukkot (Tishrei 15), and Shemini Atzeret (Tishrei 22). This period is fixed, during which no adjustments are made.

Days of week of holidays

Main article: Days of week on Hebrew calendar

*Postponed to not be held on Shabbat

Measurement of hours

Every hour is divided into 1080 halakim or parts. A part is 3⅓ 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.

While calculations of days, months and years are based on fixed hours equal to ¹/₂₄ of a day, the beginning of each halachic day is based on the local time of sunset. The end of the Shabbat and other Jewish holidays is based on nightfall (Tzeis Hacochavim) which occurs some amount of time, typically 42 to 72 minutes, after sunset. According to Maimonides, nightfall occurs when three medium-sized stars become visible after sunset. By the seventeenth century this had become three second-magnitude stars. The modern definition is when the center of the sun is 7° below the geometric (airless) horizon, somewhat later than civil twilight at 6°. The beginning of the daytime portion of each day is determined both by dawn and sunrise. Most halachic times are based on some combination of these four times and vary from day to day throughout the year and also vary significantly depending on location. The daytime hours are often divided into Shaos Zemaniyos or "Halachic hours" by taking the time between sunrise and sunset or between dawn and nightfall and dividing it into 12 equal hours. The earliest and latest times for Jewish services, the latest time to eat Chametz on the day before Passover and many other rules are based on Shaos Zemaniyos. For convenience, the day using Shaos Zemaniyos is often discussed as if sunset were at 6:00pm, sunrise at 6:00am and each hour were equal to a fixed hour. For example, halachic noon may be after 1:00pm in some areas during daylight saving time.

Accuracy

Seasonal drift

The Hebrew calendar's mean year is 365.2468 days long (exactly 365 days 5 hours 55 minutes and 25+²⁵/₅₇ seconds - ie. the molad/monthly interval × 235 months per 19-year cycle ÷ 19 years per cycle). As the present-era mean northward equinoctal year is about 365.24219 days long (365 days 5 hours 49 minutes and zero seconds), the Hebrew calendar mean year is about 6 minutes and 25+²⁵/₅₇ seconds longer than the solar tropical year. This results in a "drift" of the Hebrew calendar of about a day every 224 years.

Also, the mean Gregorian calendar year is 365.2425 days long (365 days 5 hours 49 minutes and 12 seconds), resulting in a drift of the Hebrew calendar in relation to the Gregorian calendar of about a day every 231 years.

The impact of the drift is reflected in the drift of the date of Passover from the vernal full moon:

*Note: Passover commences at sunset preceding the date indicated.

The result of the drift is that the underlaying date of the vernal equinox has shifted by about 6 days since the arithmetically-based calendar came into use, and results in the month of Nisan starting in a later lunation in three years of the 19-year cycle: in years 8, 11 and 19. This will increase to four of the 19 years in year 2200.

Molad intervals

The value 29-12-793 for the molad interval was taken from Ptolemy's Almagest (2nd century CE), and is equal to 29.530594 days. This is as close to the correct value of 29.530589 days as it is possible for a value to come that is rounded off to whole parts (¹/₁₈ minute). So the molad interval is about 0.6 seconds too long. Put another way, if the molad is taken as the time of mean conjunction at some reference meridian, then this reference meridian is drifting slowly eastward. If this drift of the reference meridian is traced back to the mid-4th century CE, the traditional (but probably incorrect) date of the introduction of the fixed calendar, then it is found to correspond to a longitude midway between the Nile River and the end of the Euphrates River. The modern molad moments match the mean solar times of the lunar conjunction moments near the meridian of Kandahar, Afghanistan, more than 30° east of Jerusalem.

In the present era actual lunar conjunction intervals can be as short as 29 days 6 hours and 30 minutes to as long as 29 days and 20 hours, a variation range of about 13 hours and 30 minutes. Furthermore, due to the eccentricity of Earth's orbit, series of shorter lunations alternate with series of longer lunations. Consequently the actual lunar conjunction moments can range from 12 hours earlier than to 16 hours later than the molad moment, in terms of Jerusalem mean solar time.

