Why Cheshvan & Kislev?
The טור (O.Ch. 428) writes, ”תשרי is always a full month (30 days) and טבת is always a missing (short) month (29days)
The months alternate one month is full and the following is short.
The months of חשון & כסלו 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+12 hours+ 793 חלקים (Approx. ¾ hr.)
A year can have 353- 354- or 355 days
The לבוש explains why חז"ל picked חשון & כסלו to change the system of alternating full and short months. and not any other month.
“The first opportunity we have to add or subtract from the month is on the month of חשון.
We can’t do it on ניסן & אייר because the 50th day of ספירה needs to be on the 6th of סיון. (by adding or subtracting a day we will have it on the 5th or the 7th )
From שבועות till יום כיפור we need to have 3x
40 days to commemorate the 3x 40 days from משה רבינו standing on the
mountain (שבועות) to bringing down the לוחות on
חדש תשרי is the king of the חדשים 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 חשון.
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