While the Gregorian calendar is solarbased, the Jewish one is lunarbased. The Gregorian year comes in two different sizes, as discussed earlier. The Jewish year comes in six. Three are classified as leap, the other three as regular. Each of the three sizes within each class is a minor variation. The three regular sizes, in days, are 353, 354 and 355. The three leap sizes are 383, 384 and 385. So "leap" means a big difference in the Jewish calendar. This is because the regular year contains twelve months, but the leap year contains thirteen, and each month corresponds to a lunar cycle (i.e., how long it takes for the moon to complete one orbit around the earth). The minor (2dayspread) variations allow for "fine tuning". Each of these minor size adjustments results in year sizes within each class that, for purposes of this discussion, I will be referring to as minimum, medium and maximum (or obviously similar terms such as mini, midsized or max), from the smallest to the largest, of course. (I have come across a number of sources that have used differing terms such as "deficient", "minimal", "incomplete" or Hebrew "chaser" to refer to minimum; "normal", "common", "in order" or Hebrew "kesidrah" to refer to medium; and "full", "complete" or Hebrew "shelemah" to refer to maximum. This led me to come up with my own terms.) So the years, with respect to their sizes, are referred to as follows:
Minimumregular: 353 days
Mediumregular: 354 days
Maximumregular: 355 days
Minimumleap: 383 days
Mediumleap: 384 days
Maximumleap: 385 days
Each lunar cycle lasts 29 days, 12 hours, 44 minutes and 3 1/3 seconds. Thus a year of exactly 12 lunar months lasts:
12 × 29 days + 12 × 12 hours + 12 × 44 minutes + 12 × 3 1/3 seconds =
348 days + 144 hours + 528 minutes + 40 seconds =
348 days + 6 days + 8 hours + 48 minutes + 40 seconds =
354 days + 8 hours + 48 minutes + 40 seconds
Note that when rounded off to the nearest day, this equals 354 days, a midsized regular year. A year of exactly 13 lunar months lasts:
13 × 29 days + 13 × 12 hours + 13 × 44 minutes + 13 × 3 1/3 seconds =
377 days + 156 hours + 572 minutes + 43 1/3 seconds =
377 days + 6 days + 12 hours + 9 hours + 32 minutes + 43 1/3 seconds =
383 days + 21 hours + 32 minutes + 43 1/3 seconds
Note that when rounded off to the nearest day, this equals 384 days, a midsized leap year. For convenience, there is also a special kind of unit used for Jewish calendar purposes, which is referred to as the part. It equals 3 1/3 seconds. Thus there are 18 of these per minute (and the moon takes 29 days, 12 hours, 44 minutes and 1 part to orbit the earth). 40 seconds = 12 parts. 43 1/3 seconds = 13 parts. (Pretty neat, huh?)
The twelve months in a Jewish nonleap year (along with their lengths, in days, for a midsize, i.e., 354day, year) are:
Tishri (30)
Cheshvan (29)
Kislev (30)
Tevet (29)
Shevat (30)
Adar (29)
Nisan (30)
Iyyar (29)
Sivan (30)
Tammuz (29)
Av (30)
Elul (29)
Note that the above sequence shows the month lengths consistently alternating between 30 and 29 days. This arrives at a total of 354 days. Keep in mind, though, that this is for a mediumregular year. But what about the other types of years? What is the name of that 13th month?? Here is the sequence of months for a leap year (along with their lengths, in days, for a midsize, i.e., 384day, year):
Tishri (30)
Cheshvan (29)
Kislev (30)
Tevet (29)
Shevat (30)
1 Adar (30)
2 Adar (29)
Nisan (30)
Iyyar (29)
Sivan (30)
Tammuz (29)
Av (30)
Elul (29)
There are a few surprises here. First, the extra month is added not at the end of the year (after Elul) but rather in the middle. Second, this extra month takes on a name that is already in use, i.e., Adar. As a result, the alreadypresent Adar and the additional one each take on a number as well, specifically 1 Adar and 2 Adar (Some place the number after the "Adar", i.e., "Adar 1" and "Adar 2"; take your pick—I myself also like "1st Adar" and "2nd Adar"). And third, one of them has 30 days instead of 29! So what happens to the holidays (like Purim), birthdays, anniversaries, etc. that are celebrated during Adar in a nonleap year? Are they celebrated in 1 Adar or 2 Adar during a leap year? Answer: the Adar with 29 days (just like the Adar of a nonleap year), i.e., 2 Adar!
So now we have an idea of what the two year classes (regular and leap) are like. As for the small variations within each class, they are affected by two months: Cheshvan and Kislev. In a midsized year, as discussed above, Cheshvan has 29 days, and Kislev has 30. But both Cheshvan and Kislev have only 29 days each in a minisized year. In a maxisized year, however, these two months both have 30 days apiece. These rules apply whether the year's classification is leap or nonleap.
