# Hebrew calendar: Wikis

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The Hebrew calendar (Hebrew: הלוח העבריha'luach ha'ivri) or Jewish calendar is a lunisolar calendar used by Jews. Today, the calendar is predominantly used for religious observances and by all official institutions in the State of Israel, as well as by Jewish farmers in Israel as an agricultural framework.

The calendar 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. Following the conquest of Jerusalem by Pompey in 63 BCE (see also Iudaea province), Jews began additionally following the imperial civil calendar (which was decreed in 45 BCE) 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]

During Temple times and through the Tannaitic period, the Hebrew calendar was observational, with the beginning of each month determined by the high court based on the testimony of witnesses who had observed a new crescent moon. Periodically, the court ordered an extra month added to keep Passover in the spring, again based on observation of natural events. Through the Amoraic period and into the Geonic period, the purely empirical calendar was displaced by calendrical rules, which finally became systematically arranged into a computed calendar. The principles and rules of the current calendar are fully described by Maimonides 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 (Latin for "in the year of the world"), abbreviated AM and A.M., (Hebrew: לבריאת העולם‎), and are numbered from the epoch that, by Rabbinical reckoning, is the date of the creation of Adam. 30 September 2008 through 18 September 2009 corresponded to Hebrew year 5769; the Hebrew year 5770 began at sundown on the evening of 18 September 2009 and will end on 8 September 2010.

## 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. 15 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] so the leap-month mentioned above is intercalated periodically to keep this festival in the northern hemisphere's spring season. Since the adoption of a fixed calendar, intercalations in the Hebrew calendar have been at fixed points in a 19-year cycle. Prior to this, 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, 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.

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.

## 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..."[5] in the Creation story. Accordingly, it runs from sunset (start of "the evening") to the next sunset. However, some apply special rules at very high latitudes when the sun remains above or below the horizon for longer than a civil day.[6]

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, there are varying opinions as to where the day changes. One opinion uses the antimeridian of Jerusalem. (Jerusalem is 35°13’ east of the prime meridian, so the antimeridian is at 144°47' W, passing through eastern Alaska.) Other opinions exist as well.

### 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 (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",[7] so that in ritual liturgy a phrase like "Yom Reviʻi bəShabbat" means "the fourth day in the week".[8]

### 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,"[9]. 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."[10]

### 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.[11] 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 (12:2, Exodus 13:4, 23:15, 34:18, Deut. 16:1) (first; literally "spring", which originally probably meant "the ripening of barley"); Ziv (1 Kings 6:1, 6:37) (second; literally "light"); Ethanim (1 Kings 8:2) (seventh; literally "strong" in plural, perhaps referring to strong rains); and Bul (1 Kings 6:38) (eighth). 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, which was similar in structure to the Hebrew one.

Hebrew names and romanized transliteration may somewhat differ, as they do for חשוון / Marheshvan or כסלו / Kislev: 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, Tishri, and Adar.

Hebrew names of the months with their Babylonian analogs
Other
Length Babylonian analog Holidays/
Notable days
Notes
1 נִיסָן Nīsān Nisan Nissan 30 days Nisanu Passover Called Abib (Exodus 13:4, 23:15, 34:18, Deut. 16:1)
and Nisan (Esther 3:7) in the Tanakh.
2 אִיָּר / אייר ʼIyyār Iyyar Iyar 29 days Ayaru Pesach Sheni
Lag B'Omer
Called Ziv in 1 Kings 6:1, 6:37.
3 סִיוָן / סיוון Sīwān Siwan Sivan 30 days Simanu Shavuot
4 תַּמּוּז Tammūz Tammuz Tamuz 29 days Du'uzu Seventeenth of Tammuz
5 אָב ʼĀ Av Ab 30 days Abu Tisha B'Av
Tu B'Av
6 אֱלוּל ʼĔlūl Elul Elul 29 days Ululu
7 תִּשׁרִי Tišrī Tishri Tishrei 30 days Tashritu Rosh Hashanah
Yom Kippur
Sukkot
Shmini Atzeret
Simchat Torah
Called Ethanim in 1 Kings 8:2.
First month of civil year.
8 מַרְחֶשְׁוָן / מרחשוון Marešwān Mareshwan Marcheshvan
Cheshvan
29 or
30 days
Arakhsamna Called Bul in 1 Kings 6:38.
9 כִּסְלֵו / כסלוו Kislēw Kislew Kislev
Chisleu
Chislev
29 or
30 days
Kislimu Hanukkah
10 טֵבֵת Ṭēē Tebeth Tevet 29 days Tebetu Tenth of Tevet
11 שְׁבָט Šəā Shevat Shvat
Shebat
30 days Shabatu Tu B'Shevat
12* אֲדָר א׳ Adar I* 30 days *Only in leap years.
12 / 13* אֲדָר / אֲדָר ב׳ ʼĂār 29 days Adaru Purim

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

### New year

A shofar made from a ram's horn is traditionally blown in observance of Rosh Hashanah, 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 1 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 civil new year, and the point at which the year number advances. Certain agricultural practices are also marked from this date.[12]

However, the first month of the year referred to in Exodus 12:2 is Aviv (now called Nisan): "This month shall be to you the beginning of months". This is referred to as the ecclesiastical new year, which means that the civil new year, Rosh Hashanah, actually begins in the seventh month of the ecclesiastical year.

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]."[13]

In ancient Israel, the start of the ecclesiastical new year (ie. Nisan) was determined by reference to Passover. Passover begins on the 14th day of the month of Nisan, (Leviticus 23:4-6) which corresponds to the full moon of Nisan. As Passover is a spring festival, the 14th of Nisan begins on the night of a full moon after the vernal equinox. To ensure that Passover did not start before spring, the tradition in ancient Israel held that the 1st of Nisan would not start until the barley is ripe, being the test for the onset of spring.[14] If the barley was not ripe an intercalary month (Adar II) would be added.

Edwin Thiele has concluded that ancient Kingdom of Israel counted years using the ecclesiastical new year (which was the practice of Babylon, as well as other countries of the region), while the Kingdom of Judah counted years using the civil new year,[15] a practice followed to this day.

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 determined that the answer is Tishrei, and this is now reflected in the prayers on Rosh Hashanah.[16]

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.

The multiplicity of new years for different purposes has long been in use. By the time of the redaction of the Mishnah, Rosh Hashanah 1:1 (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.[17]

### Epoch

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

Since about the third century CE, the Jewish calendar has used a calendar era anno mundi ("in the year of the world"), abbreviated AM. 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, 7 October 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.[18] Thus, adding 3760 before Rosh Hashanah 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.

Before the adoption of the current year numbering system, other systems were in use. For example, during the Greek period, Seleucid era counting was used: eg. 1 Maccabees 1:54. During the Baylonian captivity, Ezekiel counted the years from the first deportation, that of Jehoiachin, (eg. Ezekiel 1:1-2). The era year was then called "year of the captivity of Jehoiachin". (eg. 2 Kings 25:27)

### Karaite calendar

For several centuries, many Karaite Jews, especially those outside Israel, followed the calculated Rabbinic calendar, because it was not possible during the exile to retrieve accurate new moon sightings, and aviv barley data from the land of Israel, which had to be relayed to the entire Karaite Jewish community. However, since the establishment of the State of Israel, and especially since the Six Day War, most Karaite Jews have made Aliyah, and can now again use the observational calendar.

