APPENDIX –
Next Part Determining the Day of the Week of the Molad of Tishri
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INSTRUCTIONS FOR CALENDAR CALCULATION
The Hebrew calendar uses a variety of basic terms. You are now familiar with most of them. To begin, the average length of a day is 24 hours. A day, as defined by God, begins at the time of sunset. For purposes of calculation, the average time of sunset is 6:00 PM. An hour is subdivided into 1,080 parts. One part equals about 3 1/3 seconds, and is further divided into 76 moments. One moment is equal to a small fraction of a second. We will not need to worry with the details of calculating moments, but it is good to be aware that such a precise measurement of time exists.
All of the above facts, along with more details, will begin to make sense as we start fitting the pieces of the puzzle together.
| Note that the lunar month is: | |||
| 29 days | 12 hours | 44 minutes | 2.841 seconds |
| Now this equates to: | ||
| 29 days | 12 hours | 793 parts |
In demonstrating the Hebrew calendar, it is necessary to explain some of the basic levels of calculation—we must “prove all things” (I Thes. 5:21). In order to prove something, you have to acquire a basic understanding of the subject. Certainly, an entire course in calendar calculation would go into what we are covering in far greater detail. So, we are mainly seeking an overview, but some examples of calculations will be necessary to appreciate the Hebrew calendar.
As noted above, a lunar month is equal to 29 days, 12 hours and 793 parts. In calendar calculations, using parts is far superior to the usage of minutes and seconds. From this time forward, we will use only parts. “Parts,” as units of time, were used by the Jews long ago in the counting of time, and we understand that this was an element of the calendar from the beginning. Remember that 1 hour = 1,080 parts. A solar year is equal to 365 days, 5 hours and 997 parts. One solar year does not exactly equal 12 lunar months. We should now demonstrate the difference in these time frames.
| 29 days | 12 hours | 793 parts (one lunar month) | x 12 (multiply days, hours and parts independently by 12) | 348 days | 144 hours | 9,516 parts |
To “reduce” the product of the equation to the lowest terms, we begin by dividing the parts by 1,080 to extract the hours from this term—the remainder stays in the parts column. So, 9,516 divided by 1,080 equals 8 full hours added to the hours column, and a remainder of 876 in the parts column. (You can practice these steps if you choose, but it is not necessary as long as you understand the procedure.)
Next, to reduce the hours to days, divide the 152 (144 + 8) hours by 24. This produces 6 extra days to add to the days column and leaves a remainder of 8 hours in the hours column. So the “reduced” answer is: 354 days, 8 hours, 876 parts. Remember that this was the total of 12 lunar months. We will subtract this expression from the solar year to establish the difference between one solar year and 12 lunar months.
| 365 days | 5 hours | 997 parts (A solar year) |
| 10 days | 21 hours | 121 parts (the answer) |
In subtracting 8 hours from 5 hours, it becomes necessary to borrow 1 day from the days column and then subtract the 8 hours from 29 (5 + 24) hours, which gives an answer of 21 hours. The net days become 10, since we borrowed from the 365 days, leaving only 364 from which to subtract.
From the above demonstration, we have established that a solar year is longer than 12 lunar months by 10 days, 21 hours and 121 parts. So herein resides the primary problem with most types of calendars—how to keep both the lunar and solar aspects of the calendar in balance. Again, only one calendar does this correctly—the Hebrew calendar.
The following 2 pages repeat information already covered in the text—but they are needed here for review:
Before proceeding, we have to re-introduce a crucial element from astronomy. This is the 19-year time cycle. Precisely every 19 years, the sun, earth and moon come back to the same location relative to each other. This was understood by ancient astronomers and still stands as one of the many axioms of astronomy in relation to our solar system. To reconcile the difference in the solar and lunar “years,” 7 years are established as leap years in every 19-year cycle. To summarize, 7 leap years contain 13 months and the other 12 years (called common years) contain 12 months, amounting to a total of 235 months in a 19-year time cycle. To see the pattern of leap years in a 19-year time cycle, notice the following layout. The leap years are highlighted to clarify the pattern.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Now that the concept of 19-year time cycles has been introduced, we must proceed to the clarification of other terms. We will be addressing these time cycles again, shortly. (Some of the calendar authorities use the term “intercalary” for the term “leap”. We will use only the term “leap” in this booklet.)