Furthermore, the discrepancy between the molad interval and the mean synodic month is accumulating at an accelerating rate, since the mean synodic month is progressively shortening due to gravitational tidal effects. 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 tides slow Earth's rotation rate even more, the mean synodic month is becoming gradually shorter in terms of mean solar time.

Implications for Jewish ritual

This figure, in a detail of a medieval Hebrew calendar, reminded Jews of the palm branch (Lulav), the myrtle twigs, the willow branches, and the citron (Etrog) to be held in the hand and to be brought to the synagogue during the holiday of sukkot, near the end of the autumn holiday season.

Although the molad of Tishrei is the only molad moment that is not ritually announced, it is actually the only one that is relevant to the Hebrew calendar, for it determines the provisional date of Rosh HaShanah, subject to the Rosh HaShanah postponement rules. The other monthly molad moments are announced for mystical reasons. With the moladot on average almost 100 minutes late, this means that the molad of Tishrei lands one day later than it ought to in (100 minutes) ÷ (1440 minutes per day) = 5 of 72 years or nearly 7% of years!

Therefore the seemingly small drift of the moladot is already significant enough to affect the date of Rosh HaShanah, which then cascades to many other dates in the calendar year and sometimes, due to the Rosh HaShanah postponement rules, also interacts with the dates of the prior or next year. The molad drift could be corrected by using a progressively shorter molad interval that corresponds to the actual mean lunar conjunction interval at the original molad reference meridian. Furthermore, the molad interval determines the calendar mean year, so using a progressively shorter molad interval would help correct the excessive length of the Hebrew calendar mean year, as well as helping it to "hold onto" the northward equinox for the maximum duration.

If the intention of the calendar is that Passover should fall near the first full moon after the northward equinox, or that the northward equinox should land within one lunation before 16 days after the molad of Nisan, then this is still the case in about 80% of years, but in about 20% of years Passover is a month late by these criteria (as it was in Hebrew year 5765, an 8th year of the 19-year cycle = Gregorian 2005 AD). Presently this occurs after the "premature" insertion of a leap month in years 8, 19, and 11 of each 19-year cycle, which causes the northward equinox to land at exceptionally early moments in such years. This problem will get worse over time, and so beginning in Hebrew year 5817 the 3rd year of each 19-year cycle will also be a month late. Furthermore, the drift will accelerate in the future as perihelion approaches and then passes the northward equinox, and if the calendar is not amended then Passover will start to land on or after the summer solstice around Hebrew year 16652, or about 10885 years from the present. (The exact year when this will begin to occur depends on uncertainties in the future tidal slowing of the Earth rotation rate, and on the accuracy of predictions of precession and Earth axial tilt.)

The seriousness of the spring equinox drift is widely discounted on the grounds that Passover will remain in the spring season for many millennia, and the text of the Torah is generally not interpreted as having specified tight calendrical limits. On the other hand, the mean southward equinoctial year length is considerably shorter, so the Hebrew calendar has been drifting faster with respect to the autumn equinox, and at least part of the harvest festival of Sukkot is already more than a month after the equinox in years 9, 1, 12 and 4 of each 19-year cycle (these are the same year numbers as were mentioned for the spring season in the previous paragraph, except that they get incremented at Rosh HaShanah). This progressively increases the probability that Sukkot will be cold and wet, making it uncomfortable or impractical to dwell in the traditional succah during Sukkot. The first winter seasonal prayer for rain is not recited until Shemini Atzeret, after the end of Sukkot, yet it is becoming increasingly likely that the rainy season in Israel will start before the end of Sukkot.

"Rectifying" the Hebrew calendar

Given the importance in Jewish ritual of establishing the accurate timing of monthly and annual times, some futurist writers and researchers have considered whether a "corrected" system of establishing the Hebrew date is required, due to the small but accelerating changes in the actual lunar cycle interval. Further religious questions include how such a system might be implemented and administered throughout the diverse aspects of the world Jewish community.