Karaites use the lunar month and the solar year, but the Karaite calendar differs from the Rabbinic calendar in a number of ways.

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.[19] 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 aviv),[20] rather than using the calculated and fixed calendar of Rabbinic Judaism. Occasionally this results in Karaites being one month ahead of other 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.

Furthermore, the seasonal drift of the Rabbinic calendar is avoided, resulting in the years affected by the drift starting one month earlier in the Karaite calendar.

Also, the four rules of postponement of the Rabbinic calendar are not applied, as they are not found in the Tanakh. This affects the dates observed for all the Jewish holidays by one day.

## 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.

#### Persian period: evidence of the papyri

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.[21][22]

#### Later postexilic period: evidence of the Mishnah

In the Maccabean, Herodian, and Mishnaic periods, according to the evidence of the Mishnah and Tosefta, 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.[23] 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.[24] These observations were compared against calculations.[25] When thirty days elapsed since the last new moon, the witnesses were readily believed.

At first the beginning of each Jewish month was 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.[26] 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.[27]

#### Evaluation of the Mishnaic evidence

It has been noted[28] that the procedures described in the Mishnah and Tosefta are all plausible procedures for regulating an empirical lunar calendar. Fire-signals, for example, or smoke-signals, are known from the pre-exilic Lachish ostraca.[29] Furthermore, the Mishnah contains laws that reflect the uncertainties of an empirical calendar. Mishnah Sanhedrin, for example, holds that when one witness holds that an event took place on a certain day of the month, and another that the same event took place on the following day, their testimony can be held to agree, since the length of the preceding month was uncertain.[30] Another Mishnah takes it for granted that it cannot be known in advance whether a year's lease is for twelve or thirteen months.[31] Hence it is a reasonable conclusion that the Mishnaic calendar was actually used in the Mishnaic period.

The accuracy of the Mishnah's claim that the Mishnaic calendar was also used in the late 2nd temple period is less certain. One scholar has noted[32] that there are no laws from Second Temple period sources that indicate any doubts about the length of a month or of a year. This led him to propose that the priests must have had some form of computed calendar or calendrical rules that allowed them to know in advance whether a month would have 30 or 29 days, and whether a year would have 12 or 13 months.

### 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 were in place by 823, according to a treatise by the Muslim astronomer al-Khwarizmi (c. 780–850 CE). Al-Khwarizmi'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.[33][34]

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.[35]

### Modern calendar

The Arch of Titus depicting the objects from the Temple being carried through Rome.

Between 70 CE and 1178 CE, the observation based calendar was gradually replaced by a mathematically calculated one.[36] Except for the epoch year number, the calendar rules reached their current form by the beginning of the 9th century, as described by al-Khwarizmi in 823.[33][34]

There is a tradition, first mentioned by Hai Gaon (d.1038 CE), that Hillel b. R. Yehuda "in the year 670 of the Seleucid era" (i.e. 358–359 CE) was responsible for the new calculated calendar with a fixed intercalation cycle. Later writers, such as Nachmanides, explained Hai Gaon's words to mean that the entire computed calendar was due to Hillel b. Yehuda. Maimonides, in the 12th century, 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." Taken together, these two traditions suggest that Hillel b. Yehuda (whom they identify with the mid-4th century Jewish patriarch Ioulos, attested in a letter of the Emperor Julian[37], and the Jewish patriarch Ellel, mentioned by Epiphanius[38]) instituted the computed Hebrew Calendar because of persecution. H. Graetz attempted[39] to link the introduction of the computed calendar to a sharp repression following a failed Jewish insurrection that occurred during the rule of Constantius and Gallus. A later writer, S. Lieberman, argued[40] 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.[41][42][43] Furthermore, two Jewish dates during post-Talmudic times (specifically in 506 and 776) are impossible under the rules of the modern calendar, indicating that its arithmetic rules were developed in Babylonia during the times of the Geonim (seventh to eighth centuries).[44] The Babylonian rules required the delay of the first day of Tishrei when the new moon occurred after noon.

The Talmuds do, however, indicate at least the beginnings of a transition from a purely empirical to a computed calendar. 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.[45] 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 the computations" not to set the first day of Tishrei or the Day of the Willow on the sabbath.[46] This indicates that there was a group which "made computations" and was in a position to control, to some extent, the weekday on which Rosh Hashanah would fall.

### Practice

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[47]. 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"[48], suggesting a fairly consistent intercalation scheme that kept Nisan 14 approximately between the Phamenoth 10 (March 6 in the 4th century CE) and Pharmuthi 10 (April 5). 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.[49]

In 1178, Maimonides included all the rules for the calculated calendar and their scriptural basis, including the modern epochal year in his work, Mishneh Torah. The rules detailed in Maimonides' code are those used throughout the Jewish world today.

## Principles

### Measurement of month

Synodic month

A synodic month is the period between two lunar conjunctions, such as between two new moons. Since the actual length of a synodic month varies by several hours from month to month, the calendar is based on a long-term average length called the mean synodic month. The virtual lunar conjunctions at the start of each mean synodic month are called molads. The mean synodic month used in the Hebrew calendar is exactly $\tfrac{765433}{25920}$ days, or 29 days, 12 hours, and 793 parts (44+1/18 minutes) (ie 29.5306 days). This interval exactly matches the mean synodic month determined by the Babylonians before 250 BCE[50] and as adopted by the Greek astronomer Hipparchus and the Alexandrian astronomer Ptolemy. Its remarkable accuracy (less than one second from the true value) is thought to have been achieved using records of lunar eclipses from the eighth to fifth centuries BCE.[51]

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 – 2930 – 29 – 30 – 29 – 30 – 29 – 30 | year 2 | 29 – 30 – 29 – 30 – 3029 – 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" / "קביעה" (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 30 days and Cheshvan has 29 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 I, is added, preceding Adar II (sometimes called "the real Adar"). 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. This connection with the major scale is more remarkable in the context of 19 equal temperament.

