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WQ Archive 91 - 100

Weekly Question Archive 91 - 100

by Remy Landau

Question 91

Weekly Question 91 is no longer available.

Question 92

Which will be the last day to have the same year value in both the Hebrew and the Gregorian calendar?


Correspondent Winfried Gerum made a study of the time period during which the Hebrew and Gregorian year counts are equal.

This topic was first touched upon in Question 29. But it seems that Winfried Gerum has the definitive answers.

It is assumed that both the Hebrew and Gregorian calendars keep their rules fixed over the intended period of time.

The accuracy of the Hebrew calendar is fixed by the value of the mean lunation period coupled to the 19 year cycle of 235 lunar months.

That leads to an average Hebrew year length of 365.2468 days.

The mean Gregorian year is 365.2425 days.

Hence, the average Hebrew year is slower than the mean Gregorian year by about one day in every 230 years.

Consequently, the Gregorian year count, while still distant from the Hebrew year count, will eventually catch up to and exceed the Hebrew year count.

Correspondent Winfried Gerum predicts that the Gregorian year value will exceed the Hebrew year value the day after 3 Tishri 317,850,512 corresponding to 31 December 317,850,512.

Thank you Winfried Gerum for these truly amazing facts.

The molad of the first Adar 5760H took place on Shabbat at 13h 24m 14hl (about 7:25 am on Shabbat 5 February 2000g).

Since this was also Shabbat MeVorchim, that is, the Shabbat preceding the new month, the molad clearly occurred prior to its announcement during the Birkat HaHodesh observance of that Shabbat's morning services.

Question 93

[Relative to 5760H] When next will the molad occur prior to the Birkat HaHodesh observance of the Shabbat morning service?


Question 64 noted that among the interesting features of the current Hebrew year,
the molad of Sivan 5760H will occur on Friday 2 Jun 2000g at 16h 21m 0hl, which is PRIOR to the Shabbat M'Vorchim announcing the month of Sivan whose first day will coincide with Sunday 4 Jun 2000g.

Not only did correspondent Larry Padwa send in the correct answer, he also remembered that a previous question had discussed the matter, and stated as follows

In less than two months.

Rosh Chodesh Sivan is on Sunday June 4, Shabbat M'varchim is June 3,
and the Molad is Friday June 2.

I believe that I saw this on your website a while back.

Thank you Larry Padwa.

The topic Moladot found in the Additonal Notes shows the times of the moladot for a five year period, with the current year in the middle. Inspection of the values in that section also shows the answer to Weekly Question 93.

The Weekly Question will take a brief pause to enjoy the holiday of Pesach.

Hag Sameach!

Several correspondents have asked if it would be possible to repeat previous questions. The next question is very timely, and appeared as the first Weekly Question.

Question 1

What do the months of Iyar and Tishrei have in common?


If you happen to have a Hebrew calendar handy, please note that on a week by week basis, the days in the month of Iyar are laid out exactly in the same way as the first 29 days in the subsequent month of Tishrei.

There are exactly 147 days from the first day of Iyar to the first day of the following Tishrei. This represents a complete number of weeks. And so, the first day of Iyar always is the same day of the week as the first day of the following Tishrei.

For example, whenever the first day of Iyar is Monday, the first day of the following Rosh Hashannah will also be Monday, as happens to be the case for Iyar 5758H (1998g) and Rosh Hashannah 5759H (1998g).

Therefore, Iyar and Tishrei have in common the same day of the week for their first day of the month.

Correspondent Benjamin W. Dreyfus correctly noted that both the months of Iyar and Tishrei could never begin on either Sunday, Wednesday, or Friday.

Thank you Benjamin W. Dreyfus for sharing this observation with us.

The next question is also repeated.

Question 2

On which day of the week do Hebrew months most frequently begin?


Correspondent Dwight Blevins provided a correct response to the question.

Based on random sampling, the most frequent first day of the month is Monday, followed by Wednesday... It appears that Monday falls out at about 17 to 18% of the total.

