Why Cheshvan & Kislev?
The Tur (O.Ch. 428) writes ,”Tishrei is always a full month (30days)
and Teves is always a missing (short) month (29days)
The months alternate one month is full and the following is short.
The months of Cheshvan & Kislev are exceptions. Some years both
months are full.(שנה שלמה ). Some years both months are short
( חסרה ) and some years one is full and the other is short (כסדרה)“
The reason for this is to equalize the months. A lunar cycle is
29 days+12hours+ 793 Chalokim (Aprox. ¾ hr.)
The Levush explains why did Chazal pick Cheshvan & Kislev
and not any other month when we do not always alternate full
and short months .
“The first opportunity we have to add or subtract from the month
is on the month of Cheshvan.
We can’t do it on Nissan & Iyar because the 50th day of Sefirah
has to fall on the 6th of Sivan.
(by adding or subtracting a day we will have it on the 5th or the 7th )
From Shavuos till Yom Kippur we need to have 3 x 40 days.
to commemorate the 3x 40 days from Moshe Rabeinu standing
on the mountain (Shavuos) and bringing down the Luchos on
Chodesh Tishrei is the king of the Chodoshim and the Month
with Yomim Tovim (ירח האתנים ) we can’t make it a חסר .
Therefore the first opportune time is in the month of Cheshvan.