### 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
Day of week Number of days
Monday 353 355 383 385
Tuesday 354 384
Thursday 354 355 383 385
Saturday 353 355 383 385

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

Days of week of holidays
Purim Passover
(first day)
Shavuot
(first day)
17 Tammuz/
Tisha B'Av
Rosh Hashanah/
Sukkot/
Shmini Atzeret/
(first day)
Yom Kippur Chanukah
(first day)
10 Tevet Tu Bishvat
Sun Tue Wed Tue Thu Sat Wed or Thu Wed, Thu, or Fri Tue, Wed, or Thu
Tue Thu Fri Thu Sat Mon Fri or Sat Fri or Sun Thu or Sat
Thu Sat Sun Sun* Mon Wed Sun or Mon Sun or Tue Sat or Mon
Fri Sun Mon Sun Tue Thu Mon Tue Mon
*Postponed from 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).[52] 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 (Tzeth haKochabim) 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 Sha`oth Zemaniyoth or "Halachic hours" by taking the time between sunrise and sunset or between dawn and nightfall and dividing it into 12 equal hours. The nighttime hours are similarly divided into 12 equal portions, albeit a different amount of time than the "hours" of the daytime. 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 Sha`oth Zemaniyoth. For convenience, the modern day using Sha`oth Zemaniyoth 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. Within the Mishnah, however, the numbering of the hours starts with the "first" hour after the start of the day. [53]

## 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 365.2424 days long, the Hebrew calendar mean year is slightly longer than this 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:

Comparison of vernal full moon to
actual dates of Passover: 2001–2020[54]
In Gregorian dates
Year Astronomical vernal full moon Passover*
2001 8 April 8 April
2002 28 March 28 March
2003 16 April 17 April
2004 5 April 6 April
2005 25 March 24 April
2006 13 April 13 April
2007 2 April 3 April
2008 21 March 20 April
2009 9 April 9 April
2010 30 March 30 March
2011 18 April 19 April
2012 6 April 7 April
2013 27 March 26 March
2014 15 April 15 April
2015 4 April 4 April
2016 23 March 23 April
2017 11 April 11 April
2018 31 March 31 March
2019 21 March 20 April
2020 8 April 9 April
*Passover commences at sunset preceding the date indicated.

The value 29d12h793p for the molad interval is identical to the value in the Babylonian System B (about 300 BCE), and in Ptolemy's Almagest (2nd century CE), and is approximately equal to 29.530594 days.[52] 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 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 (a 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.[55]

### Irregularities and "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 one of its official calendars (along with the Gregorian 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 5 Iyar, Jerusalem Reunification Day on 28 Iyar, and the Holocaust Commemoration Day on 27 Nisan (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, though only rarely do people make use of this option) and on the mastheads of newspapers.

The Jewish New Year (Rosh Hashanah) 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 "Silvester Night" — "ליל סילבסטר") by holding all-night parties on the night between 31 December and 1 January. 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 12 Heshvan. 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 4 November. 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.

1. ^ Exodus 12:2
2. ^ The Babylonians also employed a lunisolar calendar derived from the Sumerian calendar.
3. ^ Josephus, Antiquities 3.248-251, Loeb Classical Library, 1930, pp. 437-438.
4. ^ Tosefta Sanhedrin 2.2, Herbert Danby, Trans., Tractate Sanhedrin Mishnah and Tosefta, Society for Promoting Christian Knowledge, London and New York, 1919, p. 31. Also quoted in Sacha Stern, Calendar and Community: A History of the Jewish Calendar Second Century BCE-Tenth Century CE, Oxford University Press, 2001, p. 70.
5. ^ Gen 1:5, Gen 1:8, Gen 1:13, Gen 1:19, Gen 1:23, Gen 1:31 and Gen 2.2.
6. ^ "In higher latitudes, where during the summer the sun does not sink below the horizon, and during the winter does not rise above it, the days are counted in summer from midday., i.e., from one upper crossing of the meridian by the sun to the next crossing; in the winter, from midnight to midnight, i.e., from one lower crossing of the meridian by the sun to the next," Entry "Calendar" in The Jewish Encyclopedia Volume 3, Funk and Wagnalls, New York, 1916.
7. ^ For example, according to Morfix מילון מורפיקס, Morfix Dictionary, which is based upon Prof. Yaakov Choeka's Rav Milim dictionary. But the word meaning a non-Talmudic week is שָׁבוּע (shavuʻa), according to the same "מילון מורפיקס".
8. ^ For example, when referring to the daily psalm recited in the morning prayer (Shacharit).
9. ^ Numbers 10:10.
10. ^ Sanctification of the New Moon. Translated from the Hebrew by Solomon Gandz; supplemented, introduced, and edited by Julian Obermann; with an astronomical commentary by Otto Neugebauer. Yale Judaica Series, Volume 11, New Haven: Yale University Press, 1956
11. ^ Gen 7:11 says "... on the seventeenth day of the second month—on that day all the springs of the great deep burst forth..." and Gen 8:3-4 say "...At the end of the hundred and fifty days the water had gone down, (4) and on the seventeenth day of the seventh month the ark came to rest on the mountains of Ararat..." There is an interval of 5 months and 150 days, making each month 30 days long.
12. ^ See Maaser Rishon, Maaser Sheni, Maaser Ani.
13. ^ Josephus, Antiquities 1.81, Loeb Classical Library, 1930.
14. ^ The barley had to be "eared out" (ripe) in order to have a wave-sheaf offering of the first fruits according to the Law. Jones, Stephen (1996). Secrets of Time.
15. ^ Edwin Thiele, The Mysterious Numbers of the Hebrew Kings, (1st ed.; New York: Macmillan, 1951; 2d ed.; Grand Rapids: Eerdmans, 1965; 3rd ed.; Grand Rapids: Zondervan/Kregel, 1983). ISBN 082543825X, 9780825438257
16. ^ 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.
17. ^ M. Rosh Hashanah 1, in Herbert Danby, trans., The Mishnah, Oxford University Press, 1933, p. 188.
18. ^ A minority opinion places Creation on 25 Adar AM 1, six months earlier, or six months after the modern epoch.
19. ^ The Karaite Korner: The New Moon in the Hebrew Bible
20. ^ The Karaite Korner: Aviv (Barley)
21. ^ Sacha Stern, "The Babylonian Calendar at Elephantine", Zeitschrift für Papyrologie und Epigraphik 130 , 159–171(2000).
22. ^ Lester L. Grabbe, A History of the Jews and Judaism in the Second Temple Period, Volume 1: Yehud: A History of the Persian Province of Judah, T&T Clark, London, 2004, p. 186.
23. ^ M. Rosh Hashanah 1.7
24. ^ M. Rosh Hashanah 2.6-8
25. ^ b. Rosh Hashanah 20b: "This is what Abba the father of R. Simlai meant: 'We calculate the new moon's birth. If it is born before midday, then certainly it will have been seen shortly before sunset. If it was not born before midday, certainly it will not have been seen shortly before sunset.' What is the practical value of this remark? R. Ashi said: Confuting the witnesses." I. Epstein, Ed., The Babylonian Talmud Seder Mo'ed, Soncino Press, London, 1938, p. 85.
26. ^ M. Rosh Hashanah 2.2
27. ^ b. Betzah 4b
28. ^ Sacha Stern, Calendar and Community, Oxford University Press, 2001, pp. 162ff.
29. ^ James B. Pritchard, ed., The Ancient Near East: An Anthology of Texts and Pictures, Vol. 1, Princeton University Press, p. 213.
30. ^ M. Sanhedrin 5.3: "If one testifies, 'on the second of the month, and the other, 'on the third of the month:' their evidence is valid, for one may have been aware of the intercalation of the month and the other may not have been aware of it. But if one says, 'on the third', and the other 'on the fifth', their evidence is invalid."
31. ^ M. Baba Metzia 8.8.
32. ^ Solomon Gandz, "The origin of the Two New Moon Days", Jewish Quarterly Review (New Series), v. 40, 1949-50. Reprinted in Shlomo Sternberg, ed., Studies in Hebrew Astronomy and Mathematics by Solomon Gandz, KTAV, New York, 1970, pp. 72-73.
33. ^ a b E.S. Kennedy, "Al-Khwarizmi on the Jewish calendar", Scripta Mathematica 27 (1964) 55–59.
34. ^ a b "al-Khwarizmi", Dictionary of Scientific Biography, VII: 362, 365.
35. ^ See The Remaining Signs of Past Centuries.
36. ^ Sacha Stern, Calendar and Community.
37. ^ Julian, Letter 25, in John Duncombe, Select Works of the Emperor Julian and some Pieces of the Sophist Libanius, Vol. 2, Cadell, London, 1784, pp. 57-62.
38. ^ Epiphanius, Adversus Haereses 30.4.1, in Frank Williams, trans., The Panarion of Epiphanius of Salamis Book I (Sects 1-46), Leiden, E. J.Brill, 1987, p. 122.
39. ^ H. Graetz, Popular History of the Jews, (A. B. Rhine, trans.,) Hebrew Publishing Company, New York, 1919, Vol. II, pp. 410-411. Quoted in Sacha Stern, Calendar and Community, p. 216.
40. ^ S Lieberman, "Palestine in the 3rd and 4th Centuries", Jewish Quarterly Review, New Series 36, pp. 329-370(1946). Quoted in Sacha Stern, Calendar and Community, pp. 216-217.
41. ^ Sacha Stern, Calendar and Community: A History of the Jewish Calendar Second Century BCE-Tenth Century CE, Oxford University Press, 2001. In particular section 5.1.1, discussion of the "Persecution theory."
42. ^ Samuel Poznanski, "Ben Meir and the Origin of the Jewish Calendar", Jewish Quarterly Review, Original Series, Vol. 10, pp. 152-161(1898).
43. ^ "While it is not unreasonable to attribute to Hillel II the fixing of the regular order of intercalations, his full share in the present fixed calendar is doubtful." Entry "Calendar", Encyclopedia Judaica, Keter, Jerusalem, 1971.
44. ^ Samuel Poznanski, "Calendar (Jewish)", Encyclopaedia of Religion and Ethics, vol. 3.
45. ^ Yerushalmi Megillah 70b.
46. ^ Yerushalmi Sukkah 54b.
47. ^ Eduard Schwartz, Christliche und jüdische Ostertafeln, (Abhandlungen der königlichen Gesellschaft der Wissenschaften zu Göttingen. Philologisch-Historische Klasse. Neue Folge, Band viii, Berlin, 1905.
48. ^ Peter of Alexandria, quoted in the Chronicon Paschale. Corpus Scriptorum Historiae Byzantinae, Chronicon Paschale Vol. 1, Weber, Bonn, 1832, p. 7
49. ^ Sacha Stern, Calendar and Community, pp. 87-97, 146-153.
50. ^ Neugebauer, Astronomical cuneiform texts, Vol 1, pp 271-273
51. ^ G. J. Toomer, Hipparcus' Empirical Basis for his Lunar Mean Motions, Centaurus, Vol 24, 1980, pp. 97-109
52. ^ a b Otto Neugebauer, "The astronomy of Maimonides and its sources", Hebrew Union College Annual 23 (1949) 322–363.
53. ^ See, for example, Berachot chapter 1, Mishnah 2.
54. ^ Towards a common date of Easter World Council of Churches, 1997.
55. ^ Bromberg, Irv. ""The Rectified Hebrew Calendar."". Retrieved 2007-10-31.

