THE JEWISH CALENDAR =================== ABOUT THIS PROGRAM JCAL.TXT (this file) is an explanation of the Jewish calendar. It is distributed with JCAL.COM, a program that calculates dates of the Jewish calendar. JCAL.COM was written in Turbo Pascal and is based on two descriptions of the Jewish calender which I recommend as additional reading on the subject: 1. The Jewish Calender Mystery Dispelled by George Zinberg Vantage Press, 1963 2. The Encyclopedia Judaica THE JEWISH CALENDAR The Jewish calendar is believed to have been introduced by the patriarch Hillel II in the year 358, the Jewish year 4119. It is a lunisolar calendar, having ties to both the moon and sun's cycle. The months were tied to the lunar cycle. Today we know the actual lunar cycle to be 29 days, 12 hours, 44 minutes and 3 1/2 seconds. This is approximately 29 1/2 days. As a starting point, a "normal" year in the Jewish calendar consists of 12 months alternating between 30 and 29 days. This normal year has a length of 354 days which is short by about 11 days from the solar year. If this was left uncorrected we would find the holidays shifting through the seasons. Since many of the holidays have an agricultural significance, this would not be permissible so further adjustments are made by varying some months between 29 and 30 days and by periodically introducing a leap month. One solar year is 365 days, 5 hours, 48 minutes, and 46 seconds. Twelve lunar months are 354 days, 8 hours, 48 minutes, and 40 seconds. The difference of these two figures is 10 days, 21 hours, and 6 seconds. The developers of the calendar needed to find a periodic correction for this error. One could not simply add one month every three years, for example, because this would introduce a correction of 29 or 30 days instead of the actual three year error of 31 days, 3 hours and 18 seconds. The annual difference over 19 years is 206 days, 15 hours, 1 minute and 15 seconds. This is very close to seven lunar months which come to 206 days, 17 hours, 8 minutes, and 23 1/3 seconds. It was decided to introduce a leap month (AdarII) seven times every nineteen years. It is this large periodic correction that causes the Jewish holidays to vary each year with respect to our Gregorian calendar. At first, the leap years were allowed to vary within the 19 year cycle for agricultural reasons but eventually a fixed pattern of leap years was established. The 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years are leap years. Adar II, a 29 day month, is added after Adar. Adar is increased by one day to 30 days on a leap year giving the leap year 30 days more than the ordinary year. If left at that the Calendar would look like this: Tishri 30 days Heshvan 29 days Kislev 30 days Tevet 29 days Shevat 30 days Adar 29 days (30 on a leap year) AdarII 29 days (inserted 7 times every 19 years) Nisan 30 days Iyyar 29 days Sivan 30 days Tammuz 29 days Av 30 days Elul 29 days This would be a reasonably accurate calendar with months based on the lunar cycle and with a correction for the solar year. But two problems exist with the Jewish holidays. First, since Yom Kippur (Tishri 10) is a fast day it is undesirable for it to fall on a Friday or Sunday adjacent to the Sabbath. Second, Hoshanah Rabba (Tishri 21) should not fall on a Saturday since the Sabbath would interfere with certain rituals. Both of these holidays occur in the first month, Tishri, so as a corollary it can be said that Rosh Hashanah (Tishri 1, the New Years Day) should not fall on a Wednesday, Friday, or Sunday. The way that Tishri 1 is controlled is by ALTERING THE LENGTH OF THE PREVIOUS YEAR. In other words, in the Jewish calendar the last day of the year is controlled to make Rosh Hashanah of the next year fall on the desired day. This is accomplished by lengthening or shortening the year by a day. Heshvan may be lengthened to 30 days and Kislev may be shortened to 29 days. When Heshvan is lengthened the year is called "full" and when Kislev is shortened the year is called "de- ficient". This means that three "types" of non-leap years can exist having totals of 353, 354, and 355 days. Furthermore, a leap year can also be deficient, normal or full and have lengths of 383, 384, and 385 days. The six possible types are thus: /-----REGULAR-----\ /------LEAP YEAR------\ Month DEF NORM FULL DEF NORM FULL ============================= ====================== Tishri 30 30 30 30 30 30 Heshvan 29 29 30 29 29 30 Kislev 29 30 30 29 30 30 Tevet 29 29 29 29 29 29 Shevat 30 30 30 30 30 30 Adar 29 29 29 30 30 30 Adar II -- -- -- 29 29 29 Nisan 30 30 30 30 30 30 Iyyar 29 29 29 29 29 29 Sivan 30 30 30 30 30 30 Tammuz 29 29 29 29 29 29 Av 30 30 30 30 30 30 Elul 29 29 29 29 29 29 TOTALS 353 354 355 383 384 385 We now see that there are six different lengths possible to the Jewish year 353, 354, 355, 383, 384 and 385. By the application of certain rules discussed below it is possible to accommodate all possible variations with only these six lengths. The process of setting the day of the week for Rosh Hashanah of a particular year consists of finding the new moon day of Tishri for that year, delaying it according