Why a Second Month of Adar?

This March 11 we will celebrate another Rosh Chodesh for another month of Adar, “Adar Bet” or Adar 2.

This anomaly occurs seven times in a cycle of 19 years. Why?

In Parashat Bo (EXodus Ch.12 V.2), We are instructed to mark the month of Nisan as the “beginning of the months” of the year for you. Later in Exodus Ch.13 V.10, we are instructed to “keep this ordinance in its season”

Ibn Ezra comments that, like the Egyptians, the Israelites employed a solar calendar. But lunar years are not equal to solar years; the seasons of plowing and harvest depend on the movement of the sun as it travels to the north or the south, so the calendars needed to reconcile or match. And here is how it is done. Please get your calculators ready.

Let’s start with our secular calendar; A Solar year is 365.242 days (almost 365 and ¼ day. That is why on the Gregorian (Solar) Calendar a day is added in February every four years.

The word Chodesh has the same root (shoresh) as Chadash or renew; What renews? The moon. The renewal cycle lasts for 29.5306 days, this is what is a Lunar month which is almost a (Solar)month, however, shorter.

A Lunar year of 12 lunar months would be (12 x 29.5306) 354.3672 days. Or 10.875 (*) days shorter. So an adjustment needs to be made otherwise the festivals would not coincide with the season. Muslims do not adjust their calendar, note how Ramadam moves every year 11 days earlier, and only coincides with the season once every 33 years.

We needed to find the right period to add a month to the years, and this requires a little more math. If we were to add one month every two years, we would be short by almost ten days, on the other hand, if we were to add one month every three years, that would push every cycle by three days. Using a greater fraction like adding two months out of seven years gets us closer so seven years of 365.242 days equals 2556 days minus seven lunar years plus two lunar months ((2×29.5306)+(7×354.3672)) or (86 months of 29.5306 days) 2540 days; this means that we would be off by 16.7 days, almost half a month.

To find the right number of months to be added in a period of several years, we need to find the fraction that would match the ratio of an average solar month to the difference of the days a lunar year is shorter than the solar year. Or 30.43 days divided by 10.875 (*) days this is 2.7987 and the closest is 19 divided by seven = 2.714, as we will see the rest is compensated by making some months 30 days instead of 29 days in certain years.

Now, the next problem to solve is to know which year will be a leap year and which will be normal, because 19 cannot be equally divided by seven and it will be solved with music.

In music, the 19 Equal Division of the Octave (EDO) has a semitone in between E and F and B and C ( if you look at the Piano Keyboard that semitone does not exist)

By making C=19 we can start the cycle with C♯ as 1, D♭ as 2, and D as 3, as follows:

Note

C♯

D♭

D♯

E♭

E♯

F♭

F♯

G♭

G♯

A♭

A♯

B♭

B♯

C♭

Year

That is playing twice every semitone and adding one in between E and F and B and C; So now if you go back to the piano keyboard and play all the natural notes in the Octave (the highlighted green blocks) you would be playing the years that are leap years. Which are 3, 6, 8, 11, 14. 17 and 19.

How do we know which year is a leap year? By dividing the year by 19 and finding the reminder, so for 5784 when divided by 19 the reminder is 8 which also marks its place in the cycle, 5787 will be the next leap year.

Another time we will discuss why we add a couple of days here and there, not just to catch up but also to ensure that Yom Kippur never falls on a Friday or Sunday.

Written by Alberto Quiroz

Join Women of Holy Blossom for Shacharit Service: Monday, March 11, 2024, 7:30 am ET, in-person or via Zoom at https://zoom.us/j/93902401402?pwd=dGlOR2dEcGs1RVc0OVFwdkFtOVo5UT09
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For upcoming dates and why Rosh Chodesh is special for women see https://holyblossom.org/rosh-chodesh/