When you post the answer to the question on the web, are you planning to give us the break down of all percentages of the seven days as related to the descending order of frequency? Hope so. That might prove interesting.

Thank you Dwight Blevins for the correct answer and also the suggestion.

The statistics on the frequency of the first day of the Hebrew months can be found in the
Additional Notes under the topic of The First Day of the Month.

The following table demonstrates the weekday distribution of the first day of each month over the full Hebrew calendar cycle of 689,472 years.

Start of Month Distribution by Week Day
Sun Mon Tue Wed Thu Fri Sat Totals
Totals 1033845 1463854 989787 1345474 1153940 1282540 1258240 8527680

Correspondent Dr. Marsha B. Cohen suggested the next question.

Question 94

Which day, or days, of Pesach fall on the same weekday as the immediately preceding Purim?


The first day of the festival of Pesach is exactly 30 days after the celebration of Purim.

That means that 5 days later, 5 whole weeks will have elapsed. Consequently, the 35th day away from Purim coincides with the 6th day of Pesach.

Therefore, the 6th day of Pesach always falls on the same day of the week as the immediately preceding Purim.

For example, Purim 5760H coincided with Tue 21 Mar 2000g,
and the 6th day of Pesach 5760H coincided with Tue 25 Apr 2000g.

Correspondent Larry Padwa provided a correct response to the question.

The sixth day of Pesach (20 Nissan) is exactly five weeks after
Purim (14 Adar or 14 Adar II), and therefore falls on the same
day of the week as Purim.

Thank you Larry Padwa for the correct answer.

And Thank You also correspondent Marsha B. Cohen for having suggested
Weekly Question 94.

The next question is repeated.

Question 3

On which day of the week does Rosh Hodesh most frequently begin?


Each weekday will see the first day of Rosh Hodesh in a frequency that is between 11.6% up to 17.2%. So the weekdays are not too widely separated in terms of the number of times that they will each catch the first day of Rosh Hodesh.

The weekday that most frequently is associated with the first day of Rosh Hodesh is Tuesday. Over the full and complete cycle of the Hebrew calendar (689,472 Hebrew years), the first day of Rosh Hodesh will fall on Tuesday 1,463,854 times out of a possible 8,527,680 months in that cycle.

Therefore, Rosh Hodesh most frequently begins on Tuesday.

Question 95

Presently, what is the latest arrival time of the molad?


The latest possible arrival time for any molad is 23h 422p on the first day of the new month. That limit to the timing is the consequence of the Dehiyyah Molad Zakein. This absolute maximum arrival of the molad will first occur on the first day of Shevat 128,459H (Sat 23 Jun 124,700g).

Presently, no molad can exceed the latest arrival time of 23h 410p on the first day of any month.

This means that the maximum possible arrival time of the molad is continuing to increase.

Question 96

When did the molad first arrive at its presently latest time?


The latest possible arrival time for any molad is 23h 422p on the first day of the new month. That limit to the timing is the consequence of the Dehiyyah Molad Zakein. This absolute maximum arrival of the molad will first occur on the first day of Shevat 128,459H (Sat 23 Jun 124,700g).

Presently, no molad can exceed the latest arrival time of 23h 410p on the first day of any month.

The first time that the molad occurred at this currently latest time was
the first day of Shevat 3906H (Thu 30 Dec 145g).

The answer assumes that the fixed Hebrew calendar calculations existed then as they do today.

Correspondent Donald Cymrot asked the following question.

Question 97

Why is it impossible for a 385 day year to start on Tuesday?


Correspondent Larry Padwa was the first to send in an answer with the necessary logic. However, he did make a rather interesting observation which will be the subject of the next question. As Larry Padwa states:

If the first day of a year is Tuesday, then the Molad Tishrei for that year must be between 18h 00p Monday, and 17h 1079p Tuesday (inclusive).

Now if the year in question were to have 385 days, it would have to be a leap year. The increment from Molad Tishrei of leap year X to that of year X+1 is 5d 21H 589p.