to the rules below and determining the length and consequently the type of the previous year. The new moon can be found easily by knowing the exact time of any previous new moon and then adding the appropriate number of lunar cycles. The original calendar calculations were done in days, hours, minutes and "parts". A part is 3 1/2 seconds so there are 18 parts in a minute. In the Jewish calendar, year 1 is considered to be the year of the creation and the years are counted from then. We are now in year 5746. The new moon of Tishri of the year 1 occurred on Sunday at 23 hours, 11 minutes, and 6 parts. Any other new moon can be found by adding the appropriate number of lunar cycles of 29 days, 12 hours, 44 minutes, and 1 part to that time. As a shortcut only "remainders" (after multiples of whole weeks are discarded) have to be added for large numbers of years thus making the calculation much easier. For example we must add 2 days, 16 hours, 33 minutes, and 1 part to a particular new moon to find the new moon exactly "one 19-year cycle" later. Or 2 days, 23 hours, 5 minutes, and 10 parts have to be added to a particular new moon to find the new moon exactly 100 cycles (1900 years) later. Once the new moon day of a particular year is determined Tishri 1 will be on that day except when falling into one of the exceptions below: 1. When the new moon occurs on Wednesday, Friday, or Sunday, or 2. When the new moon occurs at noon or later, or 3. When the new moon of an ordinary year occurs on Tuesday at 11 minutes and 6 parts after 3 AM or later, or 4. When, at the termination of a leap year, the new moon occurs on Monday at 32 minutes and 13 parts after 9 AM or later. It is then shifted one day later. When 2, 3, or 4 occur, if the new day falls within exception 1 it is shifted a second day. The first exception is to allow the two holidays stated above to fall on the permissible days. The others are for mathematical reasons. Briefly, these last three rules assure that all possible situations are accommodated by the six different year lengths described above. Otherwise additional types and lengths of years would be required. For more details see the references sighted above. When the adjustment in day-of-the-week is made a calculation can be made as to the length required by the previous year because its new years day is also known by the same process. This must take into account whether the previous year is a leap year as required by the 19 year cycle. By taking the year lengths and discarding multiples of 7 days the number of days added from one new year day to the next is: Deficient 3 days Normal 4 days Full 5 days Deficient- Leap 5 days Normal-Leap 6 days Full-Leap 0 days Because of rules 2, 3 and 4 above these are the only combinations mathematically possible and cover all situations. From this table the type of the "previous" year is determined. We now know all we need to know about a particular year to define it. We know its New Years day and its type (and consequently its length). What needs to be done now is to find the corresponding Gregorian date. The correlation to the Gregorian calendar is very unsophisticated. There is NO DIRECT RELATIONSHIP BETWEEN THE JEWISH AND GREGORIAN CALENDARS. They both are related to the solar cycle but according to independent rules. The only way to determine a corresponding Gregor- ian date is to know a correspondence that occurred earlier than the desired date and calculate forward from it. The calculation can be sped up by using multiple reference points (spaced, say, one century apart) and calculating from the nearest one. 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 Sosigenes to make reforms to the calendar. He added 90 days to the year 46 B.C. to correct for the seasonal drift and adjusted the lengths of the months as we know them, today. He introduced the leap year by adding one day to February every four years. The use of the leap year was an improvement but not entirely accurate. The true solar year is 365 days, 5 hour, 46 minutes, and 46 seconds. One 366 day year every four years equates to an average year of 365 days 6 hours. Every four years an error of 44 minutes, 56 seconds was added. By the 16th century the accumulated error was ten days. Pope Gregory revised the calendar by suppressing the 10 days between October 5th and October 15th of 1582 and ordained that years ending in hundreds should not be leap years unless they are divisible by 400. (1800 and 1900 were not leap years but 2000 is.) This Gregorian calendar is the one we use today. Incidently, the Gregorian reform compensates by 72 hours (3 days) 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. SHAREWARE Rather than selling this program I am placing it in the public domain and request that you first try the program and then, if you find it useful, pay a $10 registration fee which will entitle you to free upgrades except for postage and disks. Send the registration fee along with the program revision number to: Lester Penner 25 Shadow Lane Great Neck, NY 11021 You may send information about bugs to the same address or to Compuserve 75236,1572. Enjoy, Les Penner