So the months and their lengths, in days, can be summed up in the following table:


TABLE 1. Months of the Jewish calendar and their lengths. 
Notice that each month is the same from year to year, regardless of type, with Cheshvan, Kislev and the "Adars" being the only exceptions.
Which years are leap years? The earth's orbit around the sun affects the answer to this question. After all, the year is supposed to somehow be synchronized with the seasons, which in turn depend upon the earth's orbital positions. At this time, the Gregorian calendar, as far as leap years are concerned, occurs in cycles of 400 years each, in an effort to match up with the earth's orbit time as much exactly as possible. The average length of year in this case is still not perfect, but it should (hopefully) suffice for a long time to come before a timing adjustment is needed. As for the Jewish calendar, the size of its leaprelated cycle is only 19 years. Each such cycle has its years classified according to the sequence below:
1. Regular
2. Regular
3. Leap
4. Regular
5. Regular
6. Leap
7. Regular
8. Leap
9. Regular
10. Regular
11. Leap
12. Regular
13. Regular
14. Leap
15. Regular
16. Regular
17. Leap
18. Regular
19. Leap
The year in this sequence for a given Jewish year can be determined by dividing that given year by 19. Whatever the remainder is, that indicates the year in the above sequence—however, if the remainder is 0, then the 19th year in this sequence is used. For example, for the year 5759, the remainder is 2 (the quotient is 303), so the 2nd year (a regular year) in the 19year cycle is used. But for the year 5757, the remainder is 0, so the 19th year (a leap year) is used. Note that while regular years can occur consecutively (but only up to two in a row), leap years cannot.
Before going on, I feel that I should define what a "day" is, with respect to its beginning and end, for purposes of this discussion. Unless otherwise stated (or obviously implied), the day begins and ends at 12:00 midnight. This is the normal approach in a typical modern Western society. But in the Jewish system, the day begins and ends about a quarter of a day earlier—when evening starts, the traditional time of which occurs at sunset. However, a modern Jewish approach fixes this time at 6:00 p.m. For this discussion, let's refer to these day types as Western (midnighttomidnight), traditional Jewish (sunsettosunset) and modern Jewish (6 p.m.to6 p.m.).
The Jewish calendar year begins with the first day of the month of Tishri, a day more popularly known as Rosh Hashanah (which means "head [of] the year"). The new moon (the start of a lunar cycle) corresponding to this day is also known as the molad (which means "birth") of Tishri. Under normal conditions, Rosh Hashanah is observed on the same day that this new moon takes place. But this sameday observance does not always happen. Many times, Rosh Hashanah—and thus the beginning of the new year—is shifted until a later day. This delay can be either one or two days (but not more than that) and can be caused by one or more of the following four conditions—also known as "restrictions" or, in Hebrew, dechiyyot (singular, dechiyyah):
Dechiyyah 1: The PM Condition
The new moon occurs at 12:00 noon or later (the "p.m." half of the day). If the
new moon, i.e., the moon's middle alignment (centered as much as possible) between the sun and the
earth, occurs at 12:00 noon or later on a given Western day, Rosh Hashanah is shifted to the next
day. Of course, this means for a Jewish day that this "PM" shifting occurs only if the new
moon takes place between 12:00 noon and the beginning of the evening (when evening arrives, so does
the next Jewish day). This shifting is done due to the moon not being visible until the
next Jewish day (since the dark side of the moon is facing the earth at the time of the
middle alignment, a certain amount of time must pass before the moon can be seen). Note that this
even allows for the possibility of the moon becoming visible at some point in the evening
immediately following an afternoon that contained the new moon.
Dechiyyah 2: The S/W/F Condition
Rosh Hashanah is set up to take place on a Sunday, Wednesday or Friday. If the new moon
occurs on any of these three days, Rosh Hashanah is shifted to the next day. But what if a PM
condition for a Saturday, Tuesday or Thursday occurred, resulting in this holiday being shifted from
that day to a Sunday, Wednesday or Friday, respectively? In that case, Rosh Hashanah must be shifted
again by another day (to Monday, Thursday or Saturday, respectively).
So why can't this holiday be observed on a Sunday, Wednesday or Friday? Rosh Hashanah (the 1st day of Tishri) on a Sunday would result in Hoshana Raba (the 21st day of Tishri, i.e., the 7th day of the festival of Sukkot) on a Saturday, which is the weekly Shabbat (Jewish Sabbath), a day of rest (interference with 7 Hakafot). If Rosh Hashanah were to take place on a Wednesday or Friday, this would result in the following Yom Kippur (the 10th day of Tishri) taking place on a Friday or Sunday respectively, both of which are adjacent to Saturday. This results in two consecutive days of strict prohibition against performing work, including food preparation.
