When the Torah commands us to create a calendar, it includes two different responsibilities: First, to have Rosh Chodesh and the length of each month determined on the basis of when the new moon appears, and, second, to have the holiday of Pesach fall in the spring and the holiday of Sukkos in the autumn (in the northern hemisphere). Thus, we have two separate and very different requirements, one of having the months determined by the moon, which is a little more than every 29½ days, and having years that coordinate with the seasons, which follow the solar year, which is a bit less than 365¼ days.
To accomplish that the dates and holidays should fall according to the seasons, the halacha is that some years have 12 months, or approximately 354 days, and others have 13 months, or approximately 384 days. This ensures that the holidays fall in their appropriate seasons. The mitzvah of the Torah is that the head of the Sanhedrin should be in charge, every month, to decide whether a month is 29 days long or 30, and of deciding whether a year should have an extra month. In the latter case, he appointed a special committee, comprised of members of the Sanhedrin, to review the relevant information and determine whether the year should be 13 months (a leap year) or only 12 (a common year).
By the way, after the destruction of the Beis HaMikdash, the main Beis Din was not located in Yerushalayim, but wherever the Nasi of the Jewish people resided, as long as it was in Eretz Yisrael. This included several communities at various times of Jewish history, including Teverya, Yavneh, and Shafraam.[i] Indeed, during this period, if the head of the Beis Din was in the Diaspora and there was no one of his stature remaining in Eretz Yisrael, the special Beis Din met outside the land of Israel.[ii]
Initially, all these decisions were made by the heads of the Sanhedrin, and, indeed, when Moshiach comes, we will again have this system. This was the system in place for thousands of years – from the time of Moshe Rabbeinu until about 250 years after the destruction of the second Beis Hamikdash. At that time, the head of the Sanhedrin, Hillel Hanasi (not to be confused with his ancestor, Hillel Hazakein), realized that, because of Roman persecution, the Sanhedrin’s days were numbered and it would be necessary to switch to a different system for determining the calendar. Hillel Hanasi implemented a temporary Jewish calendar, which is the one that we currently use. Although many people refer to it as a “permanent calendar,” it will be in use only until we again have a Sanhedrin, which will then be in charge of the calendar.
Hillel’s calendar kept the same basic structure of 29- and 30-day months and 12- and 13-month years, but it is based purely on calculation and not on observation. The two major changes in this new calendar are:
- A Leap of Fate
The leap years now occur following a regular pattern of seven leap years and 12 non-leap (usually called “common”) years in a 19 year cycle. The third, sixth, eighth, eleventh, fourteenth, seventeenth and nineteenth years of the cycle are always leap years, and the rest are common years. This year is the nineteenth year of the cycle, and thus is a leap year.
- The Haves versus the Have-nots
The length of most months is now predetermined. Tishrei, Shvat, Adar Rishon (which exists only in a leap year), Nissan, Sivan and Av always have 30 days; whereas Teiveis, regular Adar (in a common, non-leap year), Adar Sheini (in a leap year), Iyar, Tamuz and Elul are always only 29 days long. The two months of Cheshvan[iii] and Kislev are the only months whose length varies, sometimes 29 days and sometimes 30.[iv] A year in which both Cheshvan and Kislev have only 29 days is called chaseirah, lacking or defective; one in which Cheshvan has 29 days and Kislev has 30 is called kesidrah, as expected or regular; and one in which both Cheshvan and Kislev have 30 days is called sheleimah, full or excessive.
The terms chaseirah, kesidrah, and sheleimah apply in both common and leap years.[v] Thus, in the new calendar, all common years are either 353 days (if both Cheshvan and Kislev have 29 days), 354 days (if Cheshvan has 29 days and Kislev has 30) or 355 days (if both Cheshvan and Kislev have 30 days); all leap years are either 383 days (if both Cheshvan and Kislev have 29 days), 384 days (if Cheshvan has 29 days and Kislev has 30) or 385 days (if both Cheshvan and Kislev have 30 days). Since Adar in a common year always has 29 days, Adar Rishon always has 30 days, and Adar Sheini always has 29 days, like the regular Adar, the addition of an extra month of Adar in a leap year always adds exactly thirty days.
