History and Rules of the Jewish Calendar

Background

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.

Sanhedrin
During the period of the Second Temple (built between 519 and 516 BC.) and for three centuries after its destruction, a council of the Sanhedrin (the governing body of the time) decreed when the new months would begin and when adjustment was needed to compensate for the seasonal shifts. The start of each month was established by observing the arrival of the new moon. The council would meet on the thirtieth day of the month to hear the testimony of "two trustworthy witnesses" as to whether they observed the new crescent moon on that day. If they had, that day was declared the first of the new month. If they did not, then the next day was declared the first of the new month.

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.

Greek Roots
In 432 BC the Athenian astronomer Meton reformed the Athenian calendar based on an approximate relationship between the solar and lunar cycles. He had observed that every nineteen years the occurrences of the new and full moons returned to the same time with respect to the solar cycle. This pattern is known as the Metonic cycle. Actually, in nineteen years the annual difference (10 days, 21 hours and 6 seconds) accumulates to 206 days, 15 hours, 1 minute and 54 seconds. This accumulation is equal (within two hours) to seven lunar months (which come to 206 days, 17 hours, 8 minutes and 23 1/3 seconds). So if seven lunar months were added over a nineteen year period the lunar and solar cycles could be more or less maintained in synchronization.

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.

Biblical Roots
The chronology of the bible was calculated directly from the bible text and is given in the Talmud (a collection of Rabbinic writing created during the Hellenistic Age). The rabbis derived the following chronology:

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.

Basic Calendar Calculations
The rules for the present Jewish calendar system are believed to have been published by the patriarch Hillel II in the year 358, the Jewish year 4119. Jews had dispersed throughout the world and could no longer depend on word from Jerusalem for instruction. Rather than having the Sanhedrin determine when to add the leap month (Adar II), it was decided to introduce it exactly seven times every nineteen years. Furthermore, it was established that leap years would be the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of the cycle. Adar II, a 29-day month, would be added after Adar. Adar would be increased by one day to 30 days in a leap year giving the leap year 30 days more than the ordinary year.

Thus the Calendar would appear as shown below:

Tishri 30 days
Heshvan 29 days
Kislev 30 days
Tevet 29 days
Shevat 30 days
Adar 29 days (30 on a leap year)
Adar II 29 days (inserted 7 times every 19 years)
Nisan 30 days
Iyar 29 days
Sivan 30 days
Tammuz 29 days
Av 30 days
Elul 29 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.

Jewish Holidays

Notes

1. If date falls on Saturday it takes place on following day, Sunday.
2. If date falls on Friday or Saturday it takes place on preceding Thursday.
3. Adar II if leap year.
4. Established 1951.
5. Established 1949.

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
The Jewish calendar calculation is based on the following three steps. First, the new moon date and time (called the Molad) is calculated and the start of each month is first targeted for that date. Second, the day of Rosh Hashanah is adjusted according to rules discussed below. Third, a leap month is periodically introduced to maintain synchronization with the solar year. However, the processes of adjusting the occurrence of Rosh Hashanah are somewhat complex. It is accomplished by lengthening or shortening the prior year by one day. The month of Heshvan may be lengthened to 30 days and Kislev may be shortened to 29. When Heshvan is lengthened the year is called "full" and when Kislev is shortened the year is called "deficient". Otherwise it is called "normal". This means that three "types" of regular years can exist having totals of 353, 354 or 355 days. Furthermore, a leap year can also be deficient, normal or full and have lengths of 383, 384 or 385 days. Thus, the six possible types are:

Notice that the period from Nisan 1 to Tishri 1 is always the same: 177 days, regardless of the type of year.

By the application of certain rules discussed below it is possible to accommodate all the requirements of the Jewish calendar with a sequence of years having only these six lengths. Note that in a regular year Adar may be called "Adar I" or simply "Adar" whereas in a leap year the two Adars are called "Adar I" and "Adar II".

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.

A set of rules has been established for determining how to position the day of Rosh Hashanah, given the day of the Molad.

Determining if a year is a leap year is done by simply calculating its position in the 19-year cycle which began in the year 1.

As was mentioned above, the duration between lunar cycles is 29 days, 12 hours, 44 minutes and 3 1/3 seconds. If the time of one Molad is known, the time of successive or previous ones can be determined by adding or subtracting multiples of this interval. From this process it is calculated that the first new moon of the year 1 took place on Sunday evening at 11 minutes, 20 seconds after 11 PM.

