Since this is a leap year, in which we add an extra month for Adar, this year has 385 days – making it the longest year that our current Jewish calendar can have. Therefore, I am presenting:
The Longest Year
“Thirty days hath September / April, June and November.” If we were to adapt this poem to, l’havdil, our current, standardized Jewish calendar, we would say that thirty days hath Tishrei, Shvat, Nissan, Sivan, Av, and sometimes Cheshvan1 and Kislev. But the idea of having a standardized Jewish calendar seems to run counter to several mishnayos in Rosh HaShanah. In those mishnayos, we see that whether a specific month has 29 days or 30 days depends on whether witnesses saw the new moon and testified in beis din early enough to declare the 30th day Rosh Chodesh (that is, the first day of the next month). In addition, the Gemara2 states that at times Elul could be 30 days long — which cannot happen in our calendar.
How did our empirical calendar become so rigid and predictable? The Torah (Shemos 12:2) commands the main beis din of the Jewish people (also known as the Sanhedrin), or a beis din specially appointed by them, to declare Rosh Chodesh upon accepting the testimony of witnesses who observed the new moon.3 The purpose of having eyewitnesses was not to notify the beis din that the moon had appeared; the beis din had extensive knowledge of astronomy and could predict exactly when and where the new moon would appear and what size and shape it would be.4 The Torah obligated the beis din to wait for witnesses, however, and they could only rule on whether the 30th day would be the last day of the old month or would become the first day of a new month, based on testimony. If no witnesses to the new moon arrived on the 30th day, then the 31st day became Rosh Chodesh, regardless of the astronomic calculations (Mishnah Rosh HaShanah 24a). At that point in Jewish history, any month could be either 29 or 30 days.
The Torah also commands us that Pesach must always fall during the spring (Devarim 16:1). This seemingly innocuous mitzvah actually requires considerable manipulation of the calendar, since months, derived from the word moon, are determined by the length of time from one new moon to the next, which is a bit more than 29½ days. A lunar year is, or more accurately, twelve lunar months are, almost exactly 354 days. The seasons of the year, on the other hand, are calculated according to the solar year, because seasons change based on where the sun’s most direct rays strike the earth. This varies daily, as the most direct rays move from the north Tropic of Cancer to the south Tropic of Capricorn and back again. A solar year is a bit less than 365¼ days, and is based on the length of time it takes the earth to rotate around the sun. Since Pesach must always take place during the spring, the calendar cannot be twelve lunar months every year, because over time, the eleven-day discrepancy between the lunar and solar years would cause Pesach to wander through the solar year and occur in all seasons.5
The Two “Other” Calendars
There are four calendars commonly in use in the world today, two of which make no attempt to resolve the discrepancy between solar and lunar years. The most common secular calendar (the Gregorian or Western calendar) is based solely on the sun. Although the year is nominally broken into twelve months, the use of the word “months” here is a significant departure from its original meaning. In the Gregorian calendar, months have no relationship to the cycles of the moon. Most secular months have 31 days, while the lunar cycle is only about 29½ days, and even secular months that have 30 days do not relate to any phase or change in the moon. Similarly, the length of February as a month of either 28 or 29 days has nothing to do with the moon. Thus, although the word month should correspond to the moon, the Gregorian calendar is purely a solar one, with the borrowed term, “month,” given a meaning detached from its origin.
Another calendar that is seeing increased use today is the Muslim one, which is purely a lunar calendar of twelve lunar months, some 29 days and some 30. In truth, a pure lunar calendar has no real “year,” since a year is based on the relative locations of the sun and the Earth and the resultant seasons, while a lunar “year” of twelve lunar months completely ignores seasons. The word “year” is used in the Muslim sense only as a basis for counting longer periods of time, but has no relationship to the sun. In fact, the Muslim “year” is only 354 or 355 days long — almost eleven days shorter than a solar year. Therefore, a Muslim who tells you that he is 65 years old is really closer to 63 according to a solar year count. He has counted 65 years, each of which is at least ten days shorter than a real (solar) year. (I trust that Guinness takes these factors into account when computing world records for longevity and the like.)
The Muslim year “wanders” its way through the seasons, taking 33 years until a specific month returns to the exact same point in the solar year in the previous cycle. In the interim, that month has visited each of the other seasons for several consecutive years.
13 month years
There are two commonly used calendars whose months are based on the moon, and years are based on the sun. The traditional eastern Asian calendar, usually referred to as the “Chinese Calendar” and the Jewish calendar, both accommodate this by having some years that are thirteen months and others that are twelve. The methods used by these two calendars to decide which month is doubled and when are quite different. Since our articles are on halacha, I will not discuss the details on how the Chinese calendar decides which month to double and when to do so.
The Jewish Calendar
As we have seen, we are commanded to create a calendar that uses the lunar cycle to define the months, but also to keep our months in sync with the seasons, which are dependent on the sun, in order to determine the dates of the Yamim Tovim. The only way to do so is to occasionally add a month, thereby creating a thirteen-month year, to offset the almost eleven-day difference between twelve lunar months and a solar year. The result of this calendar is that although each date does not fall exactly on the same “solar date” every year, it falls within a close range relative to the solar year. Who determined which years have thirteen months?