(Because the nineteen-year cycle synchronizes the lunar calendar with the solar year, the Hebrew and English dates of births, anniversaries and other occasions usually coincide on the nineteenth anniversary of the event. If yours does not, but is off by a day or two, do not fret. Your record keeping is accurate, but the cycle of nineteen years only relates to whether it is a leap year, not to whether the years are of the exact same length. The lengths of Cheshvan and Kislev are determined by other factors, and this will affect whether your 19th, 38th or 57th birthday or anniversary exactly coincides with its Hebrew/secular counterpart, or whether it is slightly off.)
The new calendar bases itself on an estimate, an average time that it takes the moon to revolve around the Earth. This molad calculation is that each new moon appears 29 days, 12 hours, and 793 chalakim (singular: chelek) or 793/1080 of an hour after the previous new moon. Once one knows when the new moon, called the molad, occurred on the previous Rosh Hashanah, one could now add either 12 or 13 times the above figure and determine the time of the molad in the next year, which is the most important factor in determining the date of the next Rosh Hashanah. (The term chelek, used on Shabbos Mevorchim when announcing when the molad is, equals 1/1080 of an hour, or 3 and 1/3 seconds.)
There is one other factor: Sometimes Rosh Hashanah takes place not on the day of the molad, but the next day, because the molad occurred on the afternoon of Rosh Hashanah and would not be visible in Eretz Yisrael until the next day. When Rosh Hashanah was determined by the observation of witnesses, this information was important not only in determining when Rosh Hashanah falls, but also for interrogating potential witnesses testifying to the appearance of the new moon. However, Hillel’s calendar is no longer dependent on witnesses, Rosh Hashanah is still not established on a day when the molad falls on its afternoon, but is postponed. Based on this information, one can determine which day should be Rosh Hashanah in the coming year.
Another major innovation
Did you ever notice that Yom Kippur never falls on Friday or Sunday? If it did, we would observe two consecutive days that both have the stringency of Shabbos. Indeed, when the calendar was based on observation, this could and did happen.[vi]
However, Hillel Hanasi’s calendar included some innovations that were not part of the earlier calendar. His calendar does not allow Yom Kippur to fall on either a Sunday or a Friday, thus avoiding the difficulty of having two Shabbos-like days fall consecutively. Hillel Hanasi’s calendar also does not allow Hoshana Rabbah to fall on Shabbos, which would cause the cancellation of the Hoshanos ceremony. As long as the calendar was determined on the basis of eyewitness testimony, it was halachically more important to have Rosh Chodesh fall on its correct day than to be concerned about difficulties created when certain holidays fall on or next to Shabbos.[vii] However, once we are fulfilling the mitzvah in a less-preferred way with Hillel’s “permanent” calendar, keeping Yom Kippur from falling on Friday or Sunday, and Hoshana Rabbah from falling on Shabbos, are factors to be included in establishing the calendar.
In order to accommodate these innovations, Rosh Hashanah could fall only on Monday, Tuesday, Thursday or Shabbos, since if it falls on Sunday, Hoshana Rabbah falls on Shabbos; if Rosh Hashanah falls on Wednesday, Yom Kippur falls on Friday; and if Rosh Hashanah falls on Friday, then Yom Kippur falls on Sunday. This would mean that when Rosh Hashanah in the coming year would naturally fall on Sunday, Wednesday or Friday, an extra day is added to the calendar to make sure that Rosh Hashanah falls on Monday, Thursday or Shabbos instead.[viii] This calendar concept of guaranteeing that Rosh Hashanah not fall on Sunday, Wednesday or Friday is called לא אד”ו ראש, lo adu rosh, meaning that the beginning of the year, Rosh Hashanah, does not fall on א, the first day of the week, Sunday; ד, Wednesday; or ו , Friday. It is predominantly for this reason that there was a need to have Cheshvan and Kislev sometimes 29 days and sometimes 30, in order to make the exact length of the years flexible.