## References

• 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.

# Bible wiki

Up to date as of January 23, 2010

## Days

From the remotest time to the present the Israelites have computed the day (yôm) from sunset to sunset, or rather from sunset to the appearance of the first three stars which marked the beginning of a new day [Cf. Lev. 23:32; II Esd. (Nehem.) 4:21; etc.]. Before the Babylonian Exile the time between sunrise and sunset was divided into "morning", "midday", and "evening" (Ps. 54:18; Heb. 55:17); but during the stay in Babylon the Hebrews adopted the division into twelve hours (Cf. John 11:9), whose duration varied with the length of the day. On an average, the first hour corresponded to about 6 a.m.; the third hour to 9 a.m.; the end of the sixth to noon; while at the eleventh the day was near its close. Earlier than this division of the day by hours was that of the night into three watches: the first till midnight; the second or middle watch (cock-crow) till 3 a.m.; and the third or morning watch till about 6 a.m.

## Weeks

Seven consecutive days form the week, or second element of the Jewish calendar. As in our ecclesiastical calendar, the days of the Jewish week are numbered, not named. They are called the first day, the second day, the third day, and so on to the seventh, which last is also called "sabbath" (shábbath) a name likewise used to designate the week itself. The sixth day, our Friday, is also known in the New Testament, in Josephus, and in Rabbinical writings as "the eve of the sabbath", or as "the day of the preparation", the paraskeué, a term still employed by the Latin Church in connection with Good Fridays (Cf. Mark 15:42; Josephus, Antiquities of the Jews, XVI, vi, 2; Talmud of Jerusalem, Treatise Pesahîm, chap. iv, I).

## Months

The third and most important element in the Jewish arrangement of time is the month. The two Hebrew words for month are yéráh, and hodésh, whose primitive meaning, "moon", "new moon", points to the dependence of the Jewish month on the phases of the moon. As a matter of fact, the Hebrew months have always been lunar, and extended from one new moon to another. The beginning of the month with the appearance of the new moon was--as it is still--of great practical importance among the Hebrews, inasmuch as the first of every month was to be observed as New Moon's Day, and certain feasts were affixed to the 10th, 14th, or other days of the month. The earliest appearance of the new moon was long ascertained by direct observation, and authoritatively settled by a commission of the Sanhedrin, and the intelligence then made known to the Jews at large, first by means of fire signals, and later on through special messengers. In the present day, and for many centuries, this very primitive manner of fixing the beginning of the month has given way to a systematic calculation of the latter's duration, and the Jewish calendar is now constructed on the basis of a mean lunation of 29 days, 12 hours, 44 min., and 30 sec. Besides being indicated by means of numerals, the first month, the second month, etc., the Hebrew months have been designated in the course of Jewish history by two sets of names. Of the former set--going back probably to Chanaanite times--only four names have survived in the Hebrew Bible. These are: Abhîbh (A.V. Ex. 13:4, 23:15; Deut. 16:1), subsequently the first month; Zíw (III K. 6:1), subsequently the second month; Ethanîm (III K. 8:2), subsequently the seventh month; and Bûl (III K. 6:38), subsequently the eighth month. The latter set of names, certainly of Babylonian origin, began to be used after the Exile. Of its twelve names now found in the Jewish calendar only seven occur in the Hebrew text, but the whole twelve appear as the main divisions of the Megillath Ta'anith (Scroll of Fasting), which in its original form is referred to a date before the Christian Era. These twelve names are as follows:

• Nîsan (Nehem. 2:1; Esth. 3:7)
• 'Iyyar (not named in Scripture)
• Sîwan (Esth. 8:9; Baruch 1:8)
• Támmûz (Cf. A.V. Ezek. 8:14)
• 'Abh (not named in Scripture)
• 'Elûl (Nehem. 6:15; I Mach. 14:27)
• Tíshrî (not named in Scripture)
• Márhéshwan, or simply Héshwan (not named in Scripture)
• Kíslew (Zach. 7:1; Nehem. 1:1)
• Tebeth (Esth. 2:16)
• Shebhat (Zach. 1:7, I Mach. 16:14)
• 'Adar (I Esdras 6:15; Esth. 3:7, 8:12, etc.)

