The Jewish Calendar

The history of the Jewish calendar traces back until the second millenium BCE. At these times, a luni-solar calendar seems to have been in use already, in which the decision of intercalating a month was made according to observations. Only four months had names (Abib, Ziv, Bul, Ethanim)(1), the other months having been designated with their numbers. In 587 BCE, Jerusalem was destroyed by the Babylonian king Nebukadnezar II. and many Jews deported to Mesopotamia, where, influenced by the Babylonian month names, the Jewish months got their names. After the Persian king Kyros had defeated the Babylonian Empire, the Jews were allowed to return to Jerusalem, were a small state was created, which consisted of the city itself an some area around it. This state was part of Persia and later of the Seleucid(2) Empire and Egypt. This is the period known as the time of the Second Temple (538 BCE until 70 CE).

Not only intercalation, but also the beginning of each month was determined by observation. A calendar council gathered on the 30th day of each month and consulted witnesses, which had to report on the visibility of the moon's crescent. Had the crescent been visible, the actual day was declared to be the first day of the new month. Otherwise, the new month began only with the following day. The decision was published and sent to all communities by fire signals. But, according to reports from the second century CE, Samaritans gave false signals, causing many Jews to fall into error. The message was therefore carried to the communities by messengers, but with many Jewish communities too far away to be reached in time, the actual date became uncertain. Therefore, the Jews celebrated all feasts on two consecutive days, making sure, that any feast was observed. Only Yom Kipur was observed only on one day.

The Jewish state gained independence again in 140 BCE, and by the end of the century a Jewish kingdom had evolved. Soon the throne was disputed giving the Romans possibilities to get involved. In 63 BCE, Palestine was occupied by Roman troups led by Pompeius. The Jewish state remained formally independent, but in fact had to obey Roman orders. In this time, the Sanhedrin was created, which became the highest authority on problems whithin the Jewish state, including the determination of the calendar, which was observation-based, yet.

Following quarrels between Greek and Jewish inhabitants of Palestine, a full-scale Jewish uprising developed in 66 CE. The Romans sent Vespasian to suppress the rebellion. After Nero's death a civil war broke out in the Roman Empire itself, which Vespasian could win, becoming emperor in 69 CE. Vespasian's son, Titus, took over the lead of the Roman troups in Palestine. Eventually, Jerusalem and the Temple were destroyed in 70 CE.

The Sanhedrin was re-created by the end of the first century CE and was now led by a patriarch. With the Jews now having communities almost all over the world then known, a regular scheme for the calendar became necessary. With such rules, anyone could determine the date regardless how far he lived from Jerusalem.

After the uprising led by Bar-Kokhba (132 CE) persecutions against the Jews reached an intensity which made it almost impossible to communicate the beginnings of months and years. Now, computational rules were being established concerning the calendar, and in the beginning fourth century CE the beginnings of the months were determined by calculation, the report of witnesses having become a mere formality. There was some opposition against this practice within the Sanhedrin, and Jews in Babylon and Alexandria were told to continue to celebrate the feasts on two days, which is done by the Jews in the diaspora until today.

When Constantine became Roman emperor, the Christian religion de facto became the official religion in the empire. It was forbidden to exercise the Jewish religion at all, including to do calculations in connection to the Jewish calendar. This led, in 359 CE, to patriarch Hillel II. publishing rules for computing the calendar which had been regarded as a secret until then (3). The 19-year leap year cycle was fixed to the present order, while the era and some rules for determining New Year were set only until the 10th century. The era used until the 11th century was the era of the Seleucids, starting in 312 BCE, while from the 10th until the 16th century, the Jewish Creation era came into use, which starts in 3761 BCE.

Units for Counting Time

A day is divided into 24 hours (1 hour: sha'a) consisting of 1080 parts (khalakim) each. The hours are counted from the beginning of the day which is 6 p.m. for civil use. Writing 1 H for a Jewish hour an 1 P for a part gives

1 H = 1 h = 1080 P and
18:00 h = 0H Jewish time.

1 Tishri 5758 is thus beginning on 1 October 1997, 6 p.m. and ends 2 October 1997, 6 p.m. Finally, a part is divided into 76 moments (rega'im).

For religious purposes the period of daylight is divided into 12 hours as is the dark night making the length of this hours vary as the seasons change. Thus, the Jewish holidays begin with sunset.

Calculation of the Beginning of the Year and Jewish Creation Era

The beginning of the year is determined by cyclic calculation based on the lunar month as well as the tropical year. The conjunction of sun and moon (or new moon; in Hebrew: Molad) fixes the beginning of the month. The Molad of the month Tishri (Molad Tishri) together with some additional regulations determines New Year's Day (Rosh Ha-Shanah).

