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.

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

Each weekday will see the first day of a Hebrew month 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 some Hebrew month.

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

Therefore, the first day of the month most frequently occurs on Monday.

The festival of Rosh Chodesh always begins 29 days after the first day of a Hebrew month. When the Hebrew month has 30 days, the observance is extended to the next day which is the first day of the subsequent month.

On which day of the week does Rosh Chodesh 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.

Talmudic tradition indicates that the day for the festival of Rosh Hodesh would be determined by the Sod Haibbur which was a secret council of three scholars. One these scholars was the head of the Sanhedrin, which in ancient times was the supreme law making body of the Jewish people. The other two members also were scholars taken from this august assembly. The Talmud goes on to relate that the Sod Haibbur had to exclude from its council certain people who occupied extremely high office.

According to Talmudic tradition, which high officers were barred from the Sod Haibbur?

The Sod Haibbur also had to determine whether or not to declare a leap year through the intercalation of an extra month.

The Talmud, in tractate Sanhedrin 18b, relates that due to this function both the King and the Cohein Gadol had to be excluded from the Sod Haibbur.

The King was disqualified because he paid his armies on an annual basis and therefore would favour the leap years of 13 months.

The Cohein Gadol, on the other hand, would more likely favour the 12 month years. During the High Holidays, the Cohein Gadol had to immerse himself several times in fresh spring waters as part of the Temple rituals. And so, he probably would have preferred an earlier time of the year when these waters were a bit warmer.

In any given Hebrew year, what is the largest number of Hebrew months whose first day can coincide with the first day of their corresponding Gregorian month?

The first day of the Hebrew months tend to coincide with the first day of some corresponding Gregorian month about 38% of the time.

In 5758H the first day of Heshvan coincided with the first day of October 1997g. In 5760H, the first day of Elul will coincide with the first day of September 2000g.

In some Hebrew years, these coincidences can occur several times. In 5755H, the months of Adar, Nisan, and Iyar all started on the first days of February, April and May of 1995g.

However, no Hebrew year can have more than 3 such coincidences. In those years, the 3 Hebrew months will always have their first days coincide with the first days of February, April and May.

What is the next Hebrew year in which 3 Hebrew months will all start on the first day of their corresponding Gregorian months?

In 5755H, the months of Adar, Nisan, and Iyar all started on the first days of February, April and May of 1995g.

This will not happen again until the year 5774H. In that year the months of Adar, Nisan, and Iyar will all start on the first days of February, April and May of 2014g.

Rosh Hashannah of 5774H begins on Thursday 5 Sep 2013g. In our times, this is the earliest possible day of the Gregorian year for which any Rosh Hashannah can begin. The last time that Rosh Hashannah occurred that early in the Gregorian year was for the year 5660H, which began on Tuesday 5 Sep 1899g.

Thus, the years 5774H and 5660H share a very rare feature with each other.

The Hebrew year 5774H (2013g/2014g) also shares in common with the Hebrew year 5676H (1915g/1916g) another very rare feature.

What would be the very rare feature shared in common between the Hebrew years 5774H (2013g/2014g) and 5676H (1915g/1916g)?

The years 5774H (2013g/2014g) and 5676H (1915g/1916g) are the two years in our times which both begin the longest possible periods of 120 Hebrew years as measured from the first day of Tishrei.

Periods of 120 Hebrew years, as measured from the first day of Tishrei can be either 43822, 43823, 43824, 43825, 43851, 43852, 43853, 43854, or 43855 days long.

Coincidentally, the first Rosh Hashannah of both of these 120 year periods begins on Thursday.

Does the first Rosh Hashannah of a longest possible 120 Hebrew year period always begin on Thursday?

Periods of 120 Hebrew years, as measured from the first day of Tishrei can be either 43822, 43823, 43824, 43825, 43851, 43852, 43853, 43854, or 43855 days long.

One of the remarkable features of the longest possible 120 year periods is that their first day of Tishrei always is Thursday.

The last time that the 43,855 day period began on the first day of Tishrei was on Rosh Hashannah 5676H (1915g/1916g). The next Rosh Hashannah to open such a period will be for the year 5774H (2013g/2014g).

Simple arithmetic shows that these 2 years are 98 Hebrew years apart.

As measured from the first day of Tishrei, are all of the longest periods of 120 Hebrew years exactly 98 Hebrew years apart?

No.

The longest periods of 120 Hebrew years are 43,855 days long. Over the full calendar cycle of 689,472 years these are the distances which can be calculated between 43,855 day periods:

number of years=  27  number of times = 1260 
number of years=  71  number of times =  835 
number of years=  98  number of times = 1433 
number of years= 149  number of times = 1912 
number of years= 176  number of times =  176 
number of years= 220  number of times =  239 
number of years= 247  number of times =  353 

Each period which separates the longest 120 years from each other is a whole number of weeks.

As well, a number of the 120 year periods appear to terminate at a time when the start of Rosh Hashannah advances by yet another day in the Gregorian year. This was true of the year 922g which saw the eruption of the ben Meir - Saadia Gaon calendar controversy.

In which year or years of the 19 year Hebrew calendar cycle is Rosh Hashannah most likely to advance by another day in the Gregorian calendar?

The last time that Rosh Hashannah advanced in the Gregorian calendar was at the start of 5576H corresponding to Thursday 5 October 1815g. The next time that this will happen will be at the start of 5975H corresponding to Thursday 6 October 2214g.

Both of these years inaugurate the 9th year of the 19 year Hebrew calendar cycle. Carefully examining the calendar drift tables shown in the Additional Notes, it becomes apparent that after a certain distance into the drift the advancement of the Hebrew year into the Gregorian year only occurs at the start of the 9th year of a 19 year cycle.

However, not every 9th year of the cycle will cause the Hebrew year to be advanced.

If the 9th year of a 19 year cycle seems to cause the latest arrival of Rosh Hashannah, it seems reasonable to conclude that some other year in the cycle might see the earliest possible arrivals of Rosh Hashannah.

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