Mathematics of the Jewish Calendar/Special Shabbats
There are various Shabbats that have special names; not all of them are within the scope of this book.
Shabbat Rosh Chodesh
Shabbat Rosh Chodesh (SRC) is a Shabbat that falls on Rosh Chodesh. There are two such Shabbats in every year type, and three in types 4, 5, 9 and 10.
In year types 6, 7, 13 and 14, Tishri 1 is also Shabbat, but that is Rosh Hashana, so does not count as SRC.
The Shabbat during Chanukah is Shabbat Chanukah; it may be any day except the fifth. If the first day is Shabbat, so is the last day (Shabbat Chanukah II). The day depends on the year type, as follows:
- Year types 7 & 14: 1st & 8th days
- Year types 6 & 13: 2nd day
- Year types 5 & 12: 3rd day
- Year types 4 & 11: 4th day
- Year types 2, 3, 9 &10: 6th day
- Year types 1 & 8: 7th day
Lead-up to Pesach
There are five special Shabbats in the lead-up to Pesach:
- Shabbat Shekalim: this is on Rosh Chodesh Adar (Adar II in a leap year) if this is Shabbat, otherwise it is the Shabbat before.
- Shabbat Zachor: this is the Shabbat before Purim.
- Shabbat Parah: this is the Shabbat before Shabbat Hachodesh.
- Shabbat Hachodesh: this is on Rosh Chodesh Nisan if this is Shabbat, otherwise it is the Shabbat before.
- Shabbat Hagodol: this is the last Shabbat before Pesach.
These Shabbats cannot fall on five consecutive Shabbats. Shabbats that are gaps in the sequence are called hafsakahs, and there are two of these in every year. The sequence depends on the weekday of the first day of Pesach, as follows:
- Sunday: Shekalim, Zachor, Hafsakah, Parah, Hachodesh, Hafsakah, Hagodol
- Tuesday: Shekalim, Hafsakah, Zachor, Parah, Hachodesh, Hafsakah, Hagodol
- Thursday: Shekalim, Hafsakah, Zachor, Parah, Hachodesh, Hafsakah, Hagodol
- Saturday: Shekalim, Hafsakah, Zachor, Hafsakah, Parah, Hachodesh, Hagodol
In leap years, for Shevat read Adar I and for Adar read Adar II.
Doubly Special Shabbats
Three of the Shabbats can be doubly special because they coincide with SRC, namely Chanukah, Shekalim and Hachodesh.
Chanukah: This coincides with SRC if day 6 is Shabbat. Day 7 can also be Rosh Chodesh, but not in a defective year, and Day 7 is only Shabbat in a defective year. Thus we get the double special in year types 2, 3, 9 and 10.
Shekalim: If the first day of Pesach is Sunday (year types 5, 6 & 11) it coincides with SRC.
Hachodesh: If the first day of Pesach is Saturday (year types 4, 9 & 10) it coincides with SRC.
Thus no double special occurs in year types 1, 7, 8, 12, 13 or 14; one occurs in year types 2, 3, 4, 5, 6 and 11; two occur in year types 9 and 10.
Another way is to consider the pre-Pesach period together with the following Chanukah, classified by year type of the later year. (The year type gives the weekday of Rosh Hashana, hence of the previous Pesach.) This currently corresponds to events in the same Gregorian year. This produces the following list of double specials:
- Year types 1, 8: Hachodesh
- Year types 2, 9: Hachodesh and Chanukah
- Year types 3, 10: Shekalim and Chanukah
Otherwise there are none.