## Years

The twelve months thus named made up the ordinary year (shanah), or next important element in the Jewish calendar. As they were lunar months they formed a mean year of 354 days, a year consequently shorter than the solar year by ten or eleven days. This difference, as can be readily seen, would have, in the course of time, completely disordered the months in relation to the seasons of the year; thus the first month, or Nîsan, (corresponding to the end of March or the beginning of April), in the middle of which the first ripe barley was to be presented to Yahweh in connection with the paschal feast (Ex. 12:1 sqq., 13:3 sqq; Lev. 23:10-12), might have fallen in the middle of winter; and some other festivals depending likewise on the products of the seasons would also have been materially interfered with. Hence it was soon felt--how soon cannot now be ascertained--that the difference between the lunar and the solar years should be equalized by the intercalation of a month. The year in which such an intercalation should be made was for a while determined by an authoritative decision of the Sanhedrin, and ultimately fixed in a permanent manner by astronomical calculation. In a cycle of nineteen years the third, sixth, eighth, eleventh, fourteenth, seventeenth, and nineteenth are made leap-years with an average length of 384 days, by the addition of a month following the twelfth ('Adar), and usually called We-'Adar (Second Adar). It is plain, therefore, that the Jewish year has long been, and still is, a luni-solar year. The Hebrew year thus far described is one constituted in harmony with ritual requirements, and hence it is called the sacred Jewish year. Together with it the Jews have had from time immemorial what may be called a common or civil year commencing in the month of Tíshrî (corresponding generally to part of September and part of October), on or immediately after the new moon following the autumnal equinox. The beginning of the Hebrew civil year practically coincides with that of seed time in Palestine, while the beginning of the sacred year corresponds to that of the harvest season in the same country.

## Eras

There now remains to consider the era, or last element of the Jewish calendar. As might well be expected in connection with a people whose history has been so checkered, the Hebrews have adopted various points of time from which to reckon the succession of years. Their principal ancient eras have been:

• the one which was dated from the deliverance from Egypt;
• the regnal era, or computation of time from the year of accession of the Jewish kings to the throne;
• the Seleucid era, introduced after the Babylonian Exile, beginning 312 B.C., and used by the Jews probably till the twelfth century. For centuries they have employed their present method of counting by anno mundi (A.M.). (See the table below for the yearly arrangement of the principal festival days.)

According to the current Jewish reckoning the calendar is dated from the Creation of the World, which is considered to have taken place 3760 years and 3 months before the commencement of the Christian Era. To find the number of the Hebrew year, beginning in the autumn of a given year of our common era, we have to add 3761 to the number of the latter. Thus the Jewish year beginning September, 1908, is 5669 A.M.

## THE JEWISH CALENDAR

 Hebrew Month Sacred Year Civil Year Ordinary Year Leap Year During 20th c first of month occurs between Principal Feasts Nîsan 1 7 30 (days) 30 March 13- April 11 1. New Moon 14. Paschal lamb killed 15-21. Paschal Feast (Firstfruits of barley offered) 'Iyyar 2 8 29 29 April 12- May 11 1. New Moon 14. Second Passover Sîwan 3 9 30 30 May 11- June 9 1. New Moon 6. Pentecost (Firstfruits of wheat harvest) Támmûz 4 10 29 29 June 10- July 9 1. New Moon 7. Fast. Taking of Jerusalem by Titus 'Abh 5 11 30 30 July 9- Aug. 7 1. New Moon 7. Fast. Destruction of the Temple 'Elûl 6 12 29 29 Aug. 8- Sept. 6 1. New Moon Tíshrî 7 1 30 30 Sept. 6- Oct. 5 1-2. New Year's Feast 10. Day Of Atonement 15-21. Feast of Tabernacles. (Firstfruits of wine and oil) Márhéshwan (Héshwan) 8 2 29+ 29+ Oct. 6- Nov. 4 1. New Moon Kíslew 9 3 30- 30- Nov.4- Dec. 3 1. New Moon 25. Feast of the Dedication of the Temple Tebheth 10 4 29 29 Dec. 4- Jan. 2 1. New Moon 7. Fast. Siege of Jerusalem Shebbat 11 5 30 30 Jan.2- Jan. 31 1. New Moon 'Âdar 12 6 29 29 Feb. 1- March 2 1. New Moon 14, 15. Feast of Purim [We-'Âdar] (Inter- calary) (Inter- calary) (...) (29) March 3-March 13 1. New Moon 14, 15. Feast of Purim ---- 354 ---- 384
Portions of this entry are taken from The Catholic Encyclopedia, 1907.
Facts about Jewish Calendar (Catholic Encyclopedia)RDF feed

# Genealogy

Up to date as of February 01, 2010

### From Familypedia

Calendars
</div>
Common use Astro · Gregorian · Islamic · ISO · Julian
Calendar Types
Lunisolar · Solar · Lunar

Selected usage Armenian · Bahá'í · Bengali · Berber · Bikram Samwat · Buddhist · Chinese · Coptic · Ethiopian · Germanic · Hebrew · Hindu · Indian · Iranian · Irish · Japanese · Javanese · Juche · Korean · Malayalam · Maya · Minguo · Nanakshahi · Nepal Sambat · Tamil · Thai (Lunar – Solar) · Tibetan · Turkish · Vietnamese· Yoruba · Zoroastrian
Calendar Types
Original Julian · Runic

The Hebrew calendar (Hebrew: הלוח העברי‎ ) or Jewish calendar is the calendar used by Jews for religious purposes. It is a lunisolar calendar used to reckon the Jewish New Year and to determine the dates for Jewish holidays, the appropriate Torah portions for public reading, Yahrzeits (dates to commemorate the death of a relative), and which daily Psalm is to be read, among many ceremonial uses. Originally the Hebrew calendar was used by Jews for all quotidian purposes, but by the era of the Roman occupation (1st Century BCE), Jews were compelled to follow the imperial civil calendar for all civic matters such as the payment of taxes and dealings with government officials.

The Hebrew calendar's epoch (reference date), 1 Tishrei 1 anno mundi, 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.[1] Thus, adding 3760 or 3761[2] to any Julian/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).