Thus if a leap year began on Tuesday, the Molad Tishrei for the following year would be between Sunday 15h 589p and Monday 15h 588p. All the times in this range cause Rosh HaShannah of the following year to be on Monday, thus making a 385 day year beginning on Tuesday impossible.

In fact, this shows that all leap years beginning on Tuesday are 384 days long.

Correspondent Eric Presser also provided a similar response.

Correspondent Dwight Blevins saw a mystical musical connection in the fact that any Hebrew year beginning on Tuesday could not be followed by a 385 day year. Here is what Dwight Blevins said:

The abundant length, 385 day, 13 month lunar year is unique among the six types of years by length of days. The count of 385 days stands alone in that it crosses points with not just one, but two of the important artifacts of the laws which regulate harmonic or circular resonance. The evidence of this function of circular resonance is quite evident in both the laws of music and the calculations of the Hebrew calendar. This should not be too surprising since the physics of both sciences operate on the energy of the number seven, and has to do with those things which go round and round in circular propigation. This has much to do with the age old mystery of why the combination of 7 and 11 are considered to be “lucky” numbers. But, why is it that this type of year can never begin on the week day of Tuesday? The answer to this simple question, in an amazing way, may be a clue that probes at the very core of how the HC operates, and may also help to explain some of the mysterious myths and riddles of lunar calendar calculations. It all has to do with a mathematical constant we call “Pi,” and the simple fact that a week of seven days, or a musical scale of seven notes, can be enclosed with a 360 degree circle that amounts to a circumference of 22. This disection by the diameter of seven, creates two hemispheres of 11. Thus, the statement, “after seven comes eleven!” The science of modern mathematics has defined and refined this simple structure of the 22 increment sphere, disected by a seven straight line, as the constant, 3.14159, or “Pi.” Nevertheless, the Sages of many millennia ago understood it in the crude form of 22/7ths--the digits, of which, sum to 2 + 2 + 7 = 11. Some, even today, still believe the ancient 6th century BC physicist and philosopher, Pythagoras, was a bit strange in his theory of the harmony of the spheres. Yet, his findings, even today, we still recognize. His crude observation of the increment tones of beating hammers on the anvil of a blacksmith shop, we now call the diatonic scale of music! It is nothing more than the harmonic divisions of the tones of a plucked string. These tones travel in circles of resonant repetition, based on the number seven--a small snapshot of how just about everything travels that moves in harmonic cycles--from the atoms of a wooden desktop to the swirling galaxies of our universe.

But, back to the question. What does all this have to do with the 385 day lunar year? The number 385 is exactly 55 cycles of seven, but, also, 35 cycles of number 11. Both numbers have much to do with principles of repeating tones of resonant cycles or circles. Moreover, the combinations of 7 + 11 and 55 + 35 form multiples of 9, of which, the double of 9 = 18--the parts per minute of the HC standard. All this being the case, it is rather ironic that this very resonant number of seven (i.e., 385) will not work for years in which Tishrei 1 falls on Tuesday! Why is it particularly amazing that 385 days will not work for Tuesday? Because, based on the harmonic relationship of 7 and 11, it is this same note, or day of the week in the 4th octave, third position (i.e., Tuesday) of the seven increment natural scale of music, which has become world standard Middle C, for stringed instruments, at 264 hertz (24 x 11 = 264). But, again, why does Tuesday, of all days of the four part Tishrei declarations, not function as a declaration for the 385 day year?

