History and Rules of the Jewish Calendar
In biblical days, time was measured by observation of both the sun's pattern of motion and the lunar phases. The solar motion served to establish the duration of the year while the waxing and waning of the moon was a practical way to subdivide the year into months. But, unfortunately, the solar year and the lunar cycles are not synchronized. While the present calendar (Gregorian) had its roots in the lunar cycle as evidenced by the length of the months and even the word "month" itself, it was adjusted to the solar year in order to maintain the seasonal references - its relation to the lunar phases was eventually abandoned. The Jewish calendar, on the other hand, maintains both the lunar and solar relationship and also adjusts for certain religious requirements. The establishment of such a calendar was a remarkable accomplishment for a people living more than 2,000 years ago.
Today it is known that one solar year is approximately 365 days, 5 hours, 48 minutes and 46 seconds. The lunar cycle is approximately 29 days, 12 hours, 44 minutes and 3 1/3 seconds (actually 2.841 seconds by current measurement). Therefore, twelve lunar months are 354 days, 8 hours, 48 minutes and 40 seconds, which falls short of a solar year by almost eleven days (10 days, 21 hours and 6 seconds). This difference will play an important role in the calendar calculations.
Of course, a practical calendar must have a whole number of days in each month. Since the lunar month is very nearly 29 1/2 days, a calendar that has twelve months alternating between 29 and 30 days (averaging 29 1/2) would essentially follow the lunar cycle. In fact, this sequence forms the basis for the Jewish calendar. Such a year would have a length of 354 days, short by about eleven days from the solar year. If this were left uncorrected the seasons would quickly drift from their relationship to the months. However, many Jewish festivals are related to agricultural events and must occur during specific seasons.
Once the council had made their declaration the new month was announced by means of fire signals to inform the communities outside of Jerusalem. Distant villages, which could not always receive prompt notice, would celebrate the new moon for two days to be sure they had included the correct day. Some holidays were also celebrated for two days due to the uncertainty of the new moon.
The council was empowered to compensate for the solar and lunar differences by mandating that a "leap month" be inserted in the calendar every second or third year as the eleven-day difference accumulated. (To correct for the solar error and still maintain the lunar relationship it is necessary to make any correction a month at a time rather than a day at a time as in the Gregorian calendar.) They allowed for some flexibility, considering astronomical facts as well as religious and agricultural requirements. They observed the state of the crops, considered the need to make the Passover journey by way of muddy roads and tried to insert the leap month in an advantageous way.
For the early Jews the day began and ended at sundown rather than at midnight. (Genesis says, "... and there was evening, and there was morning, one day"). For purposes of the Jewish calendar it still does. The new day (and hence the start of the Sabbath or a holiday) begins at sundown. However, for calendar calculations the day is considered to begin and end at 6 o'clock in the evening, Jerusalem time. The hour of 6 PM is therefore considered hour "zero". The hour was subdivided into 1080 "parts". So a part was 3 1/3 seconds and there were 18 parts in a minute. Each part was divided into 76 "moments". So there were 22.8 moments in a second. Many texts still refer to the use of "parts" but "seconds" are used in JCAL for Windows.
Ancient names for the months are mentioned in Deuteronomy and Kings I but little else is known about the names of the months until the period of the Kings. At that time there was a reformation of the calendar and the months were referred to by their ordinal numbers (first, second, third month, etc.) and the start of the year was changed to the spring. By the end of the period of the Second Temple the months had again received new names that are used today. The names are Babylonian and were probably adopted shortly after the Babylonian Exile.
The Bible refers to Nisan, the month of spring and Passover, as
the first month. Ancient writings actually refer to four different new years:
Nisan 1 for Kings and festivals, Elul 1 for tithing of animals, Tishri 1 for the
calendar and Shevat 1 or 15 for trees. Tishri 1 is now observed as the beginning
of the year.
