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Determining the Day of the Week of the Molad of Tishri

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In computing the day upon which the Molad of Tishri falls, it is necessary to measure from a benchmark. This is the date generally used for all calendar calculations. The benchmark is the Molad of Tishri, 3761 B.C. Specifically, that Molad of Tishri was on the 1st day of the week, the 23rd hour and 204th part. You will see how this benchmark is used in calculations.

Suppose we needed to find the day of the week on which the Molad of Tishri falls in any given year. Keep in mind that if the days of a year were evenly divided by 7, then the Molad of Tishri would fall on the same day of the week on the following year. Since all years do not have an equal number of weeks, we need to calculate the number of days exceeding an even number of weeks in a given year. Once we know this, we can easily tell the day of the week on which the corresponding Molad of Tishri will fall.

Three more facts are necessary in calculating the day of the week for the Molad to occur:

(1) The average common year exceeds an even number of weeks by: 4 days, 8 hours, 876 parts.

(2) The average leap year exceeds an even number of weeks by: 5 days, 21 hours, 589 parts.

(3) A 19-year time cycle exceeds an even number of weeks by: 2 days, 16 hours, 595 parts.

One clear fact should emerge from the study of the 7-day weekly cycle. We saw that the calendar makes no alterations on the weekly cycle in any way. Again, some have implied that the calendar adjustments shift the weekly Sabbath. This has never been the case.

At this point, we will delay the introduction of new concepts and walk through a simple series of calculations in order to better familiarize you with the concepts presented thus far. We are now ready to determine the day of the week of the Molad by applying the concepts that have been briefly introduced.

In this first calculation, we will find the day of the week in which the Molad of Tishri occurred in A.D. 1964. We will only be looking for the day of the week (1st, 2nd, 3rd, etc.), rather than the day of the month. The method is simple, but accurate to the point that we can be 100 percent sure of the answer—as long as the calculation is correct. Again, the purpose of walking through these calculations is to demonstrate the accuracy of the various techniques of finding the respective solutions. Do not worry about remembering the exact sequence or the exact details of these demonstrations. As already emphasized, the intent of covering these points is to give the reader an overview and appreciation for the exactness and methodical structure of God’s calendar.

1964 as a Sample

To determine the day of the week in which the Molad of Tishri fell in the year A.D. 1964, we first establish the span of years between the benchmark of 3761 B.C. and the year A.D. 1964 (3,761 + 1,964 = 5,725).

Now, in counting from some year in the A.D. span of time, back to the benchmark of 3761 B.C., we must subtract 1 since there is no year zero (5,725 – 1 = 5,724). So there are 5,724 years between the benchmark and 1964.

Next, we divide this number by the number of 19-year time cycles to simply determine how many time cycles are contained in this span of time (5,724 / 19 = 301 plus 5 years left over).

If you use a calculator, you get 301.2631578. The .2631578 is equivalent to 5 years. You can multiply that decimal expression by 19 to get 5 years, or simply divide 5,724 by 19, using old-fashioned long division and you will get a remainder of 5.

Now we take these 301 time cycles, with the 5 years left over, as the basis for our calculation. We will take the 301 and multiply by the amount that every 19-year time cycle exceeds an even number of weeks. (This was covered in the preceding section and will be presented again below.)

Next we will take the 5 years left over and classify these 5 years into the number of common years and the number of leap years. This process is simple. We look at the 19-year time cycle pattern and simply observe how many of these years are common (not underlined) and how many are leap years (underlined).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

In counting from 1 to 5, we find that 4 of the years are common and only 1 is a leap year. So we will multiply 4 by the amount of time that a common year exceeds an even number of weeks. Then we will add the length of time that one leap year exceeds an even number of weeks.

Now we will write out these expressions (as introduced in the preceding pages): 301 multiplied by 2 days, 16 hours, 595 parts (301 X [the excess occurring in each time cycle])

4 multiplied by 4 days, 8 hours, 876 parts (4 X [the excess occurring in each common year])

1 multiplied by 5 days, 21 hours, 589 parts (1 X [the excess occurring in each leap year])

These respective expressions will be expanded as they are multiplied:


602 days 4,816 hours 179,095 parts (the excess in 301 time cycles)
16 days 32 hours 3,504 parts (the excess in 4 common years)
5 days 21 hours 589 parts (the excess in 1 leap year)
623 days 4,869 hours 183,188 parts (total)


Earlier, we explained how to reduce terms when we began the sections on calculations. We now take the above total and reduce it to the lowest terms: 832 days, 22 hours, 668 parts (the reduced total).

Next, this reduced total is divided by 7 to see how many days exceed an even number of weeks. So 832 / 7 = 118 weeks plus 6 days left over. This excess is 6 days, 22 hours, 668 parts.

This excess amount indicates how far forward the Molad of Tishri moved in the span of time between 3761 B.C. and A.D. 1964. Now we have to add this excess to the exact time of the Molad of Tishri of 3761 B.C.


1 day 23 hours 204 parts (Molad in 3761 B.C.)
6 days 22 hours 668 parts (forward movement since 3761)


7 days 45hours 872 parts (total)
8days 21hours 872 parts (reduced to lowest terms)
Now subtract 7 days to determine excess.
1 day 21 hours 872 parts (final answer)


This final answer shows that, in A.D. 1964, the Molad of Tishri occurred on the 1st day of the week, at the 21st hour and 872nd part. This would be Sunday at about 9:00 PM, according to the Roman reckoning of the day from midnight to midnight. You observed in this calculation that a definite sequence of procedures had to be carried out in an orderly fashion. The calculation revealed the precise day of the week of the Molad of Tishri in 1964.

This same procedure would have been used to calculate the day of the week for the Molad of Tishri for any other year, as well. The calendar is extremely precise and the calculations can be depended upon to project any future Molad with equal precision. We will also see how the calculations can be extended to the day of the month. But first a short review will be helpful.


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