The mean lunar month is taken as 29 d 12 H 793 P (29 d 12 h 44 min 31/3 s). The epoch of the calculation of the moladot is Sunday, 6 October 3761 BCE, 23:11:20h, expressed in the Julian calendar. As explained above, in the Jewish calendar this is already Monday, 5 H 204 P which is from when the Jewish days, months, and years are counted. The following moladot can easily be calculated by repeatingly adding the mean length of a Molad (29 d 12 H 793 P).

The astronomical new moon can occur as much as 14 hours before or after the cyclic calculation but this has no practical meaning. The beginning of the month can be shifted one or two days by the regulations explained later.

Twelve such months make 354.3713 days which is about 11 days short of the tropical year. To keep the calendar aligned with the seasons, a cycle of 19 years consists 12 common years and 7 leap years (shanah me'uberet), the latter being lengthened by an additional month. It is not possible to add single days for the months must be kept aligned with the moon's phases. A year is a leap year when the number leaves a remainder of 0, 3, 6, 8, 11, 14, or 17 when divided by 19.

Knowing the Molad Tishri of a specific Jewish common year the Molad Tishri of the succeeding year can thus be calculated by simply adding twelve times the mean Molad, or adding thirteen times the mean Molad in case it is a Jewish leap year.

The day of the Molad Tishri is New Year's day (Rosh Ha-Shanah), with the following 5 exceptions (dekhiyyot):

Exceptions 1 to 3 have religious reasons while irregular lengths of years are avoided by exceptions 4 and 5.

This somewhat intricate determination of Rosh Ha-Shanah can be illustrated by some examples.

Example 1:

The Molad Tishri of the Jewish year 5719 is on 13 September 1958, 21 H 510 P which is 13 September 1958, 3:28:20 p.m. in the Gregorian calendar.

Because of the Molad occurring after 18 H, Rosh Ha-Shanah is to be shifted to the next day which is Sunday. Therefore, because Rosh Ha-Shanah must not be a Sunday, it is delayed another day to Monday which results in 1 Tishri 5719 being 15 September 1958.

Example 2:

The Molad Tishri of 5745 occurs on 25 September 1984, 17 H 976 P (25 September 1984, 11:54:13.3 a.m.). 5745 is a common year, and 25 September 1984 is a Tuesday. Because of the Molad Tishri being after 9 H 204 P and before 18 H Rosh Ha-Shanah has to be shifted two days to Thursday, 27 September 1984. Thus 1 Tishri 5745 corresponds to 27 September 1984, Gregorian.

The exception "Gatrad" avoids a common year having 356 days. This can easily be seen in the following table which shows the moladot of a Jewish common year of which the Molad Tishri occurs on Tuesday, 9 H 204 P. Tishri* designates the Tishri of the following year. The lengths and names of the months are explained later. (DW - day of week)

 MonthDays DWMolad 
Tishri0Di9 H 204 P
Kheshvan29Mi21 H 997 P
Kislev59Fr10 H 710 P
Tevet88Sa23 H 423 P
Shevat118Mo12 H 136 P
Adar148Mi0 H 929 P
Nisan177Do13 H 642 P
Iyyar207Sa2 H 355 P
Sivan236So15 H 68 P
Tammuz266Di3 H 861 P
Av295Mi16 H 574 P
Elul325Fr5 H 287 P
Tishri*354Sa18 H 0 P

Molad Tishri of the succeeding year occurs exactly on 18 H which calls for shifting Rosh Ha-Shanah of that year to the next day. This being a Sunday Rosh Ha-Shanah must be shifted another day to Monday. This shift by two days would result in the old year having 354 (last line of the table) + 2 (the shift because of "Yakh-Adu") = 356 days which is not allowed.

Example 3:

Molad Tishri of the Jewish leap year 5688 occurred on Monday, 26 September 1927, 16 H 271 P (26 September 1927, 10:15:03.3 a.m.). The Jewish year 5688 is thus a common year following immediately after a leap year. Because of "Betutakpat" Rosh Ha-Shanah must be shifted one day. 1 Tishri 5688 was therefore on 27 September 1927.

"Betutakpat" gives the preceeding leap year a length of 383 days, which is the minimum length allowed.

Leaving "Betutakpat" aside and assuming that the Molad Tishri of the leap year occurs on Tuesday exactly at 18 H, the following table would result (abbreviations as shown above):

 MonthDaysDWMolad 
Tishri0Di18 H 0 P
Kheshvan30Do6 H 793 P
Kislev59Fr19 H 506 P
Tevet89So8 H 219 P
Shevat118Mo20 H 1012 P
Adar148Mi9 H 725 P
Adar II177Do22 H 438 P
Nisan207Sa11 H 151 P
Iyyar236So23 H 944 P
Sivan266Di12 H 657 P
Tammuz296Do1 H 370 P
Av325Fr14 H 83 P
Elul355So2 H 876 P
Tishri*384Mo15 H 589 P

The Molad Tishri of the common year following the leap year occurs exactly from when the shift of Rosh Ha-Shanah because of "Betutakpat" is to be made. The first line of the table shows that Rosh Ha-Shanah of the leap year must be shifted from Tuesday to Thursday ("Yakh-Adu"). Whithout taking into account "Betutakpat" this leap year had a length of 384 (last line of the table) - 2 (postponement for "Yakh-Adu") = 382 days, the minimum length of a leap year being 383 days. The shift of Rosh Ha-Shanah of the following common year gives the leap year a length of 383 days.