Thus the Calendar would appear as shown below:
Tishri 30 days
Such a calendar would be reasonably accurate, with months based on the lunar cycle and with a correction for the solar year. To understand the other adjustments however, it is necessary to consider the Jewish holidays. The following table shows the traditional Jewish holidays.
1. If date falls on Saturday it takes place on following day,
Two problems exist with respect to these holidays. First, since Yom Kippur (Tishri 10) is a major fast day, it is undesirable for it to fall on a Friday or Sunday, adjacent to the Sabbath, because of limitations that would be imposed on the preparation for (or breaking of) the fast. Second, Hoshanah Rabba (Tishri 21) should not fall on a Saturday since the Sabbath laws would interfere with certain rituals. Both of these holidays occur in the first month, Tishri, so it can be said that Rosh Hashanah (Tishri 1, the New Year's Day) must not fall on a Wednesday, Friday, or Sunday.
The Four Rules to Meet
Solar and Lunar Requirements
Notice that the period from Nisan 1 to Tishri 1 is always the
same: 177 days, regardless of the type of year.
The process of establishing the calendar for a particular year consists of the following steps:
a) determine if the year is a leap year,
b) find the day of the Molad (new moon) of Tishri for that year,
c) adjust its Rosh Hashanah date according to the rules explained below,
d) similarly, determine the Rosh Hashanah date of the next year,
e) determine the length of the year (and hence its type) to fill
the duration between the two Rosh Hashanah days.
The time of the Tishri Molad for any year can be determined by performing the previous calculation. But, since the lunar cycle repeats every 19 years, shortcuts can be taken. For example, it is only necessary to add 2 days, 16 hours, 33 minutes and 3 1/3 seconds to a particular new moon to find the day of the new moon exactly one 19-year-cycle later. Or 2 days, 23 hours, 5 minutes and 33 1/3 seconds have to be added to a particular new moon to find the new moon exactly 100 cycles (1900 years) later.
Now the following rules are applied:
Rule 2: When the new moon occurs at noon (18 hours after the
start of the day at sunset) or later, or
When Rules 2, 3, or 4 apply, if delaying Rosh Hashanah by one day causes it to fall within Rule 1, it is delayed a second day.
Explanation of the Four Rules
The second rule is an astronomical adjustment which considers the relationship between the observation of the new moon and the actual time of the lunar conjunction. Since the moon is in conjunction with the sun when it is "new", its first crescent is most readily observed just after sunset on the evening of the conjunction, but the actual conjunction may have occurred many hours before. The duration between the true conjunction and the observation of this first crescent is a complex calculation which takes into account the season, the lunar latitude and the geographical latitude and longitude of the place of observation. The second rule is an adjustment for the factors relating to the observation of the first crescent moon from the city of Jerusalem.
The third rule accommodates the limitation imposed by having only the six possible year-lengths given above. If the new moon occurred on the stated time (or later) the Rosh Hashanah new moon of the following year would occur on Saturday at noon (or later). This can be seen by adding 4 days, 8 hours, 48 minutes and 40 seconds (the time that must be added to a new moon to find the new moon exactly 12 lunar months later) to 2 days, 3 hours, 11 minutes and 20 seconds. This would call for the application of the first two rules and the postponement of the Rosh Hashanah from Saturday to Monday. This, in turn, would require a year length of 356 days (50 weeks plus 6 days), which is not accommodated. So the Rosh Hashanah is postponed to Thursday (Rule 1 applies) and the year is 354 days long.
The fourth rule is also necessary to accommodate the year length
limitations but occurs very infrequently. If one subtracts the time necessary to
calculate the new moon exactly 13 lunar months earlier (5 days, 21 hours, 32
minutes and 43 1/3 seconds) one finds that the new moon at the start of the year
occurred at 12 noon on Tuesday. Under Rules 1 and 2 it would have been postponed
until Thursday. This, in turn, would have required a 382-day leap year (54 weeks
plus 4 days), which is not accommodated. So Rosh Hashanah is postponed to
Tuesday and the year is 383 days long.
