# Mathematics of the Jewish Calendar/The main festivals and fasts

The Jewish religion has many festivals (chagim, singular chag) and fasts (tzom or ta'anit). Their dates are of course determined by the Jewish calendar rather than the Gregorian one.
The Sabbath, festivals and fasts end just after the end of evening twilight. Festivals, and the fasts of Yom Kippur and Tisha B'Av, start just before sunset. Other fasts start just before morning twilight. These times must be calculated for each town's longitude and latitude. The definition of twilight may vary between different Jewish communities.
The day before the Sabbath or a festival or fast is known as Erev (literally, "evening", as in the English phrase "Christmas Eve"). Thus we have Erev Shabbat, Erev Succot, Erev Tisha B'Av, etc.
For historical reasons outside the scope of this book, some festivals that are observed for only one day in Israel are observed for two in the rest of the World by orthodox Jews. (Many non-orthodox movements have rejected this second day.) These are noted below in each case.

## Rosh Chodesh

Rosh Chodesh is the New Month (literally, the Head of the Month). It is the first day of each month. Additionally, if the previous month has 30 days, the 30th day of the previous month is also Rosh Chodesh. Thus for example, Rosh Chodesh Sivan is always just one day since Iyar has 29 days. However, since Sivan has 30 days, 30th Sivan is the first day of Rosh Chodesh Tammuz and 1st Tammuz is the second day.
Since Cheshvan and Kislev are of variable length, Rosh Chodesh Kislev and Tevet may each last either one or two days.
Since 1st Tishri is Rosh Hashana, it is rarely given the name Rosh Chodesh Tishri, although technically it is.
Consecutive Rosh Chodeshes (or, in Hebrew, Rashei Chodashim) fall on consecutive days of the week. This is because two Rosh Chodeshes are necessarily separated by exactly four weeks (2nd - 29th of the month), whether that month has 29 or 30 days. For example, if 1st Nisan is Sunday, we have
    1 Nisan: Rosh Chodesh Nisan: Sun
    30 Nisan: 1st day Rosh Chodesh Iyar: Mon
    1 Iyar: 2nd day Rosh Chodesh Iyar: Tue
    1 Sivan: Rosh Chodesh Sivan: Wed
    30 Sivan: 1st day Rosh Chodesh Tammuz: Thu
    1 Tammuz: 2nd day Rosh Chodesh Tammuz: Fri
    etc.
(Note when applying this rule that 1 Tishri must be counted.)

## Ten Days of Repentance

The Aseret Yeme Teshuva or Ten Days of Repentance are the first ten days of Tishri. The first two days are Rosh Hashana (even in Israel) and the tenth is Yom Kippur. There are seven days between these festivals; one and only one of these must be Sabbath and this is called Shabbat Shuvah (The Sabbath of Return or Repentance).
The day after Rosh Hashana is Tzom Gedalyahu (the Fast of Gedaliah). However, if this day is Shabbat Shuvah, the fast is postponed until Sunday, to avoid fasting on the Sabbath.
Although Yom Kippur is also a fast day, it may fall on Sabbath, since it is so holy that it overrides the normal prohibition of fasting on Sabbath.

## Succot

Succot or Tabernacles is also in Tishri. This is one of the festivals where the duration differs between Israel and the rest of the world.

### Israel

The festival lasts eight days, from 15 to 22 Tishri inclusive. The first and last days are full festivals. The other days, called Chol Hamoed or the Intermediate Days, are semi-festivals when most types of work are permitted. Unless the first and last days are Shabbat, one of the intermediate days will be Shabbat so is called Shabbat Chol Hamoed.
The eighth day is technically a different festival, called Shemini Atzeret (the eighth day of assembly). It is largely devoted to celebrating the reading of the Torah, so is also known as Simchat Torah or Rejoicing of the Law.
The day after the festival (23 Tishri) is known as Isru Chag (the binding of the festival) and has a somewhat joyous nature.