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:

Tishri 1 (Rosh Hashanah) will be on the day of the Molad except when falling into one of the four exceptions below (which is more often than not), in which case it is then delayed by one day.

Rule 1: When the new moon occurs on Wednesday, Friday, or Sunday, or

Rule 2: When the new moon occurs at noon (18 hours after the start of the day at sunset) or later, or

Rule 3: When the new moon of an ordinary year occurs on Tuesday at 11 minutes and 20 seconds after 3 am or later, or

Rule 4: When, at the termination of a leap year, the new moon occurs on Monday at 32 minutes and 43 1/3 seconds after 9 am or later.

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 first rule causes the two holidays mentioned above to fall only on the permissible days.

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.

Selecting the Year Type
At this point, the Rosh Hashanah day calculation is made for the next year. The starting day and ending day of the year are then known as well as whether it must be a leap year. The year type is chosen from the six possibilities according to the length required. A simple way to chose the type is to use the table showing the number of days added from one New Year's Day to the next.

Days Added to Year for Various Year Types

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.

Correlation to the Gregorian Calendar
The correlation to the Gregorian calendar is very unsophisticated. Simply stated: there is no direct relationship between the Jewish and Gregorian calendars. They both are related to the solar cycle but according to totally different rules. Every date, in the course of the 19-year cycle can fall within a range of thirty days. The only way to determine corresponding Gregorian dates is to:

1) Have a known correspondence as a reference point. (Saturday, September 30, 1989, corresponds to Tishri 1, 5750.)

2) Count how many days in one calendar system exist between the reference date and the desired date.

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.

Anniversaries
Anniversaries can present a special problem for the Jewish calendar because there are often days that occur in one year which are absent in another. In the Gregorian calendar there is only one special case to consider, February 29th. People born or married on that date can simply decide to celebrate on February 28th or March 1st for years that are not leap years. But the Jewish calendar has an entire leap month as well as two months which can vary in length, so special rules have been established. The anniversary of the death of a close relative (called a Yahrzeit) is of particularly importance and has unique rules associated with it.

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.

Weekly Readings
The five books of the Old Testament (Torah) are divided into 54 weekly portions which are read, one each Sabbath, throughout the year. Only the last portion, Ve-Zot-ha-Berakhah, is not read on the Sabbath but on Simchat Torah. The new cycle begins on the Sabbath after Simchat Torah. Each weekly portion has an accompanying reading from one of the Prophets (Haftarah). These are all listed below.