Simple as it may be, the following explanation may well be a major part of the answer. All other days of the Tishrei 1 dates, based on the laws of harmonic circular resonance, are either multiples or inverted decimal fractional deratives of the number seven. Tuesday IS NOT! Since the Tishrei cycle appears to run a course of Tuesday through Monday, let’s look at Thursday first. Thursday, by the laws of circular resonance to the number 11 (based on the diatonic scale), is 330/385 days = 0.8571428 = 6/7ths. Saturday is 396/385 days = 1.0285714. Ignoring decimal places, we can see the artifact of seventh in this number. That is, the one (1) being a whole multiple of seven, can be discarded, but 0.0285714 is an artifact of 2/7ths. The next day in the cycle is Monday, and amounts to 495/385 = 1.285714. Again, dismissing the whole, we have 0.285714, or 2/7ths. HOWEVER, TUESDAY is 264/385 = 0.6857142. This fraction IS NOT a multiple or inversion of the seven day function, and, therefore, would not work mathematically for a 385 day Tuesday-Tuesday, Tishrei 1 interval. Coincidentally, if the cycle is equated as running from Tuesday through Monday (since the circle joins at Mon.-Tue.), then the sequence is 3-5-7-2, and as a function of seven in the cycle of resonant lunar declarations, which begins at Tuesday, the course is 3572/7 = 510.28571. The whole of 510 bein discarded, the remainder is 0.28571 x 7 = 2 or Monday--the last day of the Tishrei 1 cycle, which then, starts again at the next day, Tuesday.

Since the number seven is an HC standard, any point of annual declaration (i.e., Tishrei 1) must fall within the seven day weekly cycle. Monday, Thursday, and Saturday falls with the declaration cycle, but Tuesday does not! From a start point of Tuesday, any declaration falling up to and including the next Monday, for the first day of the next year, is within the seven day cycle. Tuesday would be eight days later, falling beyond the maximum of seven, and therefore, outside the possible cycle limits. Now, we may logically conclude, this reasoning is a bit philosophical and invalid because we could say the same thing for Monday-Monday, Thursday-Thursday, and Saturday-Saturday. This is not the case, and we can explain why.

Any straight line can be folded into a circle, and every circle can be detached and formed into a straight line. Thus, we have formula for calculating diameters, circumferences, radius, etc. We can do the same thing with the circle of HC declarations, but must be careful to break or attach the calendar circle at resonant points. The only two adjacent declarations of the HC circles falls at Monday-Tuesday. This is the only juncture that may be attached or detaced without creating a fractured pattern of the declaration cycle. We cannot break the circle at Wednesday-Thursday, for instance, because these two days are not cut from the same piece of fabric. Thursday is a day of Tishrei 1, but Wednesday is not. Unlike elements cannot naturally be joined together. They do not attract, but due to a different pattern, reject union. Hence, we can say (within the logic of this circular reasoning) that the cycle begins at Tuesday and ends at Monday for the seven day cycle. Only the two sevenths of Monday and Tuesday have a common DNA strata (both are Tishrei 1), and can form a neutral point of connecting the end back to the beginning of the Tishrei 1 circles. From a starting point of Tuesday, as long as the first and last day of two consecuitive years remains within the Tuesday-Monday circle, we have not exceeded the possible limits of the Tishrei 1 declarations. Tuesday-Tuesday crosses the Monday-Tuesday transition or connecting point a second time, and is therefore beyond the seven day limit. Thursday, following Tuesday, is within a seven day period, Saturday is within a seven day period, and Monday is with a seven day period following Tuesday, but the next Tuesday is beyond the limit of the seven day week. Tuesday, as the second of two consecuitive Tishrei 1, 385 day lunar year declarations, based on the Tuesday-Monday Tishrei 1 cycle, falls past the seven day inclusive count, and does not agree with the fact that 385 days is an exact multiple of seven. Therefore, Tuesday-Tuesday, as week day declarations in adjacent years, will not work for the lunar year of 385 days, because the sequence is not harmonically resonant to the seven-eleven spheres of the seven day circles that make up the lunar year.

So, based on the harmonic intervals of eleven, as the half or hemisphere of a 22 increment cycle whose diameter is seven; Monday, Thursday, and Saturday are resonant points of the seven intervals (or seven inversions), but Tuesday is not. Or, stated another way, if increment one of the twenty-two increment circle is Tuesday, then increment 22 falls out at 3 x 7 + 1, and is therefore beyond the cycles of seven of the HC, which end at Monday. The conclusion is that the HC Tishrei 1 dates of adjacent years cannot fall out on the week day of Tuesday, but can occur on Monday, Thursday, and Saturday. This is a matter of where the annual cycles of lunar declarations start, and where they can end, based on the seven day logic of resonance.