Under the original system, the main beis din appointed a smaller special beis din to determine whether the year should have an extra month. This special beis din took into consideration:
1) Astronomical data, such as when Pesach will fall out relative to the vernal equinox (the spring day on which day and night are closest to being equal in length).
2) Agricultural data, such as: How ripe is the barley? How large are the newborn lambs and pigeons?
3) Weather: Is the rainy season drawing to a close? Is there a famine?
4) Convenience, or more specifically, the halachic inconvenience of creating a leap year. The shmittah year and the year following were never made into leap years, and the year before shmittah usually was.
5) Infrastructure. For example, the condition of the highways and bridges.
All of these points influenced whether the thirteenth month, the additional Adar, would be added.6 When this system was in place — during a period without interruption from the time of Moshe and Yehoshua until about 300 years after the destruction of the Beis HaMikdash — the main beis din sent written messages notifying outlying communities of the decision to create a leap year, and the reasons for their decision.7
Creation of the “Permanent” Calendar
During the later era of the Talmud, Roman persecution made it impossible to continue declaring Rosh Chodesh based on eyewitness testimony. Thus, Hillel HaNasi (not to be confused with his more illustrious ancestor, the Tanna Hillel, also sometimes called Hillel Hazakein, who lived several hundred years earlier) instituted a calendar based purely on calculation, without human observation of the new moon. Rambam explains that the mitzvah of the Torah is that if it becomes impossible to declare Rosh Chodesh and leap years on the basis of observation, then the beis din should create a permanent calendar.8 Hillel HaNasi’s calendar kept the same basic structure of 29- and 30-day months and twelve- and thirteen-month years, but it was based purely on calculation and not on the variables mentioned above.
When Hillel HaNasi created the new calendar, he incorporated in its calculations several innovations. The two major changes in this new calendar are:
1) A Leap of Fate
Leap years now follow a regular pattern of seven leap years, called me’ubaros, and twelve non-leap years, called peshutos (ordinary), in a nineteen-year cycle. The third, sixth, eighth, eleventh, fourteenth, seventeenth, and nineteenth years of the cycle are always leap years, and the rest are ordinary years. This year, 5779, is the third year of the cycle and thus is a leap year.
2) The Haves vs. the Have-Nots
The length of most months is now fixed. Tishrei, Shvat, Adar Rishon (which exists only in a leap year), Nissan, Sivan, and Av will always have 30 days; Teves, regular Adar (in a common, nonleap year), Adar Sheini (in a leap year), Iyar, Tammuz, and Elul are always 29 days long. The months of Cheshvan and Kislev are the only months that can vary — sometimes they are 29 days and sometimes they are 30 days.9 A year in which both Cheshvan and Kislev have only 29 days is called chaseirah, lacking. If Cheshvan has 29 days and Kislev has 30, the year is considered kesidrah, expected or regular. If both Cheshvan and Kislev have 30 days, the year is called sheleimah, full.10
Both ordinary and leap years can be either chaseiros, kesidran, or sheleimos. Thus, in the new calendar, all ordinary 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 Rishon always has 30 days, the addition of an extra month 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 is off by a day or two, do not fret. Your recordkeeping is accurate, but the cycle of nineteen years relates only 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, plus the fact that February 29 does not occur every secular year will affect whether your 19th, 38th, 57th, 76th, or 95th Hebrew and secular birthday or anniversary exactly coincide, or whether they are slightly off.)
Revealing Top Secret Information
In order for the new calendar to be established properly, a very carefullyguarded secret had to be revealed. Chazal had always kept secret how one can predict when the new moon is destined to appear, a calculation called the sod ha’ibur. This information had always been kept secret in order to prevent false witnesses from coming forth and testifying that they saw the moon at a time when they knew it could be seen. With the new calendar coming into use, this was no longer a concern. Moreover, people had to know the secret in order to calculate the calendar correctly. The sod ha’ibur is that each new moon appears 29 days, 12 hours, and 793 chalakim or 793/1080 of an hour after the previous new moon.11
Once one knows when the new moon, called the molad, occurred on one Rosh HaShanah, he could add the sod ha’ibur figure either twelve or thirteen times (depending on the number of months that year) 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.
Another factor had also been guarded as a secret: that Rosh HaShanah sometimes takes place not on the day of the molad, but the next available day (see below). In the old system, this happened when the molad fell on the afternoon of Rosh HaShanah and the moon 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 when interrogating potential witnesses testifying to the appearance of the new moon. Although the new calendar is no longer dependent on witnesses seeing the moon, and so we could conceivably set Rosh HaShanah even in a year when the molad falls during the afternoon, we nevertheless postpone Rosh HaShanah to the following day. Thus, creating the calendar in a way that it could be used required revealing these two secrets, so that a person could determine which day should be Rosh HaShanah in the coming year.
