Determining the Day of the Month of the Molad of Tishri

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Before introducing any new concepts, a brief review would reinforce what has already been covered. A 19-year time cycle includes 12 common years and 7 leap years. The linear pattern previously used shows the breakdown of years:

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

Counting the years not underlined in this pattern gives us the 12 common years. The underlined years are the 7 leap years.

Recall these previously covered facts:

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

(2) An 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.

Besides these points, remember that the benchmark for calculations is the Molad of Tishri 3761 B.C. This Molad occurred precisely on the 1st day at 23 hours and 204 parts.

Having covered this brief review, you should now be familiar with the technique used to determine the day of the month for the Molad of Tishri. As the calculations are explained, keep in mind that you don’t have to memorize the facts or procedures. We are walking through this process to give you the general understanding as to how the solutions are derived. Without having seen this performed in a general way, it would not be possible to appreciate the incredible precision of the Hebrew calendar. Now we need to express the 19-year time cycles in Julian years, which consist of 365 1/4 days. We now extend this expression:

365 days	6 hours
x 19

Total days (Julian) in a 19 year cycle = 6,935 days 114 hours = 6,939 days 18 hours (reduced) = 6,939 days 17 hours 1,080 parts (equivalent)

Total days (Hebrew) in a 19 year cycle = 6,939 days 16 hours 595 parts The difference in the 19 Julian years and the 19 Hebrew years = 1 hour 485 parts Since this is a calculation of Hebrew dates, the difference is expressed as -1 hour 485 parts. This difference in the 19-year cycles is expressed in Julian years as opposed to Hebrew years, because the calendar now in use by most of the world is the Roman calendar. If the whole world observed God’s sacred calendar, we would not need this translation procedure.

Above, we considered the difference in the two relative measurements of time for 19-year time cycles. Now we consider the difference in common years (for Julian vs. Hebrew). These differences are expressed below:

Julian year	-	(365 days 6 hours 0 parts)
Hebrew common year	354 days 8 hours 876 parts
difference:		- 10 days	21 hours	204 parts	(reduced)

Here, we consider the difference between leap years:

Hebrew leap year	383 days	21 hours	589 parts
Julian year	- (365 days 6 hours 0 parts)
difference:	+18 days	15 hours	589 parts

We can now apply these translation patterns to the following spans of time that we used in the previous section to determine the day of week for the Molad of Tishri of A.D. 1964. We are interested in the day of the month for that same Molad. Thus, from 3761 B.C. to A.D. 1964, we must consider the following:

(301)	19-year time cycles
4 common years	1 leap year

This calculation is surprisingly simple, and similar to the technique used to establish the day of the week. We will quickly walk through the steps. First, we take the difference in the 19-year time cycles expressed in Julian years as opposed to Hebrew years. We saw that this difference is –1 hour and 485 parts. Multiply this by 301 since there are 301 of the 19-year time cycles involved here, as indicated in the preceding paragraph. Then we will multiply the 4 common years by the difference that applies to the common years. Next, we multiply the 1 leap year by the difference that applies to leap years. Following is an extensive calculation and chart. All of these factors will be illustrated here:

-1 hour 485 parts (the difference that applies to the 19-year time cycles)

x 301 (19 year time cycles)

-301 hours 145,985 parts

	-10 days 21 hours 204 parts (the difference that applies to common years)
	x 4 (common years)
	-40 days 84 hours 816 parts

+18 days 15 hours 589 parts (the difference that applies to leap years)

x 1 (leap years)

+18 days 15 hours 589 parts

We now take the negative totals and combine them. This is then combined with the positive term and the final figure is reduced.

	-(301 hours	145,985 parts)	(from 19 yr. time cycles)
-(40 days 84 hours 816 parts) (from common years)
-(40 days	385 hours	146,801 parts)
+18 days 15 hours 589 parts (from leap years)
-(22 days	370 hours	146,212 parts)	(total difference from Hebrew to Julian)
-(43 days	1 hour	412 parts)	(reduced)

To apply the above difference, we must begin by listing the Benchmark in Julian terms:

October 6th	23 hours	204 parts	(Benchmark)
September 36th	23 hours	204 parts	(equivalent month; add 30 days and back up 1 Julian month)
August 67th	23 hours	204 parts	(equivalent month; add 31 more days and back up another month)
- (43 days 1 hour 412 parts) (the total difference subtracted from equivalent Benchmark)
August 24th	21 hours	872 parts	(preliminary answer not yet adjusted for Julian Gregorian errors)

Please note that the dates of September 36th and August 67th are not misprints. These are “equivalent months”—steps that are taken in order to exceed the value of the 43 days above. We will next proceed to adjust the preliminary answer of August 24th, 21 hours, 872 parts.