Probability of Occurrence of the Exceptions

To determine the probabily of the occurrence of any dekhiyya it is necessary to look at the conditions in which it applies.

The exception Yakh is defined in terms of the time of the day. The period which calls for Yakh is beginning at 18 H and ends at 24 H and has thus a length of six hours. Therefore it occurs with a probability of 6/24  = 1/4 = 25 %. Thos value does not take into account any further shift that may become necessary (Yakh-Adu).

The exception Adu depends on the day of week of the Molad-Tishri, applying on three out of the total seven days of a week. Furthermore, in one quarter of all cases, a shift was necessary because of Yakh already. In these cases Adu does not apply (though it applied if there was no Yakh). For the probability of Adu we can write 3/7 · (1 -1/4) = 9/28 = 32,14 %.

Yakh-Adu is a combination of Yakh (1/4) and "pure" Adu (3/7). Hence, the probability of occurrence is 1/4 · 3/7 = 3/28 = 10,71 %.

Now we can determine the probability of the Yakh exception (without a further shift caused by Adu) as 1/4 - 3/28 = 4/28 = 14,29 %.

The remaining exceptions Gatrad und Betutakpat can be treated similarly. Gatrad applies if the Molad Tischri of a common year (12/19) falls on a Tuesday (1/7) between 9 H 204 P and before 18 H (9516/25920).
The ratio 9516/25920 results from the period of time between 9 H 204 P and before 18 H, which has a length of 9516 parts and the length of a day of 25920 parts.
Thus, Gatrad's probability is 1/7 · 12/19 · 9516/25920 = 793/23940 = 3,3 %.
For Betutakpat we find 1/7 · 7/19 · 2651/25920 = 2651/492480 = 0,54 %.

The results are shown in the following table.

 ExceptionProbabilityOccurence
about
every
 
Adu 32.14 % 3.1 years
Yakh (w/o Yakh-Adu) 14.29 % 7 years
Yakh-Adu10.71 % 9.3 years
Gatrad3.31 % 30 years
Betutakpat 0.54 %  186 years

Internal Structure

The complicated fixing of Rosh Ha-Shanah results in the common year having a length of 353, 354, or 355 days. The year is called defective (shanah khasera), regular (shanah kesidra), and perfect year (shanah shelema), respectively. Because of the addition of another 30-day month, a leap year can have 383, 384, or 385 days.

A common year consists of 12 months, while a leap year has 13 months. The length of each month is 29 or 30 days. The following table shows the names and lengths of the months for the different years, the total lengths of which is to be found in the last line.

  Common Year Leap Year 
Monthdrp Monthdrp
Tishri303030 Tishri303030
Kheshvan292930 Kheshvan292930
Kislev293030 Kislev293030
Tevet292929 Tevet292929
Shevat303030 Shevat303030
Adar292929 Adar303030
---- Adar II292929
Nisan303030 Nisan303030
Iyyar292929 Iyyar292929
Sivan303030 Sivan303030
Tammuz292929 Tammuz292929
Av303030 Av303030
Elul292929 Elul292929
total353354355 383384385
d - defective, r - regular, p - perfect

The religious year begins with Nisan as the first month and ends with Adar which is the twelfth month in common years and the thirteenth month in leap years. Thus, Nisan is considered to be the first month, while Adar is the twelfth, Adar sheni in leap years the thirteenth month. Adar is counted as the last month anyway. Adar rishon and Adar sheni are sometimes called Adar I and Adar II, respectively. For Adar sheni one can find the name We-Adar occasionally.

The main festivals are:

There are minor festivals:

Further feasts are

 

 

Remarks

1
Three of the months are mentioned in the Old Testament explicitly: Ziv as 2nd month (1 Kgs. 6,1), Bul as 8th month (1 Kgs. 6,38), and Ethanim as 7th month (1 Kgs. 8,2).

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2
Palestine became part of the Empire of Alexander the Great in 332 BCE. But, soon after Alexander's death, his empire disintegrated. Of the new states, the Seleucid empire became a considerable power, while under the Ptolemaios dynasty Egypt remained an independent state until it was annexed to the Roman Empire. The small Jewish state was disputed between Egypt and the Seleucid empire during the 4th and 3rd century BCE. In 198 BCE, it eventually fell to the Seleucids.

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3
Another version says that the calendar was published as late as 500 CE, but that seems to rest on a mistake.

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