It is traditionally held that the fixed arithmetic Hebrew calendar was established on the authority of Hillel ben Yehudah, President of the Sanhedrin in Hebrew year 4119, and therefore only an equal authority (the modern Sanhedrin) can either amend it or reinstate the observational Hebrew calendar.

A 353-year leap cycle of 4366 months, including 130 leap months, along with use of a progressively shorter molad interval, could keep an amended fixed arithmetic Hebrew calendar from drifting for more than 7 millennia.^[39]

Irregularities and "Missing Years"

Main article: Missing Years

The traditional dates of events in Jewish history are often used interchangeably with the modern secular dates according to the Gregorian calendar. For example, the traditional Jewish date for the destruction of the First Temple (3338 AM = 423 BCE) differs from the modern scientific date, which is usually expressed using the Gregorian calendar (586 BCE). Implicit in this practice is the view that if all the differences in structure between the Hebrew and Gregorian calendars are taken into consideration, the two dates can be derived from each other. This is not the case. If the traditional dates of events before the Second Temple era are assumed to be using the standard Hebrew calendar, they refer to different objective years than those of the secular dates. The discrepancy is some 165 years.

The conflict does not necessarily imply that either the traditional dates or the secular dates must be objectively wrong. It is possible that the traditional dates did not use a consistent calendar matching the year count of the standard Hebrew calendar. It could be that one or more substantial calendar shifts have occurred, or the years counted might in certain periods have differed from astronomical years. Taking into account the possibility of a changing structure of the Hebrew calendar, theoretically, both the traditional dates and those of secular scholars could be correct. Even so, the account of history in the traditional sourcebook Seder Olam Rabba, and in particular its description of the period of Persian domination, seems to be irrevocably at odds with modern scientific understanding.

Furthermore, the modern Hebrew calendar cannot be used to calculate Biblical dates because new moon dates may be in error by ±2 days and months may be in error by ±2 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.

Usage in contemporary Israel

Early Zionist pioneers were impressed by the fact that the calendar preserved by Jews over many centuries in far-flung diasporas, as a matter of religious ritual, was geared to the climate of their original country: the Jewish New Year marks the moment of transition from the Dry Season to the Rainy one, and major Jewish Holidays such as Sukkot, Passover or Shavuot correspond to major points of the country's agricultural year such as planting and harvest.

Accordingly, in the early 20th Century the Hebrew Calendar was re-interpreted as an agricultural rather than religious calendar. The Kibbutz movement was especially inventive in creating new rituals fitting this interpretation.

With the creation of the State of Israel the Hebrew Calendar was made its official calendar. New holidays and commemorations not derived from previous Jewish tradition invariably were to be defined according to their Hebrew dates — notably the Israeli Independence Day on Iyar 5, Jerusalem Reunification Day on 28 Iyar, and the Holocaust Commemoration Day on Nisan 27 (close to the Hebrew date of the start of the Warsaw Ghetto Uprising).

Nevertheless, since the 1950s the Hebrew calendar steadily declined in importance in Israeli daily life, in favor of the worldwide Gregorian Calendar. At present, Israelis — except for the minority of religiously observant — conduct their private and public life according to the Gregorian Calendar, although the Hebrew calendar is still widely acknowledged, appearing in public venues such as banks (where it is legal for use on checks and other documents, for example,) and on the mastheads of newspapers.

The Jewish New Year (Rosh Hashana) is a two-day public holiday in Israel. However, since the 1980s an increasing number of secularist Israelis had taken up the habit of celebrating the Gregorian New Year (usually known as "Sylvester Night" — "ליל סילבסטר") by holding all-night parties on the night between December 31 and January 1. Prominent Rabbis have on several occasions sharply denounced this practice, but with no noticeable effect on the secularist celebrants. ^{[citation needed]}

The disparity between the two calendars is especially noticeable with regard to commemoration of the assassinated Prime Minister Yitzchak Rabin. The official Day of Commemoration, instituted by a special Knesset law, is marked according to the Hebrew Calendar - on Heshvan 12. However, left-leaning Israelis, who revere Rabin as a martyr for the cause of peace and who are predominantly secularist, prefer to hold their own mass memorial rallies on November 4. In some years the two competing Rabin Memorial Days are separated by as much as two weeks.