Two major forms of the calendar have been used. 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 origins of the Hebrew calendar are found in the Torah, which refers to the existence of several numbered but un-named months in the Noahide (pre-Jewish) period, and which recounts several calendar-based commandments, including God's commandment during the Exodus from Egypt to fix the month of Nisan as the first month of the year.[3] The development of the calendar was likely influenced by the Babylonian exile in the 6th Century BCE, during which Babylonian names for the months were adapted; the Babylonians also employed a lunisolar calendar derived from the Sumerian calendar. Following the Jewish diaspora of Roman times (c. 1st Century CE), calculations were increasingly used to fix dates, with the principles 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 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. With respect to the present-day mean solar year, the Hebrew calendar's year is longer by about 6 minutes and 25+25/57 seconds, meaning 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. This is due to the 0.6 second discrepancy between the Calendric "Molad" (lunar conjunction interval), which is fixed by Jewish Law,[4] and the actual mean lunar conjunction interval, which itself is slowly changing over time.[5]

## 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 mathematically determined.

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 runs from sunset to the next sunset, and accordingly, standard times and time zones have no place in the Jewish calendar.

The twelve regular months include: Nisan (30 days), Iyar (29 days),Sivan (30 days), Tammuz (29 days), Av (30 days), Elul (29 days), Tishrei (30 days), Marcheshvan (29 or 30 days), Kislev (29 or 30 days), Tevet (29 days), Shevat (30 days), and Adar (30 days). In the leap years an additional month, Adar II (29 days) is added.

The first month of the year is Nisan, as ordained in the Bible. The 14th of Nisan is the start of the festival of Pesach, a date also prescribed in the Bible, corresponding to the full moon of Nisan. Though it is not expressly prescribed in these terms, Pesach is a spring festival, so the 14th of Nisan is the first full moon after the vernal equinox. Therefore, from the standpoint of determining the annual calendar cycle, the principal problem is that the lunar month/new moon of Nisan must occur before the spring equinox. Since at least the 12th Century, the Hebrew calendar has determined this time mathematically, but prior to this tradition held that the 1st of Nisan does not start (and an intercalary month would be added) "until the barley is ripe."

## History

### Biblical period

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.[6] 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", originally this 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).

The Torah contains several commandments related to the keeping of the calendar and the lunar cycle. The first commandment the Jewish people received as a nation was to determine the new moon: Exodus 12:2

```states, "This month [Nissan] is for you the first of months."  Deut 16:1
refers to a specific month:  "Observe the month of Abib, and keep the passover unto the LORD thy God; for in the month of Abib the LORD thy God brought thee forth out of Egypt by night."
```

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,"[7]. Similarly in Num 28:11
```

.

### Leap months

Detail of the Ishtar Gate of Babylon, dating from the era of the Babylonian captivity.

Due to the difference in length between twelve lunar months and a solar year, a purely lunar calendar cycle would have resulted in a drift of the Hebrew calendar from the seasons. However, the Torah requires that certain festivals take place during certain seasons. This implies that a system of reconciling lunar months in the context of solar years and consequently seasons was in use. The Bible does not directly mention the addition of an "embolismic" or intercalary month that would prevent the drifting of the calendar year, however, it is hinted that the first month was started only following the ripening of barley, and according to some traditions, if the barley had not yet ripened, another monthly cycle would be interjected after the "last month" (Adar), before the first month of the year was announced.

### Babylonian exile and nomenclature

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.

Hebrew names of the months with their Babylonian analogs
Number Hebrew Tiberian Academy Common/Other Length Babylonian analog Notes
1 נִיסָן Nīsān Nisan Nissan 30 days Nisanu called Aviv and Nisan in the Tanakh
2 אִיָּר / אייר ʼIyyār Iyyar Iyar 29 days Ayaru called Ziv in the Tanakh
3 סִיוָן / סיוון Sīwān Siwan Sivan 30 days Simanu
4 תַּמּוּז Tammūz Tammuz Tamuz 29 days Du'uzu
5 אָב ʼĀḇ Av Ab 30 days Abu
6 אֱלוּל ʼĔlūl Elul Elul 29 days Ululu
7 תִּשׁרִי Tišrī Tishri Tishrei 30 days Tashritu called Eitanim in the Tanakh.
Modern first month, Rosh Hashana is celebrated in Tishrei.
8 מַרְחֶשְׁוָן / מרחשוון Marḥešwān Marẖeshwan Marcheshvan 29 or 30 days Arakhsamna often shortened to Cheshvan; called Bul in the Tanakh
9 כִּסְלֵו / כסלוו Kislēw Kislew Kislev, Chisleu 30 or 29 days Kislimu also spelled Chislev
10 טֵבֵת Ṭēḇēṯ Tevet Tebeth 29 days Tebetu
11 שְׁבָט Šəḇāṭ Shevat Shvat, Shebat 30 days Shabatu
12* אֲדָר א׳ ʼĂḏār Adar I* 30 days Adaru *Only in leap years
12 / 13* אדר / אדר ב׳ Adar / Adar II* 29 days

### Weeks and days

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

The Hebrew calendar follows the common 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 Ḥamishi (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, Gen 1:5