Remember, the months in a year alternate between 29 and 30 days, beginning with 30. This process of alternating between 29 and 30 days gives an average of 29 1/2 days. Below is a simple layout of the months as they occur, along with the days as they would fall in normal (common) years, followed by a leap year to the right. The month of Tishri is listed first since the start (new moon) of this month is the benchmark for calculating the entire year. This will be explained more fully below:
| Common Year | Leap Year | |||
| Month
Tishri |
Days
30 |
Month #
7 |
Month
Tishri |
Days
30 |
The month named V’Adar means Adar II. It comes at the end of the sacred year and is the extra 13th month only added to leap years.
We previously defined a lunar month as 29 days, 12 hours and 793 parts. So it is obvious to see the actual lunar month is 793 parts (about 45 minutes) longer than the 29 1/2 days designated for a month in the calendar. To make up for this discrepancy, adjustments were called for in the Hebrew calendar to bring the months back into balance. Two methods were used:
Heshvan (the 8th month) would be assigned 30 days in certain years, instead of the usual 29. Keslev(the 9th month) would be assigned 29 days in certain years, instead of the usual 30.
These two months are used to balance the actual lunar months, which differ by about 45 minutes (793 parts) from the months designated by the calendar. So these two months bring the lunar times back into balance. These adjustments operate independently of each other. Time cannot be lost. It has to be accounted for, and this method has worked well for millennia, long before the modern critics of the Hebrew calendar came on the scene.
Because of calendar adjustments, plus the combination of leap years and common years, we have the possibility of six different lengths of years. These six possibilities are:
| Regular Common year | = | 354 days | (12 months x 29 or 30 days) |
| Deficient Common year | = | 353 days | (Keslev with 29 days) |
| Full Common year | = | 355 days | (Heshvan with 30 days) |
| Regular Leap year | = | 384 days | (13 months x 29 or 30 days) |
| Deficient Leap year | = | 383 days | (Keslev with 29 days) |
| Full Leap year | = | 385 days | (Heshvan with 30 days) |
Let’s also do some important review of the Molad of Tishri. Again, Molad refers to the new moon that signals the beginning of a new month. Tishri is the seventh month of the sacred year. The Molad of Tishri is the most important, as far as the calendar is concerned. Tishri begins with the new moon which announces the beginning of the Feast of Trumpets. The remaining three fall Holy Days occur during this month as well. The Molad of Tishri announces not only the beginning of the seventh month, but also the beginning of the civil year. Again, this is generally comparable to the fiscal year some businesses observe, usually from July through June of the following year. The beginning of the sacred year is in the spring of the year. It begins with the month of Nisan (Abib). Passover is observed on the 14th of this month, followed by the Days of Unleavened Bread. The fact that the civil year does not coincide with the sacred year is the reason that the middle column in the above chart begins with Tishri (month #7), and the beginning of the sacred year (month #1), which is Nisan, is about midway down the chart.
Still reviewing, as the beginning of the civil year, the Molad of Tishri is counted as the focal point of the calendar year. This particular new moon is the benchmark on which the calculations are hinged. The Molad of Tishri is sometimes simply referred to as the “Molad.” As a point of interest, if someone sought to find out the length of a particular year, the procedure would be to find the Molad of Tishri for the beginning of that year, as a starter. Next, the Molad of the following year would be calculated. Then the length of the year would simply be the number of days between the two Molads. It could only be one of the six possibilities discussed earlier. Do not worry about memorizing all of these details. However, you will soon see them come into play and fit into the pattern of establishing the exact days upon which the Molad of Tishri (beginning of the Feast of Trumpets) and the other Holy Days will fall.
To summarize this section, here is a simple table that shows all six combinations of years and months. This should help reinforce what was discussed:
| Common Years | Leap Years | |||||||
| Month
Tishri |
Deficit
30 |
Reg.
30 |
Full
30 |
Mouth
Tishri |
Deficit
30 |
Reg.
30 |
Full
30 |
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