### Rest of the World

The festival lasts nine days, from 15 to 23 Tishri inclusive. The first two and last two days are full festivals. The other days, called Chol Hamoed or the Intermediate Days, are semi-festivals when most types of work are permitted. Unless the first and eighth days are Shabbat, one of the intermediate days will be Shabbat so is called Shabbat Chol Hamoed.
The eighth and ninth days technically form a different festival, called Shemini Atzeret (the eighth day of assembly). The ninth day is devoted to celebrating the reading of the Torah, so it is usually called Simchat Torah or Rejoicing of the Law, although it is the second day of Shemini Atzeret.
The day after the festival (24 Tishri) is known as Isru Chag (the binding of the festival) and has a somewhat joyous nature.

## Chanukah

The festival starts on 25 Kislev. It lasts for eight days (even in Israel), all days being of equal importance. It is 83 days after New Year except in an abundant year when Cheshvan has an extra day; in that case it is 84 days after New Year. This means that in an abundant year, the first day of Chanukah is on the same day of the week as the first day of Rosh Hashana. In other year types, it is one weekday earlier.
In a deficient year, when Kislev has 29 days, the sixth day of Chanukah is Rosh Chodesh Tevet and the last day of the festival is 3 Tevet. In a regular or abundant year, when Kislev has 30 days, the sixth and seventh days of Chanukah are both Rosh Chodesh Tevet and the last day of the festival is 2 Tevet.

## 10th Tevet

This is a fast day, generally just called Asara Betevet (which just means 10th Tevet). It is the only fast that can fall on Friday (but see Pesach); while fasting on Friday is not forbidden, it is discouraged so that you should not commence the Sabbath in a sad frame of mind.

## New Year for Trees

New Year for Trees (in Hebrew, Rosh Hashana L'Ilanot) is a minor festival that falls on 15th Shevat. It is also called Tu B'Shevat, Tu representing 15 in Hebrew letters.

## Purim

This celebrates the events described in the biblical Book of Esther. It is celebrated on 14th Adar (so is 30 days before Pesach). In cities that have been walled since the time of the biblical Book of Joshua (such as Jerusalem), it is celebrated on 15th Adar. Elsewhere, that day is called Shushan Purim and has a somewhat joyous character.
The day before Purim is the Fast of Esther (Ta'anit Esther). If this day is Saturday, fasting is forbidden. Normally, the fast would be postponed to Sunday; that cannot be done in this case, as Purim is a day of celebration and feasting. It could be moved back to Friday, but as noted above fasting on Friday is discouraged so the fast is moved back to Thursday 11th Adar.
In a leap year, all these days are observed in Adar Sheni. 14th and 15th Adar Rishon are called Purim Katon and Shushan Purim Katon respectively; katon means small.

## Pesach

Pesach is called "Passover" in English.
Erev Pesach is more important than most Erevs, for two reasons:
* On the morning of Erev Pesach, it is necessary to remove all trace of leavened bread from the home; no leavened bread is allowed throughout Pesach, so the festival in a sense begins on the morning of the day before.
* It is customary for first-born males to fast on that day, so it is called Ta'anit Bechorim (Fast of the Firstborn). If the first day of Pesach is a Saturday, the fast is on Friday, even though fasting on Friday is usually discouraged. If the first day of Pesach is a Sunday, the fast cannot be postponed to Monday, as that is still the festival of Pesach. It could be moved back to Friday, but since fasting on Friday is discouraged, the fast is moved back to Thursday 12th Nisan.
The first day is 15 Nisan, i.e. 163 days before the next New Year.

### Israel

The festival lasts seven days, from 15 to 21 Nisan inclusive. The first and last days are full festivals. The other days, called Chol Hamoed or the Intermediate Days, are semi-festivals when most types of work are permitted. Unless the first day is Shabbat, or Sunday so the seventh day is Shabbat, one of the intermediate days will be Shabbat so is called Shabbat Chol Hamoed.
The day after the festival (22 Nisan) is known as Isru Chag (the binding of the festival) and has a somewhat joyous nature.

