WQ Archive 101 - 110

Weekly Question Archive 101 - 110

by Remy Landau

Question 101

When next will Rosh Hashannah begin on a new Gregorian date?

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 katan, which gives significance to the 9th year of the mahzor katan.

The next time that a new Gregorian date will be introduced for the first day of Rosh Hashannah 5975H coinciding with Thu 6 Oct 2214g.

The new month of Elul 5760H begins on Fri 1 Sep 2000g.

Question 102

After Elul 5760H, which starts on Friday 1 September 2000g, when next will the first day of a Hebrew month coincide with the first day of a Gregorian calendar month?

Sunday 1-June 2003 falling on 1-Sivan 5763.

Question 103

What does the coming Hebrew year 5761H (Mon 30 Sep 2000g) have in common with the year in which the Gregorian calendar was introduced?

The Gregorian calendar was introduced on 19 Tishrei 5343H (15 Oct 1582g).

5343H was the 4th year of the 282nd mahzor katan (19 Hebrew year cycle),
since 5343 = 281 * 19 + 4.

The coming Hebrew year 5761H is the 4th year of the 304th mahzor katan,
since 5761 = 303 * 19 + 4.

Therefore, the coming Hebrew year 5761H (Mon 30 Sep 2000g), and the year in which the Gregorian calendar was introduced, have in common, the same place in the mahzor katan.

Correspondent Kenneth Kirchhevel shared some rather interesting information governing the months that are named in Tanach (the Bible). The next question is based on that data.

Question 104

Which calendar months are named in Tanach (the Bible)?

Correspondent Kenneth Kirchhevel shared some rather interesting information governing the months that are named in Tanach (the Bible). He noted the following:-

Here are some references for the months I told you about.
Ex. 13:4 which places Aviv as the month of the Exodus which is also the current month of ?? .
1Kings 6:1&37 for Zif as the ?? month corresponding to ??.
1Kings 8:2 for Ethanim as the ?? month corresponding to ??.
And lastly, Bul in 1Kings 6:38 the ?? month corresponding to ??, if my memory is working right.

Of course, correspondent Kenneth Kirchhevel filled in the question marks with the traditionally held information. Those ??'s are the subject of our next Weekly Question.

Question 105

What are the traditionally held correspondences of the biblically named months to the months in our present Hebrew calendar?

Correspondent Kenneth Kirchhevel shared some rather interesting information governing the months that are named in Tanach (the Bible). He noted the following:-

Here are some references for the months I told you about.
Ex. 13:4 which places Aviv as the month of the Exodus which is also the current month of Nisan .
1Kings 6:1&37 for Zif as the second month corresponding to Iyar.
1Kings 8:2 for Ethanim as the seventh month corresponding to Tishrei.
And lastly, Bul in 1Kings 6:38 the eighth month corresponding to Heshvan, if my memory is working right.

Thank you correspondent Kenneth Kirchhevel for bringing these very interesting calendar facts to our attention.

The month preceding Rosh HaShannah is today known as Elul.

Rabbi Steven S. Saltzman of the Adath Israel Congregation in Downsview, Ontario, Canada, noted a very charming fact related to the name of that month.

Question 106

The Hebrew letters which form the name Elul also represent the acronym for which very well known scriptural sentence?

The Hebrew letters used to form the name of the month Elul are alef,lamed,vov, and lamed.

These letters correspond to the first letter of each of the words in the Hebrew scriptural sentence Ani Ledodi Vedodi Li (I am my beloved's and my beloved is mine).

The expression is found in Shir HaShirim (Song of Songs or Solomon's Song) at chapter 6:3.

Thank you Rabbi Steven S. Saltzman of the Adath Israel Congregation in Downsview, Ontario, Canada, for having shared this very charming fact related to the month Elul.

Rosh Hashannah 5761H begins on Shabbat corresponding to 30 September 2000g.

The molad of Tishrei 5761H occurred on the preceding Thursday at 19h 17m 4hl.

Rosh Hashannah 5761H to be postponed by 2 days from the day of the molad of Tishrei.

The year 5761H is 353 days long and is therefore called a deficient or imperfect year.

In the 5 consecutive Hebrew years which began with 5760H, 5761H is the second of the 4 years which begin on Shabbat.

