Calendar Calculations

Last week’s question:

Why are there two months that can switch between 29 and 30 days from year to year? Why were Marcheshvan and Kislev chosen to be those two months?

 

Answer to last week’s question:

Marcheshvan and Kislev are the only two months of the year that do not always have the same number of days. They can each be 29 or 30 days (i.e., both 29, both 30, or 29 then 30, but never Marcheshvan 30 and then Kislev 29). Therefore, Rosh Chodesh Kislev and Rosh Chodesh Teves can sometimes be on one day and sometimes two days.

The reason this is necessary is because the number of days in a year can change based on the day of the week Rosh Hashanah occurs. The day Rosh Hashanah occurs is based on the molad of that Tishrei and the molad of the following Tishrei. In general, the day the molad occurs is the first day of Rosh Hashanah (see exception below).

For example, if the molad of Tishrei of a given regular year occurs on late Wednesday night/leil yom chamishi, Rosh Hashanah would occur on Thursday. Based on the calculations of how long it takes the moon to go around the earth, the molad of the next Tishrei (12 months later) would occur on Monday morning and that Rosh Hashanah would begin on Monday. If the first day of a year is on Thursday and the last day of that year (Erev Rosh Hashanah) is on Sunday, the year must have 354 days. This means that six months must have 30 days (180 total) and six months must have 29 days (174 total; 180+174=354). To facilitate this, Marcheshvan has 29 days and Kislev has 30 days. This is known as a kesidran year.

If a year requires 353 days (e.g., Rosh Hashanah is on Monday and the following Rosh Hashanah is on Thursday), then Marcheshvan and Kislev must have only 29 days (known as a choseir year). If a year requires 355 days (e.g., Rosh Hashanah occurs on Monday and the following Rosh Hashanah is on Shabbos), then both Marcheshvan and Kislev must have 30 days (a shaleim year). In a leap year, there are either 383 days (choseir – both Marcheshvan and Kislev are 29 days), 384 days (kesidran) or 385 days (shaleim). In short, Marcheshvan and Kislev facilitate the number of days that are in the year.

[There are exceptions to the molad rule above. For example, if the molad occurs on Sunday, Wednesday or Friday, Rosh Hashanah is the next day because of the rule of lo adu rosh. The other exceptions are beyond the scope of our discussion.]

Now that we understand why we need two months that can be 29 or 30 days, we still must understand why specifically these two months were selected. The Mefareish of the Rambam (Hilchos Kiddush Hachodesh 8:6) answers this question as follows. It is best to rectify the situation at the beginning of the year lest this change become forgotten later in the year. He explains that although Tishrei is even earlier, this month has Yomim Tovim and fast days, so to avoid confusion during such an important month, the rectification was left for the next two earliest months of the year, Marcheshvan and Kislev.

It should be noted that although the 30th day of Tishrei is at the end of Tishrei and would not interfere with the Yomim Tovim, which are completed a week earlier, it seems that the Mefareish is of the opinion that Chazal felt that changing the number of days any time in Tishrei would bring unnecessary confusion to such a critical month and therefore the 29/30 change was delayed until the following two months.

The Tiferes Yisroel (Shvili Derokia, ois 12, found at the beginning of Mishnayos Yochin Uboaz) brings the Mefareish and then offers a different answer. He says that these two months are far from the Yomim Tovim, and therefore, if someone gets confused, they will not make a major error (e.g., if Adar in a regular year or the second Adar in a leap year was sometimes 30 days, someone might get confused and think that Pesach is on a different day and chas vashalom eat chometz on Pesach). Marcheshvan and Kislev are far enough from any Yom Tov that any possible confusion would be corrected by Pesach.

The Tiferes Yisroel then asks: Why not choose summer months (when there would be little confusion)? He explains that the days between Pesach and Yom Kippur must be a fixed number. Between Pesach and Shavuos there are 50 days (i.e., 49 days of Sefirah from the second day of Pesach through Erev Shavuos and the first day of Shavuos is always on the 6th of Sivan). If, for example, Iyar could sometimes be 30 days, Shavuos would then occur on the 5th of Sivan. There also must be 120 days between Shavuos and Yom Kippur that match the 120 days in the midbar during this time of the year – 40 days between Shavuos and Shiva Asar B’Tammuz when Moshe Rabbeinu was on Har Sinai to bring the first luchos to Klal Yisroel, the next 40 days until Erev Rosh Chodesh Elul when Moshe davened on Har Sinai for Klal Yisroel, and the final 40 days between Rosh Chodesh Elul and Yom Kippur when Klal Yisroel received the second luchos and the Ribbono Shel Olam said, “Solachti kidvorecha.”

However, there is an obvious question. Both answers address the aspect of avoiding confusion. Indeed, the end of Marcheshvan is a good time for this, but the Kislev change brings much confusion to Chanukah. For example, if someone passed away on the last day of Chanukah (known as Zos Chanukah) that occurred in that year on the 3rd of Teves (because Kislev only had 29 days), their yahrtzeit is usually not on Chanukah because Zos Chanukah is usually on the 2nd of Teves. For this reason, the Biur Halacha (684:3, end of v’im) indicates that one must be careful to observe the yahrtzeit on the Hebrew date and not the day of Chanukah (e.g., 2 Teves and not the 7th day of Chanukah, which can be the 1st or 2nd of Teves). A similar confusion can occur with a bar mitzvah bochur.

 

So, how can Kislev have 29 or 30 days, as this causes great confusion with yahrtzeits and bar mitzvahs?

Nireh lefi aniyus daati that Kislev (the beginning and end) were specifically chosen to have 1 or 2 days of Rosh Chodesh for the following reason. One of the decrees in the takanah of the Yevonim was that Yidden should no longer have Rosh Chodesh. [As is well known, during Chanukah we always have Rosh Chodesh and Shabbos, two parts of Yiddishkeit that Yevonim tried to do away with, and Chanukah is eight days long kineged bris milah that they also tried to proscribe.] The reason the Yevonim tried to stop Rosh Chodesh is because if we have no Rosh Chodesh, we do not know when Yom Tov begins or ends. The Yevonim knew that Yomim Tovim are a critical part of Yiddishkeit. If they ban Rosh Chodesh, we can no longer celebrate Yomim Tovim properly. The Chashmona’im fought this and were successful.

To commemorate our victory over the Yevonim’s decree against Rosh Chodesh and the calendar bedavka at the beginning and end of Kislev, we “finalize” the calendar for the rest of the year. The first step is on Rosh Chodesh Kislev by having one or two days. Then, during Chanukah, with one or two days of Rosh Chodesh Teves, we finalize the calendar. The 30th day of Kislev this year will ensure that in 10 months, Rosh Hashanah begins on Monday. If Kislev only had 29 days this month, next Rosh Hashanah would begin on Sunday – something that cannot happen.

The “makeh bepatish” (final step) of the Jewish calendar each year occurs during Chanukah to show the Yevonim and enemies of Klal Yisroel that although they attempted to tamper with our heilige calendar, we will finish the building of the calendar for the entire year specifically on Chanukah, when we defeated the enemies of Klal Yisroel and the Jewish calendar.