```"... And there was evening and there was morning, one day". "One day" also translates to "first day" or "day one". Similarly, Gen 1:8
```
```and Gen 2.2
```

.

Modeled on the same verses and the reference to "...there was evening and there was morning...", the Jewish day runs from sunset (start of "the evening") to the next sunset. Accordingly, standard times and time zones have no place in the Jewish calendar. However, the stready progression of sunset around the world has its own built in time zone. These are gradual and based on observable atronomical phenomona (the sunset) and not on man-made laws and conventions.

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

### Second Temple era, c. 518 BCE - 70 CE

A stone (2.43x1 m) with Hebrew inscription "To the Trumpeting Place" is believed to be a part of the Second Temple.
In Second Temple times (c. 518 BCE - 70 CE), the beginning of each lunar month was decided on the basis of two eyewitnesses testifying to having seen the new lunar crescent at sunset. Patriarch Gamaliel II (c. 100) asked 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. According to tradition, these observations were compared against calculations made by the supreme Jewish court, the Sanhedrin. Whether or not an embolismic month was to be inserted depended on the calculated estimate of the spring equinox moment, 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.

At first the beginning of each Hebrew month was signaled to the communities of Israel and beyond by fires lit on mountaintops, but after the Samaritans and Boethusians began to light false fires, messengers were sent. The inability of the messengers to reach communities outside Israel before mid-month High Holy Days (Succot, 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.

If one back-calculates the moments of the traditional moladot using modern astronomical calculations then the closest that their reference meridian of longitude ever got to Israel was midway between the Nile River and the end of the Euphrates River (about 4° east of Jerusalem), and that was in the era of the Second Temple.

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 Tishrei (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.

### 1st-3rd Centuries CE

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

By the Roman era, some sects, such as the Essenes, used a solar calendar during the last two centuries BCE.

The Jewish-Roman wars of 66–73, 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 Talmud notes the irregular intercalation (adding of extra months) performed in three successive years in the early second century.

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.[10] 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.

Under the patriarchate of Rabbi Judah III (300-330) the testimony of the witnesses with regard to the appearance of the new moon was received as a mere formality, the settlement of the day depending entirely on calculation. This innovation seems to have been viewed with disfavor by some members of the Sanhedrin, particularly Rabbi Jose, who wrote to both the Babylonian and the Alexandrian communities, advising them to follow the customs of their fathers and continue to celebrate two days, an advice which was followed, and is still followed, by the majority of Jews living outside of Palestine.

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, suggesting the final form of the modern calendar was fixed subsequent to the 6th Century. This is despite a popular tradition, first mentioned by Hai Gaon (d.1038), which holds that the modern continuous calendar was once 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.

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.

Most of the modern rules 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, Islamic astronomy, Islamic astrology and geography. Al-Khwārizmī's study of the Hebrew 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.

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.

In 921, Aaron ben Meir, a leader of the Jewish community in Palestine otherwise unknown to history, sought to return the authority for the calendar to the Land of Israel by asserting that the first day of Tishrei should be the day of the new moon unless the new moon occurred more than 642 parts (35⅔ minutes, where a "part" is 1/1080 of an hour or 1/18 of a minute or 3⅓ seconds) after noon, when it should be delayed by one or two days. He may have been asserting that the calendar should be run according to Jerusalem time, not Babylonian. Local time on the Babylonian meridian was indeed about 642 parts (35 minutes and 40 seconds) later than (ahead of) the meridian of Jerusalem, corresponding to a longitude difference of 8° 55'.

An alternative explanation for the 642 parts is that Ben Meir may have believed, along with many earlier Jewish scholars, in a Creation theology placing Creation in the Spring season, and that the calendar rules had been adjusted by 642 parts to fit in with an Autumn date. If Creation occurred in the Autumn, to coincide with the observance of Rosh Hashana, 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 any event he was opposed by Saadiah Gaon of the Talmudic academy of Sura. 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.

### Middle Ages, codification of rules

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.

In his work Mishneh Torah, 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]

Maimonides continues, showing 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 Court and the record of their use lost.[12]

### Karaite interpretation

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

The 4 rules of postponement are not applied, as they are not found in the Tanakh. It is determined when to add a 13th month by observing the ripening of barley (called abib) in Israel, rather than the calculated and fixed calendar of Rabbinic Judaism. This puts Karaites in sync with the Written Torah, while other Jews are often a month later.

The beginning of each month is determined by the Rosh Chodesh - which can be calculated, but is confirmed by observation of the first sightings of the new moon in Israel.

For several centuries, many Karaites, especially those outside Israel, have just followed the calculated dates of the Oral Law (the Mishnah and the Talmud) with other Jews for the sake of simplicity. However, in recent years most Karaites have chosen to again follow the Written Torah practice.

## Principles

### Initial month

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 or Hebrew year has four distinct starting points, according to the Mishnah, "Rosh Hashanah 1:1":

The day most commonly referred to as the start of the New Year is the first of Tishrei, when the formal New Year festival, Rosh Hashanah ("Head of the Year") is observed. This is the beginning of the civil year, and the point at which the year number advances by one. Certain agricultural practices are also marked from this date.[13]

However, the first month of the year is Nisan, reflecting the injunction in Exodus 12:2, "This month shall be to you the beginning of months," meaning the civil New Year 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]

### Epoch

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

Its 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). This date is about one year before the traditional Jewish date of Creation on 25 Elul AM 1, based upon the Seder Olam of Rabbi Yossi ben Halafta, a second century CE sage. (A minority opinion places Creation on 25 Adar AM 1, six months earlier, or six months after the modern epoch.) Thus, adding 3760 (from September-October through December, 3761) to any Julian/Gregorian year number after 1 CE will yield the Hebrew year, ending in September-October, which roughly coincides with that Julian/Gregorian year. Owing to the slow drift of the modern Jewish calendar relative to the Gregorian calendar, this will be true for about another 20,000 years.

The traditional Hebrew 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). The scientific date takes into account evidence from the ancient Babylonian calendar and its astronomical observations. In this and related cases, a difference between the traditional Hebrew year and a scientific date in a Gregorian year results from a disagreement about when the event happened — and not simply a difference between the Hebrew and Gregorian calendars. See the "Missing Years" in the Hebrew Calendar.

### Measurement of the 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.
Traditionally "new moon" refers to the first visible crescent of the moon, an event that usually can be observed 29 or 30 days after the preceding visible crescent, producing a lunar month length of 29 or 30 days. However, an actual lunar conjunction, as scientifically defined based on the position of the moon in the lunar orbit, is a synodic month, known in Hebrew as a "molad".

The calendar is based on estimated mean lunar conjunctions called moladot spaced at intervals of exactly 29 days, 12 hours, and 793 parts (44+1/18 minutes). The traditional molad interval matches the mean synodic month as 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.

The mean interval between molads, or the adopted mean lunar month length based on calculations, is exactly 765433/25920 days, or 29 days 12 hours and 44+1/18 minutes (or 29.5306 days).

Combining the observation method with the scientific lunar month length works as follows: assuming we start at a particular new month (which we'll call "the base date"), that month will be 29 days long, with 12 hours, 44+1/18 minutes left over ("the carry forward amount"). Adding that carry forward amount to the next month will make it equal 30 days, 1 hour and 24+2/18 minutes (30.0612 days). So the second month would be 30 days long, and 1 hour 24+2/18 minutes (2 x carry forward amount) would be carried forward to be added to the next cycle, and so on. Then every 17 lunar cycles the carry forward amounts are over 24 hours, which would require an additional day to be added to whatever length that month would have been. 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.