Question 107

Can you mention at least 3 other calendar related features of the Hebrew year 5761H?

L'SHANNAH TOVAH!

1. The molad of Heshvan will occur prior to the time of the Birkat HaHodesh portion of the Shabbat morning service. So the time of that molad will have to be announced as
The molad of Heshvan occurred this morning at 8h 1m 5hl.

2. The month of Nisan begins on Sun 25 Mar 2001g thereby triggering the The Nisan Descent which is explained in the Additional Notes.

3. The year value 5761 = 7 * 823, a whole multiple of 7. According to some rabbinic traditions, this means that 5761H is a year of Shmittah which in biblical terms means a year of release in the land of Israel.

4. Pesach 5761H begins on Sunday 8 April 2001g. The start of Pesach on Sunday last happened in 5754H (1994g) and will next happen in 5765H (2005g).

The next Weekly Question has been suggested by several correspondents over the last few months.

Question 108

Without any of the dehiyyot (Rosh Hashannah postponement rules) why are the possible Hebrew year lengths 354, 355, 383, and 384 days?

The molad of Tishrei for any year H is normally expressed as a day of the week and some fraction of that day usually denoted as hours and halakim (i.e., parts).

For example, the molad of Tishrei 5761H is Thursday 19h 310p.

Let d represent the day of the molad of Tishrei and
Let f represent the fraction of that day. If m is the molad of Tishrei for year H, then m = d + f.

The INTeger portion of m is [INT(m)] = d and is the day of the molad.

The quantity to be added to the molad of Tishrei H in order to determine the time of the molad of Tishrei for year H+1 is either

354d 8h 876p if year H is a 12-month year or
383d 21h 589p if year H is a 13-month year.

In either case, let A + a represent the amount to be added to the time of the molad of Tishrei H so as to determine the molad of Tishrei H+1.

Let m1 represent the time of the molad of Tishrei H+1.

Then m1 = m + A + a = d + f + A + a

The day of the molad of Tishrei H+1 is INT(m1) = d + A + INT(f + a).

Hence, the number of days in year H is given by the expression

INT(m1) - INT(m) = d + A + INT(f + a) - d = A + INT(f + a)

Since both f and a are positive fractions of a day, INT(f + a) can be either 0 or 1.

From the last equation, it is to be noted that if (f + a) => 1 day then the 12 month year is 355 days long and the 13 month year is 384 days long, since INT(f + a) = 1.

Similarly, if (f + a) < 1 then INT(f + a) = 0 and the 12 month year is 354 days long, while the 13 month year is 383 days long.

Therefore, the possible Hebrew year lengths in the absence of the dehiyyot (postponement rules) can be either 354, 355, 383, 384 days.

The Hebrew calendar scholars added a postponement rule known as Dehiyyah Lo ADU Rosh. The rule postpones Rosh Hashannah (1 Tishrei) to the next day whenever
the day of the molad of Tishrei is either Sunday, Wednesday, or Friday. The impact of this rule is to double to 8 the number of possible Hebrew year lengths.

Question 109

Why does the Hebrew calendar postponement rule Lo ADU Rosh lead to 8 possible Hebrew year lengths?

The molad of Tishrei for any year H is normally expressed as a day of the week and some fraction of that day usually denoted as hours and halakim (i.e., parts).

For example, the molad of Tishrei 5761H is Thursday 19h 310p.

Let d represent the day of the molad of Tishrei and
Let f represent the fraction of that day. If m is the molad of Tishrei for year H, then m = d + f.

The INTeger portion of m is [INT(m)] = d and is the day of the molad.

Under Lo ADU Rosh the start of Rosh Hashannah must be delayed by one day if d modulus 7 is either 1, 4, or 6.

Let r = d + p

where

r is the day of Rosh Hashannah and p is the postponement value.

It should be realized that p can be either 0 or 1.

The quantity to be added to the molad of Tishrei H in order to determine the time of the molad of Tishrei for year H+1 is either

354d 8h 876p if year H is a 12-month year or
383d 21h 589p if year H is a 13-month year.

In either case, let A + a represent the amount to be added to the time of the molad of Tishrei H so as to determine the molad of Tishrei H+1.