The type is now easily determined by examining the day of the
week on which the year begins and ends. The application of Rules 3 and 4 above
have assured us that these are the only types necessary to accommodate all
situations. The year is now completely defined and the corresponding Gregorian
dates must be found.
3) Count the same number of days from the reference in the second calendar system.
The calculations can take advantage of certain patterns to reduce their complexity. Charts and tables have been drawn up to help or a computer can be programmed to do the calculations.
It is interesting to note that the Christian holiday of Easter
and all the holidays tied to it also retain a relation to the lunar cycle. In
the year 325, the date of Easter was set by the Council of Nicaea to be the
first Sunday after the first full moon occurring on or after the vernal equinox.
Because the calculations of the full moon and vernal equinox were too complex,
the calculation was simplified to assume that the vernal equinox is always on
March 21. Easter and Passover usually come within a week of each other, but in
some Jewish leap years Passover occurs a whole month after Easter.
1) The anniversary of a date which was the 30th of Heshvan or Kislev in a year in which that month has 29 days is observed on the 1st of the next month. There is an exception for the observance of a Yahrzeit, namely: if, in the first year after the death, the anniversary month has 29 days then the Yahrzeit is observed on the 29th of that month and continues to be observed on the 29th for all years in which the anniversary month has only 29 days.
2) The anniversary of a date in Adar of an ordinary year is observed on the same date in Adar II of a leap year except for a Yahrzeit which is observed on the same date in Adar I of a leap year.
3) The anniversary of a date in Adar I of a leap year is observed on the same date in Adar of an ordinary year. If the original date was the 30th of Adar I of a leap year then, in an ordinary year, the anniversary is observed on the 1st of Nisan. There is an exception for the observance of a Yahrzeit. A Yahrzeit is observed on the 29th of Adar in an ordinary year.
4) The anniversary of a date in Adar II is observed on the same date of Adar of an ordinary year.
There are a sufficient number of portions to accommodate
different readings on the longer years so it is necessary to double-up on some
weeks in shorter years in order that all the portions be read. Also, there are
special readings that are substituted on the holidays. These substitutions
require a complex series of adjustments to be sure that all portions are read
regardless of the year length. Special Haftarah readings are also said when
celebrating a new moon. To further complicate the matter, not all congregations
observe the same rules. JCAL for Windows shows the Torah and Haftarah reading
that normally would apply to that week as well as the substitutions that are
By the 16th century it was estimated that the accumulated error was ten days. So in the year 1582 Pope Gregory XIII revised the calendar by declaring that the day following October 4th would be October 15th, suppressing ten days. To eliminate the continuing error of one day in 128 years he ordained that centesimal years (years ending in hundreds) should not be leap years unless they are divisible by 400. (1700, 1800 and 1900 were not leap years but 2000 is.) This reduces the year length by three days every 400 years or one day every 133 1/3 years. This Gregorian calendar is the one we use today.
The Gregorian reform compensates by three days (72 hours) every 400 years. The actual excess accumulated is 74 hours, 53 minutes and 20 seconds. The error of 2 hours, 53 minutes and 20 seconds every 400 years accumulates to one day in 3323 years. Oh well, nobody's perfect.
The Gregorian calendar was adopted at once by France, Italy, Spain, Portugal and Luxembourg. Within two years most German Catholic states, parts of Switzerland and The Netherlands adopted the new calendar. The rest of The Netherlands, along with Denmark and the German Protestant states followed in 1699-1700.
The British Government imposed the Gregorian calendar on all its
possessions, including the American colonies in 1752. By this time an error of
more than one additional day had accumulated so the British decreed that the day
following September 2, 1752 should be called September 14, a correction of 11
days. All dates preceding were designated O.S., for Old Style. In addition, New
Years Day was moved to January 1 from March 25. (Under the Old Style, for
example, March 24, 1700 was followed by March 25, 1701). George Washington's
birthday, which was February 11, 1731, O.S. became February 22, 1732.