Did you ever notice that Yom Kippur never falls on Friday or Sunday? If it did, we would have to observe two consecutive days, both of which have the stringency of Shabbos. Even today we can appreciate the difficulty that this poses, although it was even greater in the era before the discovery of the principles of refrigeration.
When the calendar was based on observation, Yom Kippur did sometimes fall on either Friday or Sunday.12 However, Hillel HaNasi’s new calendar included some innovations that were not part of the earlier calendar. The new 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. It 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, the halachah favored having Rosh Chodesh fall on its most correct day, over the concerns of having two Shabbos-like days fall consecutively, or canceling the hoshanah ceremony on Hoshanah Rabbah.13 But after eyewitness testimony could no longer be used, and we were going to implement a permanent calendar that fulfilled the mitzvah in a less-preferred way anyway, the halachah then went the other way: it favored keeping Yom Kippur from falling on Friday or Sunday, and keeping Hoshanah Rabbah from falling on Shabbos.
In order to accommodate these innovations, Rosh HaShanah could now 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, 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.14 This concept of ensuring that Rosh HaShanah not fall on Sunday, Wednesday, or Friday is called
ראש לא אד”ו , 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 adding one day to the year so that Rosh HaShanah will not fall on a Sunday, Wednesday, or Friday seems simple, at times the calculation needs to take additional factors into consideration, as we will see shortly. 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 this happening is by planning in advance what will happen in the future years, and adjusting the calendar appropriately.
In order to accommodate these various calendar requirements, Hillel HaNasi established four rules, called dechiyos, which, together with the sod ha’ibur calculation and the nineteen-year rotation, form the basis of determining our calendar.15 We’ll use a sample two years calculation of the molad for Rosh HaShanah to explain a dechiyah. A few years ago, the molad calculation for Rosh HaShanah fell on Wednesday evening, and Rosh HaShanah therefore was on Thursday, which is what we would expect. But the following year’s molad fell on Tuesday, less than two hours before the end of the day. Although the molad was on Tuesday, it was too late in the day for this molad to be visible in Eretz Yisrael, and therefore Rosh HaShanah could not occur before Wednesday. However, since Rosh HaShanah cannot fall on a Wednesday, because of the rule of lo adu Rosh, it had to be pushed off to Thursday, or two days after the molad. For this reason, that year had to have an extra day, making it not only a leap year, but also a sheleimah, when both Cheshvan and Kislev have thirty days. This created a year of 385 days, the longest a year can be.16
As mentioned above, although the leap years follow a fixed 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, then 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 that year’s schedule, but also the coming year’s calendar requirements. A result of all these calculations is that although there might seem to be many potential variables used in calculating the years (the day of the week of Rosh HaShanah, whether it is a leap year or ordinary year, and whether the year is chaseirah, kesidrah, or sheleimah), for reasons beyond the scope of this article, there are only seven possible prototype years for an ordinary year, and seven for a leap year.
Each of these fourteen prototype “years” is identified 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 an ordinary year or a leap year, because this can be calculated by knowing how many days of the week there are between Pesach and Rosh HaShanah. In a common ordinary year that is kesidrah, Pesach falls two days later in the week than Rosh HaShanah. In a leap year, it falls four days later, the two additional days being the extra two days that Adar Rishon, which is thirty days long, adds to the count of the days of the week. Of course, these calculations must be adjusted one day in either direction if the year is chaseirah or sheleimah. Thus, the acronym for this year, 5779, is bais shin zayin בשז – Rosh HaShanah was on a Monday, the year is a sheleimah (both Cheshvan and Kislev had 30 days), and the first day of Pesach is on Shabbos.
1 Although the correct name of the month is Marcheshvan, we will use the colloquial name, Cheshvan.
2 Rosh HaShanah 19b, 20a.
3 Rambam, Hilchos Kiddush HaChodesh 1:1, 7; 5:1.
4 Ibid. 2:4; Ritva on the Mishnah Rosh HaShanah 18a.
5 Rambam, ibid. 4:1.
6 Sanhedrin 11a–12a.
7 Sanhedrin 11b; Rambam, Hilchos Kiddush HaChodesh 4:17.
8 Ibid. 5:2.
9 Ibid. 8:5.
10 Since Kislev is sometimes 29 days and sometimes 30, the last day of Chanukah can either be on the second or the third day of Teves.
11 The term chelek, used when announcing the molad on Shabbos Mevarchim, equals 1/1080 of an hour, or 3 and 1/3 seconds.
12 She’eilos of Rav Acha’ei Geon, 67; Rambam, Hilchos Shabbos 5:21; Ha’Emek She’eilah, ad loc., note 22.
13 Ha’Emek She’eilah, ibid.; Gri”z, Hilchos Kiddush HaChodesh.
14 Rambam, Hilchos Kiddush HaChodesh 7:1.
15 Because these dechiyos are extremely technical, we suffice with explaining one of them.
16 Technically, only one of the possible combinations will result in the year being this length. Of the fourteen different year prototypes, three are sheleimah leap years of 385 days.