# Mathematics of the Jewish Calendar/Minor fasts

The fasts listed in the previous chapter are accepted by all orthodox Jews. There are other fasts that are only observed by a minority of orthodox communities.

## Yom Kippur Katon

Yom Kippur Katon ("small" Yom Kippur) is observed on the 29th day of most months to atone for any sins committed in that month. It is normally on the day before Rosh Chodesh, i.e. 29th of the month, but is moved back to the previous Thursday if it would be on Shabbat, when fasting is forbidden, or on Friday, because it is not good to begin Shabbat while fasting; compare the Fast of Esther.
It is not observed in the months of Tishri (because it is a joyous month), Kislev (because it would fall during Chanukah), Nisan (because it is a joyous month) or Ellul (because we are about to have Rosh Hashana and Yom Kippur). In some communities, this fast is only kept in Av (to begin preparations for repentance in Ellul).

## Monday, Thursday, Monday

These are a consecutive Monday, Thursday and Monday to atone for any failings in observing Succot or Pesach. Since Tishri and Nisan are joyous months, they are postponed to Cheshvan and Iyar. The commonest custom is to fast on the Monday, Thursday and Monday following the first Shabbat after Rosh Chodesh Cheshvan and Iyar. There is no fast on Pesach Sheni (14 Iyar) if it is on Monday; instead, the last fast is on Thursday 17 Iyar. This happens if the first day of Pesach is Sunday.
The dates are as follows, depending on the day of the week of Rosh Hashana or Pesach:
Cheshvan:
* RH Mon: 6, 9, 13
* RH Tue: 5, 8, 12
* RH Thu: 10, 13, 17
* RH Sat: 8, 11, 15
Iyar:
* Pesach Sun: 7, 10, Thu 17
* Pesach Tue: 5, 8, 12
* Pesach Thu: 10, 13, 17
* Pesach Sat: 8, 11, 15
At one time, Israel Independence Day fell on Monday if the first day of Pesach was Tuesday; those who kept Israel Independence Day did not fast on that day, substituting Thursday 15th. Now it is postponed to Tuesday if it would fall on Monday, so this does not arise.
Some fast on the last Monday, Thursday and Monday in Cheshvan i.e. on or after 17th. The dates are as follows, depending on the day of the week of Rosh Hashana:
* RH Mon: 20, 23, 27; 29 is Yom Kippur Katon
* RH Tue: 19, 22, 26; 29 is Yom Kippur Katon
* RH Thu: 17, 20, 24; 27 is Yom Kippur Katon brought forward
* RH Sat: 22, 25, 29; 29 is also Yom Kippur Katon

## Shovavim Tat

This name is an acronym of the initial letters of the eight consecutive sidras Shemot, Vaera, Bo, Beshallach, Yitro, Mishpatim, Terumah and Tetsaveh (the initial vav of Vaera becoming a cholem vowel).
The original custom was that personal fasts were observed on both the Mondays and Thursdays of the weeks when these sidras are read. Nowadays, the more widespread custom is to observe them only on the Thursdays, and many only observe them in leap years. The fast is cancelled if it would coincide with Rosh Chodesh. (Fasting is also generally prohibited on Tu B'Shevat.)
These fasts may coincide with Yom Kippur Katon.
The fasts occur from mid-Tevet to mid-Adar (Adar I in leap years). The earliest date for a Monday fast is 13 Tevet and for a Thursday fast is 16 Tevet (year types 5 and 12). The latest date for a Thursday fast is 13 Adar (I) (year types 6 & 13); in a year type 6 this is also the Fast of Esther. The last fast also coincides with the Fast of Esther in year types 1 and 7, when the latter is moved back to Thursday to avoid falling on Shabbat. Thus the fasts always start after 10 Tevet and finish before Purim.