The Hebrew calendar is based on lunar as well as solar cycles. A month always starts on or near a new moon and has either 29 or 30 days (a lunar cycle is about 29 1/2 days). Twelve of these alternating 29-30 day months gives a year of 354 days, which is about 11 1/4 days short of a solar year.
Since a month is defined to be a lunar cycle (new moon to new moon), this 11 1/4 day difference cannot be overcome by adding days to a month as with the Gregorian calendar, so an entire month is periodically added to the year, making some years 13 months long.
For astronomical as well as ceremonial reasons, the start of a new year may be delayed until a day or two after the new moon causing years to vary in length. Leap years can be from 383 to 385 days and common years can be from 353 to 355 days. These are the months of the year and their possible lengths:
COMMON YEAR LEAP YEAR 1 Tishri 30 30 30 30 30 30 2 Heshvan 29 29 30 29 29 30 (variable) 3 Kislev 29 30 30 29 30 30 (variable) 4 Tevet 29 29 29 29 29 29 5 Shevat 30 30 30 30 30 30 6 Adar I 29 29 29 30 30 30 (variable) 7 Adar II -- -- -- 29 29 29 (optional) 8 Nisan 30 30 30 30 30 30 9 Iyyar 29 29 29 29 29 29 10 Sivan 30 30 30 30 30 30 11 Tammuz 29 29 29 29 29 29 12 Av 30 30 30 30 30 30 13 Elul 29 29 29 29 29 29 --- --- --- --- --- --- 353 354 355 383 384 385Note that the month names and other words that appear in this file have multiple possible spellings in the Roman character set. I have chosen to use the spellings found in the Encyclopedia Judaica.
Adar II, the month added for leap years, is sometimes referred to as the 13th month, but I have chosen to assign it the number 7 to keep the months in chronological order. This may not be consistent with other numbering schemes.
Leap years occur in a fixed pattern of 19 years called the metonic cycle. The 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of this cycle are leap years. The first metonic cycle starts with Hebrew year 1, or 3761/60 B.C. This is believed to be the year of creation.
To construct the calendar for a year, you must first find the length of the year by determining the first day of the year (Tishri 1, or Rosh Ha-Shanah) and the first day of the following year. This selects one of the six possible month length configurations listed above.
Finding the first day of the year is the most difficult part. Finding the date and time of the new moon (or molad) is the first step. For this purpose, the lunar cycle is assumed to be 29 days 12 hours and 793 halakim. A heleq (singular form of halakim) is 1/1080th of an hour or 3 1/3 seconds. (This assumed value is only about 1/2 second less than the value used by modern astronomers -- not bad for a number that was determined so long ago.) The first molad of year 1 occurred on Sunday at 11:11:20 P.M. This would actually be Monday, because the Hebrew day is considered to begin at sunset.
Since sunset varies, the day is assumed to begin at 6:00 P.M. for calendar calculation purposes. So, the first molad was 5 hours 204 halakim after the start of Tishri 1, 0001 (which was Monday September 7, 3761 B.C. by the Gregorian calendar). All subsequent molads can be calculated from this starting point by adding the length of a lunar cycle.
Once the molad that starts a year is determined the actual start of the year (Tishri 1) can be determined. Tishri 1 will be the day of the molad unless it is delayed by one of the following four rules (called dehiyyot). Each rule can delay the start of the year by one day, and since rule #1 can combine with one of the other rules, it can be delayed as much as two days.
- Tishri 1 must never be Sunday, Wednesday or Friday. (This is largely to prevent certain holidays from occurring on the day before or after the Sabbath.)
- If the molad occurs on or after noon, Tishri 1 must be delayed.
- If it is a common (not leap) year and the molad occurs on Tuesday at or after 3:11:20 A.M., Tishri 1 must be delayed.
- If it is the year following a leap year and the molad occurs on Monday at or after 9:32:43 and 1/3 sec, Tishri 1 must be delayed.
Kay