The other issue is the number of months in a year. Twelve lunar months are about 354 or 355 days (see above) 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).

### Pattern of calendar years

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

There are exactly 14 different patterns that Hebrew calendar 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 Hebrew 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 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 Hebrew leap year is one that has 13 months, a common year has 12 months. 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). Alternatively, the following expression yields the leap status of the year:

hYear is a leap year if the remainder of ( 7 x hYear + 1 ) / 19 is less than 7, where hYear is the Hebrew year number.

With 7 leap years per 19-year cycle, the average interval between leap years = 19/7 = 2+5/7 years, which means that 3-year intervals are more common that 2-year intervals.

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). 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 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.

### 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 Nisan 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 (the day prior to the Sabbath), to avoid having the previous day's fast day still going on at the start of Sabbath. 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 (Nisan 15), Shavuot (Sivan 6), Rosh Hashana (Tishrei 1), Yom Kippur (Tishrei 10), Sukkot (Tishrei 15), and Shemini Atzeret (Tishrei 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 modern fixed calendar isn't moved back to its original form of being judged by the Sanhedrin (which requires the Beit Hamikdash)

### 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. However, for example, halachic noon may be after 1:00pm in some areas during daylight saving time.

## Accuracy

### 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, year 3338 AM on the Hebrew calendar is typically equated to 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 tradional 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. For instance, 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.

### Mean year length

The mean Hebrew calendar year length is 365.2468 days, or 365 days, 5 hours 55 minutes, and 25+25/57 seconds (the molad/monthly interval × 235 months per 19-year cycle ÷ 19 years per cycle). The present-era mean northward equinoctial year is about 365 days 5 hours 49 minutes and zero seconds, so the Hebrew calendar mean year is too long by about 6 minutes and 25+25/57 seconds per year. Approximately every 224 years, those minutes add up so that the Hebrew calendar will fall a full day behind the modern fixed solar year.

In addition, since the mean Gregorian calendar year is 365.2425 days (exactly 365 days 5 hours 49 minutes and 12 seconds) and the mean Hebrew calendar year is 365.2468 days, the Hebrew calendar falls further behind the Gregorian calendar by about a day about every 231 years.

The source of the discrepancy is the difference between the molad interval and the actual lunar conjunction cycle. The molad interval is currently about 0.6 seconds too long, and the discrepancy is accumulating at an accelerating rate, since the mean lunation interval is progressively shortening due to gravitational tidal effects. The accumulated "error" since the era of Hillel II is such that the molad moments are now almost 1 hour and 40 minutes late relative to the mean lunar conjunctions at the original reference meridian, which was 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, an astonishing 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 (make the conjunction moments 16 minutes earlier if referred to the original molad reference meridian midway between the Nile River and the end of the Euphrates River, about 4° east of Jerusalem). Today, in terms of the mean solar time at the meridian of Qandahar, Afghanistan the actual lunar conjunctions vary ±14 hours relative to the traditional moladot.

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 due to the tides the Earth rotation rate slowing even more the mean synodic month is becoming gradually shorter in terms of mean solar time. The value 29-12-793 was almost exactly correct at the time of Hillel II and is now about 0.6 seconds per month too long. However, it is still the most correct value possible as long as only whole parts (1/18 minute) are used.

### 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.

Professor Irv Bromberg notes that the 19-year cycle (and indeed all aspects of the calendar) are part of codified Jewish law, and thus it would only be possible to amend it if a Sanhedrin could be convened.[15] It is traditionally assumed that this will take place upon the coming of the Messiah, which will mark the beginning of the era of redemption according to Jewish belief.

"A 353-year cycle of 4366 lunations, including 130 leap months...[along with] use of a progressively shorter molad interval, will keep the amended calendar from drifting for more than 7 millennia."[16] Adopting an astronomical calendar would require more explicit definition of the calendar rules. Other questions include whether or not a progressive molad should be used, or the actual lunar conjunction, or a prediction of new lunar crescent visibility, and which meridian of longitude should the moment be referred to.

## 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, and an average Israeli would not know what the Hebrew date is without specifically looking it up[citation needed], and questions such as "On what date does Hanukkah start this year?" are not uncommon.

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.

1. ^ A minority opinion places Creation on 25 Adar AM 1, six months earlier, or six months after the modern epoch.
2. ^ Between September-October and December, ie, after Rosh Hashana, add 3761
3. ^ Exodus 12:2
4. ^ The time interval between two consecutive calendric moladot is fixed by halakha at a constant 29 days, 12 hours, 44 minutes and one heleq (=1 part = 3.33 seconds)
5. ^ This interval grows longer by approximately 0.1 SI seconds in 500 years. The great astronomer, Rabbi Raphael Ha-Lewi of Hanover calls this molad the "correct molad" (Luhot Ha-Ibbur, part 1, 1756, title page).
6. ^ Gen 7:11 says "... on the seventeenth day of the second month—on that day all the springs of the great deep burst forth..." and Gen 8:3-4 say "...At the end of the hundred and fifty days the water had gone down, (4) and on the seventeenth day of the seventh month the ark came to rest on the mountains of Ararat..." There is an interval of 5 months and 150 days, making each month 30 days long.
7. ^ Numbers 10:10.
8. ^ For example, according to Morfix מילון מורפיקס, Morfix Dictionary, which is based upon Prof. Yaakov Choeka dictionary. But the word meaning a non-Talmudic week is שָׁבוּע (shavuʻa), according to the same "מילון מורפיקס".
9. ^ For example, when referring to the daily psalm recited in the morning prayer (Shacharit).
11. ^ http://64.233.169.104/search?q=cache:o_6wrQe6ppUJ:personal.stevens.edu/~msenator/hand0.pdf+%22Sanctification+of+the+New+Moon%22+Maimonides&hl=en&ct=clnk&cd=3&gl=us&client=firefox-a
12. ^ op.cit.
13. ^ See Maaser Rishon.
14. ^ 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.
15. ^ Bromberg, Irv. "The Rectified Hebrew Calendar.". Retrieved on 2007-10-31.
16. ^ Bromberg, Irv. "The Rectified Hebrew Calendar.". Retrieved on 2007-10-31.

## References

Wikibooks Programming:Hebrew calendar has a page on the topic of
Computer programming for the Hebrew calendar
• 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.
• Nathan Bushwick. Understanding the Jewish Calendar. Moznaim, 1989. ISBN 0940118173
• L.A. Resnikoff. "Jewish calendar calculations", Scripta Mathematica 9 (1943) 191-195, 274-277.
• Edward M. Reingold and Nachum Dershowitz. Calendrical Calculations: The Millennium Edition. Cambridge University Press; 2 edition (2001). ISBN 0-521-77752-6
• 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 723-730.

#### Date converters

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 This page uses content from the English language Wikipedia. The original content was at Hebrew calendar. The list of authors can be seen in the page history. As with this Familypedia wiki, the content of Wikipedia is available under the Creative Commons License.

# Simple English

The Hebrew Calendar is the calendar used in Judaism.

It sets the dates of the Jewish holidays, the right Torah portions for public reading, Yahrzeits (the date to think of 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 before the destruction of the Second Temple in 70 CE, and based on witnesses observing the phase of the moon, and a rule-based form first fully described by Maimonides in 1178 CE, which was adopted over a transition period between 70 and 1178.

The "modern" form is a fixed arithmetic lunisolar calendar. Because of the roughly 11 day difference between twelve lunar months and one solar year, the calendar repeats in a 19-year cycle of 235 lunar months, with an extra lunar month added once every two or three years, for a total of 7 times per 19 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.

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

[[File:|thumb|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.]] Jews have been using a lunisolar calendar since Biblical times. The first commandment the Jewish People received as a nation was the commandment to determine the New Moon. The beginning of Exodus Chapter 12 says "This month (Nissan) is for you the first of months.". The months were originally referred to in the Bible by number rather than name. Only four pre-exilic month names appear in the Tanakh (the Hebrew Bible): Aviv (first; literally "Spring", but originally probably meant the ripening of barley), Ziv (second; literally "Light"), Ethanim (seventh; literally "Strong" in plural, perhaps referring to strong rains), and Bul (eighth), and all are Canaanite names.

## 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.
• 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 723-730.