Torah Reading and the Prophets

1. Bereshit, Gen 1:1-6:8 Isa 42:5-43:11
2. No'ah, Gen 6:9-11:32 Isa 54:1-55:5
3. Lekh Lekha, Gen 12:1-17:27 Isa 40:27-41:16
4. Va-Yera, Gen 18:1-22:24 II Kings 4:1-37
5. Hayyei Sarah, Gen 23:1-25:18 I Kings 1:1-31
6. Toledot, Gen 25:19-28:9 Mal 1:1-2:7
7. Va-Yeze, Gen 28:10-32:3 Hos 12:13-14:10
8. Va-Yishlah, Gen 32:4-36:43 Hos 11:7-12:12
9. Va-Yeshev, Gen 37:1-40:23 Amos 2:6-3:8
10. Mi-Kez, Gen 41:1-44:17 I Kings 3:15-4:1
11. Va-Yiggash, Gen 44:18-47:27 Ezek 37:15-28
12. Va-Yehi, Gen 47:28-50:26 I Kings 2:1-12
13. Shemot, Ex 1:1-6:1 Isa 27:6-28:13, 29:22-23
14. Va-Era, Ex 6:2-9:35 Ezek 28:25-29:21
15. Bo, Ex 10:1-13:16 Jer 46:13-28
16. Be-Shallah, Ex 13:17-17:16 Judge 4:4-5:31
17. Yitro, Ex 18:1-20:23 Isa 6:1-7:6,9:5
18. Mishpatim, Ex 21:1-24:18 Jer 34:8-22, 33:25-26
19. Terumah, Ex 25:1-27:19 I Kings 5:26-6:13
20. Tezavveh, Ex 27:20-30:10 Ezek 43:10-27
21. Ki Tissa, Ex 30:11-34:35 I Kings 18:1-39
22. Va-Yakhel, Ex 35:1-38:20 I Kings 7:40-50
23. Pekudei, Ex 38:21-40:38 I Kings 7:51-8:21
24. Va-Yikra, Lev 1:1-5:26 Isa 43:21-44:23
25. Zav, Lev 6:1-8:36 Jer 7:21-8:3, 9:22-23
26. Shemini, Lev 9:1-11:47 II Sam 6:1-7:17
27. Tazri'a, Lev 12:1-13:.59 II Kings 4:42-5:19
28. Mezora, Lev 14:1-15:23 II Kings 7:3-20
29. Aharei Mot, Lev 16:1-18:30 Ezek 22:1-19
30. Kedoshim, Lev 19:1-20:27 Amos 9:7-15
31. Emor, Lev 21:1-24:23 Ezek 44:15-31
32. Be-Har, Lev 25:1-26:2 Jer 32:6-27
33. Be-Hukkotai, Lev 26:3-27:34 Jer 16:19-17:14
34. Be-Midbar, Num 1:1-4:20 Hos 2:1-22
35. Naso, Num 4:21-7:89 Judge 13:2-25
36. Be-Ha'alotkha, Num 8:1-12:16 Zech 2:14-4:7
37. Shela Lekha, Num 13:1-15:41 Josh 2:1-24
38. Korah, Num 16:1-18:32 I Sam 11:14-12:22
39. Hukkat, Num 19:1-22:1 Judge 11:1-33
40. Balak, Num 22:2-25:9 Micah 5:6-6:8
41. Pinhas, Num 25:10-30:1 I Kings 18:46-19:21
42. Mattot, Num 30:2-32:42 Jer 1:1-2:3
43. Masei, Num 33:1-36:13 Jer 2:4-28, 3:4
44. Devarim, Deut 1:1-3:22 Isa 1:1-27
45. Va-Ethannan, Deut 3:23-7:11 Isa 40:1-26
46. Ekev, Deut 7:12-11:25 Isa 49:14-51:3
47. Re'eh, Deut 11:26-16:17 Isa 54:11-55:5
48. Shofetim, Deut 16:18-21:9 Isa 51:12-52:12
49. Ki Teze, Deut 21:10-25:19 Isa 54:1-10
50. Ki Tavo, Deut 26:1-29:8 Isa 60:1-22
51. Nizzavim, Deut 29:9-30:20 Isa 61:10-63:9
52. Va-Yelekh, Deut 31:1-30 Isa 55:6-56:8
53. Ha'azinu, Deut 32:1-52 II Sam 22:1-51
54. Ve-Zot ha-Berakhah, Deut 33:1-34:12 Josh 1:1-18

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 often made.

Note that JCAL for Windows shows the weekly readings normally read on Monday, Thursday and the Sabbath. It does not show special weekday or holiday readings that may occur during the week.

The user is CAUTIONED to check these readings inasmuch as there will be variations from congregation to congregation.

History of the Gregorian Calendar
The calendar that we use today was first formulated in several inaccurate variations by the Romans. By the time of Julius Caesar, January was falling in autumn so he ordered his Greek mavin, Sosigenes, to make reforms to the calendar. He added 90 days to the year 46 BC to correct for the seasonal drift and adjusted the lengths of the months, as we know them to be today. On the assumption that the solar year is 365 1/4 days long he introduced the leap year by adding one day to February every four years. This is known as the Julian calendar.

The use of the leap year was an improvement but not entirely accurate. The true solar year is 365 days, 5 hours, 48 minutes, and 46 seconds. One 366-day year every four years equates to an average year of 365 days, 6 hours. Every year an error of 11 minutes, 14 seconds was added (about one day in 128 years). In the year 730 the Venerable Bede, an Anglo Saxon monk, announced that the year was in error by more than 11 minutes but, alas, they paid no attention to him and nothing was done for another 800 years.

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.

Non-European countries were slower to adopt the Gregorian calendar: Japan in 1873, Egypt in 1875, China in 1912 and Turkey in 1917. In 1918 the revolutionary government in Russia decreed that January 31, Old Style, would be followed by February 14, New Style, though the Orthodox Church has retained the Julian calendar as have other Middle Eastern Christian sects.