### Rest of the World

The festival lasts eight days, from 15 to 22 Nisan inclusive. The first two and last two days are full festivals. The other days, called Chol Hamoed or the Intermediate Days, are semi-festivals when most types of work are permitted. Unless the first and eighth days are Shabbat, or the first day is Sunday so the seventh day is Shabbat, one of the intermediate days will be Shabbat so is called Shabbat Chol Hamoed.
The day after the festival (23 Nisan) is known as Isru Chag (the binding of the festival) and has a somewhat joyous nature.

### The Counting of the Omer

Starting on the second night of Pesach, every night is counted for seven weeks. Thus on the first night, "tonight is the first night of the Omer" is said, on the next night, "tonight is the second night of the Omer", and so on. From the seventh night, weeks and days are also counted, so on the last night, "tonight is the forty-ninth night of the Omer, making seven weeks" is said.
Parts of this period of seven weeks are times of mourning, when for example weddings should not be held. The precise dates when mourning is observed vary between communities.

### Pesach Sheni and Lag B'Omer

Two days in the Omer have special significance. Pesach Sheni ("Second Pesach") is on 14th Iyar, exactly a month after Erev Pesach. In the days of the Temple, it was an opportunity to make the special Pesach offering for those unable to make it on the correct date. Lag B'Omer, the 33rd day of the Omer or 18th Iyar, is regarded by all communities as a happy day when laws of mourning during the Omer cease or are suspended.

## Holocaust Memorial Day

In many communities, 27th Nisan is observed as Holocaust Memorial Day. If 27th Nisan falls on Friday, it is pushed back to Thursday (26th Nisan), whereas if 27th Nisan falls on Sunday, it is postponed to Monday (28th Nisan).

## Israel Independence Day

This is a new festival, created following the proclamation of the State of Israel in 1948. It is normally on 5th Iyar. The rules have changed slightly over the years, but are now that it is moved back to Thursday if it would be on Friday or Shabbat and postponed to Tuesday if it would be on Monday. Thus it can only fall on Tuesday, Wednesday or Thursday. Some Jews refuse to observe it because they do not regard the creation of the State of Israel as a miracle requiring a new festival. For those who do observe it, it is a joyous day that suspends Omer mourning.
The previous day, Yom HaZikaron ("Day of Remembrance"), is a day for recalling all those killed in battle, similar to Veterans' Day or Armistice Day in other countries.

## Jerusalem Day

This is an even newer festival, recalling the recapture of the Old City of Jerusalem from Jordanian occupation in 1967. It is on 28th Iyar.
As for Independence Day, some Jews refuse to observe it and for those who do observe it, it suspends Omer mourning.

## Shavuot

This is observed on the day following the completion of counting the Omer. This would be the 50th day of the Omer, or 50 days after the first day of Pesach, hence the English term "Pentecost". Before the present fixed calendar, it would have been possible for this to be the 5th, 6th or 7th of Sivan (depending on whether Nisan or Iyar had 29 and 30 days). However, now that Nisan always has 30 days and Iyar has 29, Shavuot is now always on 6th Sivan. Outside Israel, it is observed for two days, 6th and 7th Sivan. As for Succot and Pesach, the day afterwards is called Isru Chag.
Shavuot recalls the giving of the Ten Commandments at Mount Sinai. The three days before Shavuot are called the "Three Days of Bordering", recalling the time when the Israelites were forbidden to approach the mountain. (See Exodus Chapter 19.)

## The Fasts of Tammuz and Av

These fasts fall respectively on 17th Tammuz and 9th Av, so are known in Hebrew as Shiva Assar beTanmmuz and Tisha b'Av, Shiva Assar and Tisha meaining 17 and nine in Hebrew. They are 21 days or exactly three weeks apart, hence always fall on the same day of the week as each other. The period between them is known as "The Three Weeks" and is a period of mourning. Tisha b'Av is 62 days after the first day of Shavuot.
If they fall on Saturday, then to avoid fasting on Shabbat they are postponed to the next day.
It is customary to observe certain mourning practices on the day after Tisha b'Av. These are observed on the Monday if Tisha b'Av falls on Sunday and has not been postponed. However, if Tisha b'Av falls on Saturday and was postponed to Sunday, no mourning is observed on Monday.