The wall calendars commonly used in Israel are hybrids — organised according to Gregorian rather than Jewish months, but beginning in September, where the Jewish New Year usually falls, and providing the Jewish date in small characters.

Notes

This article incorporates text from the 1901–1906 Jewish Encyclopedia, a publication now in the public domain.

References

Wikibooks Programming:Hebrew calendar has a page on the topic of

Computer programming for the Hebrew calendar

• al-Biruni. The Chronology of Ancient Nations, Chapter VII. tr. C. Edward Sachau. London, 1879.
• Ari Belenkiy. "A Unique Feature of the Jewish Calendar — Dehiyot". Culture and Cosmos 6 (2002) 3-22.
• Bonnie Blackburn and Leofranc Holford-Strevens. The Oxford Companion to the Year: An Exploration of Calendar Customs and Time-reckoning. Oxford University Press; USA, 2000. pp * Sherrard Beaumont Burnaby. Elements of the Jewish and Muhammadan Calendars. George Bell and Sons, London, 1901.
• Nathan Bushwick. Understanding the Jewish Calendar. Moznaim, 1989. ISBN 0940118173
• 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.
• 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.
• Samuel Poznanski. "Calendar (Jewish)". Encylopædia of Religion and Ethics, 1911.
• Edward M. Reingold and Nachum Dershowitz. Calendrical Calculations: The Millennium Edition. Cambridge University Press; 2 edition (2001). ISBN 0-521-77752-6

723-730.

• L.A. Resnikoff. "Jewish calendar calculations", Scripta Mathematica 9 (1943) 191-195, 274-277.
• Eduard Schwartz, Christliche und jüdische Ostertafeln, (Abhandlungen der königlichen Gesellschaft der Wissenschaften zu Göttingen. Philologisch-Historische Klasse. Neue Folge, Band viii, Berlin, 1905.
• Arthur Spier. The Comprehensive Hebrew Calendar. Feldheim, 1986.
• Sacha Stern, Calendar and Community: A History of the Jewish Calendar Second Century BCE-Tenth Century CE, Oxford University Press, 2001.
• 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.
• F.H. Woods. "Calendar (Hebrew)", Encylopædia of Religion and Ethics, 1911.

See also

• Babylonian calendar
• Jewish holidays 2000-2050
• molad
• Biblical and Talmudic units of measurement

External links

• Perpetual Hebrew / Civil Calendar
• 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.
• The Jewish Controversy about Calendar Postponements
• Jewish Calendar with Zmanim - Halachic times and date converter chabad.org
• Jewish calendar scientific explanation at the NASA web site
• Jewish Encyclopedia: Calendar
• Karaite Holidays Karaite website
• Hebrew CalendarDates and Holydays (Diaspora or Israel) for both the Traditional and the Rectified calendars)
• Hebrew - Gregorian Calendar with options (Multilingual)
• Bet Ha Bracha Hebrew Calendar

• A Hebrew calendar with Halachic times, at Yeshiva.org.il

Date converters

• Jewish Calendar for Outlook - Incorporate Jewish dates and holidays into Microsoft Office Outlook.
• Molad - Jewish Calendar with Zmanim and holidays for Mobiles.
• Jewish Calendar for many platforms
• Kaluach - Hebrew/civil calendars
• Hebcal Hebrew Date Converter
• Jewish/Gregorian/Julian Perpetual Calendar Converter - Also contains a full year view for the Hebrew Calendar.
• Sample VB.Net and Javascript code to convert the Hebrew Date to the Gregorian Date
• Jewish / Civil Date Converter
• Software program that converts Hebrew dates to the civil calendar and vice versa
• Gregorian-Mayan-Julian-Islamic-Persian-Hebrew Calendar Converter
• Kalendis Calendar Calculator
• Gregorian to Hebrew date with weekly Parshat HaShavua.

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