The Qumran Calendar
Abstract: It would be fair to assume that the Qumran calendar used the same rotation of priestly divisions current in Jerusalem. It would be very interesting indeed if we could take the data in 4Q320 and its sister texts and calculate (an assumed) year for which the 4Q320 Almanac was written, and find that it agrees with the sequence of divisions counting back from 9 Av, AD 70. As shown above, the divisions began at the inception of the First Temple on the Sabbath after Tishri 1. Also I proleptically (anachronistically) calculated the divisions backwards to the week of Nisan 1, 1012 BC, to see what division would synchronize with the week of that new moon. And it was found to be Gamul, division number 22. It so happens that the Qumran calendar in 4Q320 begins its six year cycle exactly the same way. Qumran kept the first year of the cycle so that the first division fell in the second week of Tishri (the Sabbath after Tishri 1), as at the inception of Solomon’s Temple, and they set up the cycle to follow the spring equinox, and then aimed to calculate the first Wednesday after it as the first day of their 364 day year. Somehow they had to intercalate their year, possibly by adding a week at the end of every fifth or sixth year, to keep the Wednesday new year following as closely upon the equinox as they could, or by intercalating 28 days every 23 years. The Qumran calendar assumes that the first of Nisan fell on a Wednesday on the day of the spring equinox when the world was created, and they anachronistically place division 22 (Gamul) for the first week of Creation.
A good deal of the following, is taken from the lead of John Pratt in this article: Dead Sea Scrolls May Solve Mystery. Pratt’s article is not easy to follow, mainly because he uses the Gregorian Calendar proleptically, instead of following the Julian standard of historians. The procedure is to figure out the exact nature of the lunar data in the texts and the way it aligns with the first Wednesday of the Qumran Solar year, such that the equinox is not too far before it, to justify it being the first Wednesday of the six year solar cycle. Having picked such dates, we will see which ones align with the lunar data, and we will see if the choices that remain agree with the division of Gamul as retro-calculated from 9 Av, AD 70.
The 4Q320 Almanac states that the 29th day of a lunar month fell on the 30th day of the first Solar month. Now there are a lot of ifs and assumptions involved in interpreting this document. The data may represent a real year, in which the division of Gamul fell on the first Wednesday of the first month of the Solar year of Qumran, within a week after the spring equinox, and such that the new moon, as Qumran understood it, fell on the evening of their first day of the month. It is obvious that this arrangement does not happen for every year that the Qumran calendar was used. In fact it is quite rare. The odds of matching the equinox to 7 days before a Wednesday that happens to be a new moon day in the division of Gamul are: 1/7 for the new moon to match the weekday, and 1/4 for the equinox to land in the right week (of a four week range), and 1/24 for the 22nd division to match it:
1/7 x 1/4 x 1/24 = 1/672.
The alignment happens to agree with their interpretation of Genesis chapter 1, and probably for this reason was preserved as an Extraordinary Almanac as an instructional aide. This, of course, is an assumption. The alternative is that the Almanac is purely a theory of Genesis 1, and that the lunar dates in it never corresponded to any year in the history the Essenes. In that case, 4Q320 is useless for astronomical calculation, and that could well be the case, all fraudulent appearances otherwise. The astronomical details suggest that it was being presented as representing a real year. On the other hand, the repetition of the data suggest that the lunar cycle was finished by a rough rule of approximation, i.e. alternating 29 and 30 day months, without resorting to actual observations for the entries. Knowing this, then, I do not think I am proving much, except that the Qumran documents may be interpreted with good effect in agreement with the priestly divisions counted back from 9 Av, AD 70.
According to the latest views, the 29th day of the first month in 4Q320 was the date of last visibility of the old moon. This is dated in the 30th day of the solar calendar. Thus the first day of the lunar month appears as the 2nd day of the solar calendar. In fact, what is happening is that the Solar calendar is using a sunrise epoch for the day, and the lunar calendar is using sunset epoch. The first day of the lunar month begins half way through the first solar day, at sunset. So the new moon day in the lunar calendar, and the new moon day in the solar calendar overlap in the night following the first day of the solar calendar. Thus begins the month as the Qumran sect thought it did in Genesis. A sister document plots an observation of the moon going past full, made 13 days before the month end. Scholars have concluded that this shows the 29th day to be a date of last visibility. The next day should be the first day of the next lunar month then. The Qumran sect was trying to approximate a conjunction method for their new moon (Lunar day 0), or at least that was the theory. The logic and debate of all of this is something only scroll scholars can appreciate.
The following lists the conjunction of 1. The spring equinox before a Wednesday, 2. The rotation of Gamul (division 22) in the week of that Wednesday. The only date to match the lunar data is 42 BC. The “Date” dates day 1 of the 364 day Qumran year. It is always a Wednesday. DIV gives the division number, calculated back from 9 Av, AD 70, according to the rule:
INT([(JD + 1)/7 + 3] MOD 24 + 1).
INT means take the integer part of the number and drop the decimal that may result.
JD is the Julian date. The Equinox is determined such that the center of the sun (letting refraction have its effect) must set north of due west (270 degrees). The point at the center of the sun must cross 270 going south to north before it drops below the horizon. The first day it manages to do this is defined as the spring equinox. This method is designed to simulate the observational method of people watching for the sun to set in the west to indicate that the new year has begun, usually by aligning it with a set of stones.
The quantity DB is the difference between the Qumran new year day, and the spring equinox. Values more than 7 indicate that a week should be intercalated to realign the 364 day year.
Julian Date DIV Equinox DB Phase
1655768 BC 180 March 31 Wednesday 22 3/23 8 60%
1664168 BC 157 March 30 Wednesday 22 3/23 7 54%
1672568 BC 134 March 30 Wednesday 22 3/23 7 29%
1680968 BC 111 March 29 Wednesday 22 3/23 6 88%
1689368 BC 88 March 28 Wednesday 22 3/22 6 8%
1697768 BC 65 March 27 Wednesday 22 3/22 5 99%
1706168 BC 42 March 27 Wednesday 22 3/22 5 0.5%
1714568 BC 19 March 26 Wednesday 22 3/22 4 95%
1722968 AD 5 March 25 Wednesday 22 3/22 3 13%
1731368 AD 28 March 24 Wednesday 22 3/21 3 69%
All this shows is that 4Q320’s Almanac may have been meant to apply to to real dates in 42 BC, and for the six year cycle after that. If scholars should change their minds on the much debated terms in the document, or if the Almanac only represents an ideal alignment, and not a real one, then nothing has been proved. And this probably explains why hardly anyone suggests an astronomical date for the cycle.