In the section titled, “Introductory Overview of the Calendar,” near the beginning of this booklet, the issue was discussed as to how the Gregorian calendar made adjustments to compensate for errors in the Julian calendar. Included here is a brief chart that breaks down the exact adjustments since A.D. 1582.

Years

1582-1599
1600-1699
1700-1799
1800-1899
1900-1999
2000-2099

No. of days dropped from Julian calendar

10
10 (1600 evenly divisible by 400)
11
12
13
13 (2000 evenly divisible by 400)

We will now examine another adjustment consideration due to the Julian/Gregorian leap years. The common Julian or Gregorian year is exactly 365 days, which is 1/4 of a day shorter than the average year of 365 1/4 days. Because of this, for each of the 3 years following a leap year, 6 hours must be added.

If the year in question is a leap year, then add 0 hours. If the year in question is 1 year after a leap year, then add 6 hours. If the year in question is 2 years after a leap year, then add 12 hours. If the year in question is 3 years after a leap year, then add 18 hours. Returning to our example of A.D. 1964, we had –43 days, 1 hour and 412 parts for the difference resulting from all the intervening years.

-(43 days	1 hour	412 parts)
+13 days			Julian/Gregorian leap year correction	0 hours	1964 was a leap year
-(30 days	1 hour	412 parts)	Total adjusted difference in Hebrew and Julian/Gregorian

So we go back and subtract the difference from the equivalent month of the Benchmark:

October 6th	23 hours	204 parts	(Benchmark)
September 36th	23 hours	204 parts	(equivalent month; add 30 days and back up 1 Julian month)
- (30 days 1 hour 412 parts) (total adjusted difference)
September 6th	21 hours	872 parts	(reduced)

The date of September 6th was the Julian date for Tishri 1, 1964. Notice the hours and the parts. They amount to 21 hours and 872 parts. The final answer that established Tishri 1, 1964 as the 1st day of the week also indicated 21 hours and 872 parts—exactly as we found for September 6th of 1964.

These procedures are not haphazard, but rather are detailed and precise. Having to translate this time to the Julian calendar is somewhat involved, as we observed, but it is consistent and accurate. One can project to any year in the future and precisely pinpoint the day of the week of the Molad of Tishri and the Julian day of the month on which this falls. The hours and the parts for the Molad of Tishri will always be the same exact amount from both phases of calculation—day of week and day of month. The fact that these remaining elements must agree serves as a parity check that our calculations are correct!

After going through so many steps to realize the final answer, there exists one more criterion before we realize the ultimate “final answer.” We will obtain this after allowing our proposed day and date for Tishri 1 to be checked by the “filtering process” of postponements.

In the calculation above, we have determined that Tishri 1 in 1964 fell on September 6th, on a Sunday evening at 21 hours, 872 parts. Remember, this was discussed as being Sunday at about 9:00 PM, according to the Roman reckoning of the day from midnight to midnight. By postponement rule one, the date of Tishri 1 would have been moved forward by one day since the Molad occurred after 12:00 noon on Sunday. (Even if the Molad occurred before 12:00 noon on Sunday, rule two would still have advanced Tishri 1 to Monday since this pivotal day could never fall on Sunday, anyway.)

Therefore, we conclude that in the year of 1964, Tishri 1 fell on Monday, September 7. The filtering process of postponements yields the final approved answer!

Illustrations Help The last few pages have been for the purpose of illustrating the basic calculation for the sacred calendar and for translating these times into the Julian/Gregorian calendar terms. One must understand that many additional calculations could be given, to reinforce these new concepts of calculations, but the point should have been made. We have walked through one example that served to illustrate the detailed procedures in calculating the Molad of Tishri.

Certain tables have been produced which greatly simplify and streamline the process of calculating the Molad of Tishri for any given year. Besides these tables, there are computer programs in which you merely respond to “prompts” about the Molad of Tishri. By simply typing in a year, such as 2005, the program presents the complete answer—the day of the week, day of the month for the Molad of Tishri and much more information. But one could not fully appreciate such technological shortcuts without previous experience of walking through manual calculations as presented in this Appendix.

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