It is to be noted that INT(A+a) = A

Let m1 represent the time of the molad of Tishrei H+1.

Then m1 = m + A + a = d + f + A + a

The day of the molad of Tishrei H+1 is INT(m1) = d + A + INT(f + a).

Let p1 be the postponement required for the start of Rosh Hashannah year H+1.

Then r1, the first day of Rosh Hashannah year H+1 is given as r1 = d + A + INT(f + a) + p1.

Consequently, the length of year H is given by

r1 - r = d + A + INT(f + a) + p1 - (d + p) = A + INT(f + a) + p1 - p.

Since the possible values for each of INT(f + a), p1, and p is either 0 or 1, the possible values for the expression INT(f + a) + p1 - p are either -1, 0, 1, or 2.

Consequently, for a given value of A, r1 - r has one of 4 possible values.

If A = 354, then r1 - r can be either 353, 354, 355, or 356.
If A = 383, then r1 - r can be either 382, 383, 384, or 385.

Therefore, Lo ADU Rosh causes 8 possible year lengths.

The ancient calendar scholars, using a method that is extremely simple, and well documented, eliminated the 356 and 382 day years.

The next question addresses a problem that is faced by anyone wishing to determine possible lengths of Hebrew year periods unaided by computers.

Question 110

For any possible period of Hebrew years, what are the possible number of Hebrew leap years within that period of time?

This question addresses a problem that is faced by anyone wishing to determine possible lengths of Hebrew year periods unaided by computers.

Correspondent Larry Padwa answered this question using an assumption that each period of years can be expressed in the form of 19 * K + r.

```        Number of Years    Minimum Number    Maximum Number
of Leap Years     of Leap Years
===================================================
19K                7K                7K
---------------------------------------------------
19K+1              7K                7K+1
---------------------------------------------------
19K+2              7K                7K+1
---------------------------------------------------
19K+3              7K+1              7K+2
---------------------------------------------------
19K+4              7K+1              7K+2
---------------------------------------------------
19K+5              7K+1              7K+2
---------------------------------------------------
19K+6              7K+2              7K+3
---------------------------------------------------
19K+7              7K+2              7K+3
---------------------------------------------------
19K+8              7K+2              7K+3
---------------------------------------------------
19K+9              7K+3              7K+4
---------------------------------------------------
19K+10             7K+3              7K+4
---------------------------------------------------
19K+11             7K+4              7K+5
---------------------------------------------------
19K+12             7K+4              7K+5
---------------------------------------------------
19K+13             7K+4              7K+5
---------------------------------------------------
19K+14             7K+5              7K+6
---------------------------------------------------
19K+15             7K+5              7K+6
---------------------------------------------------
19K+16             7K+5              7K+6
---------------------------------------------------
19K+17             7K+6              7K+7
---------------------------------------------------
19K+18             7K+6              7K+7
===================================================

```

Correspondent Larry Padwa also explained why there are two possible numbers of leap years for any period that is not a multiple of 19 Hebrew years.

The leap years (L) and common years (c) are distributed as follows in every 19 year cycle:

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

The period can start at any point in the cycle. Thus in the simplest case, for a period of length 1 (or 19K+1) you can start at a leap or a common year, giving two possible results. Other period lengths are similar. Thus for a three year period, starting at year 6 or 17 yields 2 leaps; any other starting point yields one leap. In general, if you start at year 6 or 17 you'll get one more leap year than if you start at year 9 or 1 for the same length period, unless the length is a multiple of 19 in which case the entire cycle is covered regardless of the starting point.

Thank you Larry Padwa for sharing with us this very thorough analysis.

One of the more prevalent practices, among the Jewish people, is that of reading the entire Mosaic text of their scriptures (Torah) over the course of one Hebrew year. At Simchat Torah, the last few verses are read, and then the entire cycle is repeated once again from Bereshit (Genesis).

The scriptural readings are divided into contiguous weekly portions, which are read in their entirety each Shabbat morning. Each division is known as a Parshah or Sedrah. These portions are arranged so as to be completely read over the course of one Hebrew year.

Correspondent Larry Padwa noted that in 5761H (2000g/2001g) Sedrah Vayyelech will only be partially read.

``` First  Begun 21 Jun 1998