The full Hebrew calendar cycle of 689,472 years consists of 8,527,680 months. This total can be easily derived by multiplying the number of months in every 19 year cycle with the number of these cycles in the full Hebrew calendar cycle. This gives 235 months * 36,288 = 8,527,680 months.

Each day of the week will coincide with the first day of a month. However, due to the initial Rosh Hashannah rule of Lo ADU it is not possible for some of the months to begin on certain days of the week. For example, Tishrei cannot begin on either Sunday, Wednesday, or Friday. Similarly, Kislev never begins on a Saturday, while the month of Tevet avoids starting on either Thursday or Saturday.

In here, the 30 day month of Adar is called Leap Adar and the weekday distribution of its first day is appended to the folowing table.

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

The months of Iyar and Tishrei have exactly the same weekday distribution for their first days. This is because the first day of the month of Iyar is exactly 147 days away from the first day of the subsequent Tishrei. Since 147 days is exactly 21 weeks, then whichever day of the week begins Iyar, will also begin 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).

The month of Kislev can begin on every single day of the week except for Saturday. This will be true for both the non-leap and the leap year distibutions.

The months of Kislev, Tevet, Sivan, Tammuz, and Elul never begin on Saturday.

The most likely start day for any month is Monday. From the above table it can be seen that the first days of the months coincide some 17.2% of the time with Monday.

Similarly, the least likely start day for any month is Tuesday. From the above table it can be seen that the first days of the months coincide some 11.6% of the time with Tuesday.

The weekday distribution of the first days for the months of Heshvan, Nisan, Iyar, Sivan, Tammuz, Av, and Elul have the same values as those for the month of Tishrei, although each may be shifted differently across the weekdays. That is because the first days of each of these months is a constant distance away from the first day of the month of Tishrei.

The month of Adar has 3 different characteristics. The first is the 29 day month which occurs in all non-leap years. The second is the 30 day month of Adar which is inserted after the month of Shevat during Hebrew leap years. And the third is the 29 day month of v'Adar which always follows the leap month of Adar.

It is to be noted that v'Adar has the same weekday distribution values as those for the month of Leap Adar. However, the values for v'Adar are shifted two days later than those for Leap Adar.

Leap Adar can start on a Thursday, but not v'Adar.

Adar cannot start on Friday in a leap year, and can never begin either on Sunday or Tuesday.

The following tables show the week day distribution of the first day of the months segregated by year lengths.

It is interesting to note that for the following year lengths, these months have exactly the same start day distribution as the month of Tishrei

          353 days - Adar   Elul
          354 days - Tammuz
          355 days - Shevat
          383 days - Adar
          384 days - Sivan
          385 days - Shevat Iyar

It is also interesting to note that the most likely week day for the first day of a month varies by year length as follows

          353 days - Monday
          354 days - Sunday Tuesday Thursday Friday (each occurs 334,994 times)
          355 days - Monday
          383 days - Monday
          384 days - Friday
          385 days - Monday

Each year type occurs with a particular frequency over the full Hebrew calendar cycle of 689,472 years. The big surprise is that over this cycle some of the week days actually catch the first days of the month with exactly the same frequency as the year types.

69,222

167,497

198,737

106,677

36,288

111,051

The 383 day years are unique in that none of its week days catch the first day of a month with the same frequency of occurrence as the 383 day years.

Some of the week days also catch the first days of the month with exactly double the frequency of the year types.

2*69,222

2*167,497

2*198,737

2*106,677

2*36,288

2*111,051

The 355 day years are unique in that none of its week days catch the first day of a month with double the frequency of occurrence as the 355 day years.

The 384 day years are the only ones to have a week day, namely Friday, catch the first day of a month at triple the frequency of occurence of the 384 day years.

First  Paged  1 Jul 1997
Next Revised 10 Jul 1997