Dechiyyah 3: The 356DAYS Condition
The size of this year is set up to be 356 days long. If the new moon occurs on a Tuesday
morning (at midnight or any time up to, but excluding, 12:00 noon), Rosh Hashanah would normally
take place on that same day. But what if this new year is a nonleap year and the new moon
occurs at exactly twenty seconds after 3:11 a.m.? If you add 12 lunar cycles to this time, you come
up with 12:00 noon on a Saturday as the new moon time corresponding to next year's Rosh
Hashanah. So if the new moon for this year's Rosh Hashanah occurs on Tuesday morning before
3:11:20 a.m., the new moon for next year's Rosh Hashanah will occur on Saturday morning
before 12:00 noon. This means that this year's Rosh Hashanah is observed on a Tuesday, and
the next Rosh Hashanah is observed on a Saturday. The resulting length for this
year is 354 days, and this is acceptable. But if that Tuesday morning new moon occurs at or after
3:11:20 for this year, a problem occurs. While this year would be set up to start
on this Tuesday, the next year would be set up to start on a Monday. This is
because next year's new moon would occur on a Saturday at or after 12:00 noon. This
triggers a PM condition, moving that Rosh Hashanah into the following Sunday. But an S/W/F condition
occurs there, so the holiday must be shifted again, this time into the following Monday. The result
of this year's length is no longer 354 days, but rather 356. That's one day too long for a
nonleap year!
The remedy for this problem is to shift this year's Rosh Hashanah past Tuesday. Shifting the holiday into Wednesday would result in a length of 355 days, which is an acceptable size. But Wednesday is not an acceptable day (S/W/F condition), so a further shift must be made into Thursday, an acceptable Rosh Hashanah day. This year's length thus becomes an acceptable 354 days. So this is exactly what is done to a nonleap year whose new moon for Rosh Hashanah occurs on a Tuesday morning at or after 3:11:20 a.m. Keep in mind that this action applies only to nonleap years. It is not necessary (and is therefore not done) for leap years. Also keep in mind that whether the next year (the beginning of which is observed on a Monday in this situation) is a leap year or not has no impact on the rules of this condition.
Dechiyyah 4: The 382DAYS Condition
The size of the previous year is set up to be 382 days long. If the new moon occurs on a
Monday morning (at midnight or any time up to, but excluding, 12:00 noon), Rosh Hashanah would
normally take place on that same day. But what if the previous year is a leap year and the
new moon for this new year (a nonleap year, since there are no consecutive leap years)
occurs at exactly fortythree and onethird seconds after 9:32 a.m.? If you subtract 13 lunar cycles
from this time, you come up with 12:00 noon on a Tuesday as the new moon time corresponding to the previous
year's Rosh Hashanah. So if the new moon for this year's Rosh Hashanah occurs on Monday
morning before 9:32:43+1/3 a.m., the new moon for last year's Rosh Hashanah occurred on
Tuesday morning before 12:00 noon. This means that last year's Rosh Hashanah was observed
on a Tuesday (always Tuesday in this situation, never Thursday—remember, the aforementioned
356DAYS condition does not apply to leap years), and this year's Rosh Hashanah is to be
observed on a Monday. The resulting length for the previous year is 384 days, and this is
acceptable. But if that Monday morning new moon occurs at or after 9:32:43+1/3 for this
year, a problem occurs. While this year would be set up to start on this Monday, the previous
year ended up being started on a Thursday. This is because last year's new moon
occurred on a Tuesday at or after 12:00 noon. This triggered a PM condition, moving that Rosh
Hashanah into the following Wednesday. But an S/W/F condition occurred there, so the holiday had to
be shifted again, this time into the following Thursday. The result of that year's length
would no longer be 384 days, but rather 382. That's one day too short for a leap year!
The remedy for this problem is to shift this year's Rosh Hashanah past Monday. Shifting the holiday for this nonleap year into Tuesday, an acceptable day for Rosh Hashanah, results in a length of 383 days for the previous year. This size is acceptable. So this is exactly what is done to a year (nonleap, of course) whose previous year is a leap year and whose (that is, this year's) new moon for Rosh Hashanah occurs on a Monday morning at or after 9:32:43+1/3 a.m. Keep in mind that this action applies only to Rosh Hashanahs marking the end of a leap year—and thus the beginning of a regular one. Also keep in mind that whether the next year (the beginning of which is observed on a Saturday in this situation) after this regular one is a leap year or not has no impact on the rules of this condition.
Hopefully, by now you know why each class of years (leap and nonleap) has those minor "fine tuning" variations spread out over a twodaywide range. It is because of these four shiftcausing dechiyyot. With this information, time tables can be constructed with essential details about what a year is going to be like, given its new moon time for Rosh Hashanah. Two such tables follow, one for regular years and one for leap years.