Thank you Larry Padwa, Eric Presser, and Dwight Blevins for sharing your most interesting responses to Weekly Question 97.

The reponse by Larry Padwa, outside of a typos, had a minor error which did not affect his correct arithmetic.

Question 98

What correction, or corrections, can be applied to Larry Padwa's response to Weekly Question 97?


As correspondent Larry Padwa stated in his answer to Weekly Question 97:

If the first day of a year is Tuesday, then the Molad Tishrei for that year must be between 18h 00p Monday, and 17h 1079p Tuesday (inclusive).

Now if the year in question were to have 385 days, it would have to be a leap year. The increment from Molad Tishrei of leap year X to that of year X+1 is 5d 21H 589p.

Thus if a leap year began on Tuesday, the Molad Tishrei for the following year would be between Sunday 15h 589p and Monday 15h 588p. All the times in this range cause Rosh HaShannah of the following year to be on Monday, thus making a 385 day year beginning on Tuesday impossible.

In fact, this shows that all leap years beginning on Tuesday are 384 days long.

The problem in Larry Padwa's answer occurs in the very opening sentence.

Mondays that follow Hebrew leap years cannot have their molad of Tishrei exceed 15h 588p. Otherwise, it would cause the previous year to rest at 382 days. As a result, such Mondays are disallowed and the Hebrew year is posponed to the next allowable day which is Tuesday.

This means that the molad of Tishrei for a Tuesday can come as early as 2d 15h 588p.

Consequently, the only correction to Larry Padwa's first line would be to include the fact that the limits of the molad's time for a Tuesday apply only to those Tuesdays at the start of LEAP years.

Thank you Larry Padwas for sharing your interesting response to Weekly Question 97.

Question 99

In which year, and for which month, will the value of the molad of Av 5760H (2000g) next reoccur?


The molad of Av 5760H is 2d 17h 884p.

This fact is needed only to confirm the answer, and not to develop the answer.

Arithmetically, the moladot repeat themselves in a cycle of 181,400 months.

Since there are 235 Hebrew months in every 19 Hebrew years, the number of years in
181,440 months is given by INT( 181440 / 235 ) = 14,668.

The remainder is 20.

Hence, this cycle represents 14,668 Hebrew years plus 20 Hebrew months.

Since 14,668 = 772 * 19, the resulting month is the same as the one that will be
20 months from Av 5760H, namely, Nisan 5762H.

The resulting Hebrew year will then be 14,668 + 5762 = 20,430H.

Therefore, the next occurrence of the value of the molad of Av 5760H will be
the molad of Nisan 20,430H (Mon 16 May 16,670g).

Question 100

In the mahzor qatan (19 year cycle), what is the significance of the 9th year?


The mahzor qatan to which we refer is noted in the 12th century work by Maimonides known as Qiddush Hilkhot HaHodesh.

It is defined by the succession of the 7 Hebrew leap years in its 19 year cycle. These years are the 1st, 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of this cycle.

Hence, the 9th year of this cycle is a 12 month year.

But for some reason, which remains to be explained, a new Gregorian date for the beginning of Rosh Hashannah is always introduced at the start the 9th year of that cycle.

For example, the Hebrew year 4683H, the 9th year of the 247th cycle, began on Thu 1 Oct 922g, the first time since year 1H that Rosh Hashannah began on Oct 1.

It is the introduction of new Gregorian dates for the beginning of Rosh Hashannah, always at the 9th year of the mahzor qatan, which gives significance to the 9th year of the mahzor qatan.

For other Additional Notes click here.
For other Archived Weekly Questions click here.
Hebrew Calendar Science and Myths

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Remy Landau

 First  Begun 21 Jun 1998 
First  Paged  5 Nov 2004
Next Revised  5 Nov 2004