Although the innovation of adding one day to the year so that Rosh Hashanah not fall on a Sunday, Wednesday or Friday seems relatively simple, it sometimes leads to more complex considerations. In some years, adjusting Rosh Hashanah to avoid Sunday, Wednesday and Friday creates a problem in the year before or the year after. Since Hillel Hanasi’s calendar did not allow a common year to be longer than 355 days and a leap year to be shorter than 383 days, the only way to avoid problems is to plan the calendar an additional year in advance and adjusting the calendar appropriately. In order to accomodate all these various calendar requirements, Hillel Hanasi established four rules, called dechiyos, which, together with the sod ha’ibur calculation and the 19 year leap year rotation, form the basis for determining our calendar.[ix]
To explain how this works, let us choose a sample year in which the molad calculation for Rosh Hashanah fell on Wednesday evening, and Rosh Hashanah therefore falls on Thursday, which is what we would expect. However, the next year’s molad for Rosh Hashanah falls on Tuesday less than two hours before the end of the day. Although the molad falls on Tuesday, it is too late in the day for this molad to be visible in Eretz Yisrael, and therefore, Rosh Hashanah cannot occur before Wednesday. However, since Rosh Hashanah cannot fall on a Wednesday because of the rule of lo adu rosh, it must be pushed off to Thursday, or two days after the molad. For this reason, that year must have an extra day. However, each year is limited how long it may be. In order to accommodate the proper dating of the second year, the year prior would have to have more days than the calendar allows. In order to resolve this, the year before is made longer than necessary. What is happening is that one Rosh Hashanah is postponed to allow that the next Rosh Hashanah should fall out in an acceptable way.
As I mentioned above, although the leap years follow an absolute nineteen-year cycle, whether the year is chaseirah, kesidrah, or sheleimah is determined by the other factors we have noted, and therefore does not follow the nineteen-year pattern. Rather, one first calculates when Rosh Hashanah should fall out based on the sod ha’ibur, checks the rules of the dechiyos to see what adjustments need to be made, and then determines on which day Rosh Hashanah should fall. As a result, whether the year in question needs to be chaseirah, kesidrah, or sheleimah requires calculating not only this year’s schedule, but also the coming year’s calendar requirements.
Based on all these calculations, there are seven prototype years for a common year and seven for a leap year that fulfill the calendar rules. Each of these fourteen prototype “years” is called by a three letter acronym in which the first letter identifies the day of the week of the first day of Rosh Hashanah, the second letter denotes whether the year is chaseirah, kesidrah, or sheleimah, and the third letter identifies the day of the week of the first day of Pesach. No letter is used to denote whether the year is common or leap, because this is understood by knowing how many days of the week Pesach follows Rosh Hashanah. In a common year that is kesidrah, Pesach falls two days later in the week than Rosh Hashanah, and in a leap year, it falls four days later, the two additional days being the extra two days that the extra month of Adar Rishon, thirty days long, adds to the day of the week count. Of course, these calculations must be adjusted one day in either direction, if the year is chaseirah or sheleimah. Either way, calculating how many days are between Rosh Hashanah and Pesach tells us whether it is a common or leap year, so there is no need to include this in the acronym.
Thus, this year 5776 is known as בשז because Rosh Hashanah fell on Monday (ב), it is a sheleimah (ש) year in which both Cheshvan and Kislev contain 30 days, and the first day of Pesach falls on Shabbos (ז).
At this point, we have the basic information to figure out how our calendar operates. Although we may not realize it, we actually already have enough information at our fingertips that we could already calculate the calendars for the coming years – indefinitely.
We understand well why our calendar involves use of the solar year – after all, our seasons, and the appropriate times for our holidays, are based on the sun. But why did the Torah insist that our months follow the moon? It seems that we could live fine without months that are dependent on the moon’s rotation around the earth!
One answer to this question is that the waxing and waning of the moon is symbolic of our own our relationship with Hashem – which is sometimes better and sometimes less so. However, we know that we can always improve that relationship, just as the moon after its waning and almost disappearing always renews itself.
[i] Rosh Hashanah 31b
[ii] Berachos 63a; Rambam, Hilchos Kiddush HaChodesh 1:8
[iii] Although the correct name of the month is Marcheshvan, we will follow the colloquial use of calling it Cheshvan.
[iv] Rambam, Hilchos Kiddush Hachodesh 8:5
[v] By the way, because Kislev is sometimes 29 days and sometimes 30, the last day of Chanukah is sometimes on the second day of Teiveis, and sometimes on the third.
[vi] She’iltos of Rav Acha’ei Geon, #67; Rambam, Hilchos Shabbos 5:21; Ha’emek She’eilah ad loc., Note 22.
[vii] Ha’emek She’ailah ibid; Gri”z, Hilchos Kiddush Hachodesh
[viii] Rambam, Hilchos Kiddush Hachodesh 7:1.
[ix] Because these dechiyos are extremely technical, I did not explain all of them.