The 84 Year Cycle and Eiruvin 56a

(Make sure to read all posts on Birkat HaChamah here)

The Gemara in Eiruvin 56a reads as follows:

ואמר שמואל אין לך תקופת ניסן שנופלת בצדק שאינה משברת את האילנות ואין לך תקופת טבת שנופלת בצדק שאינה מייבשת את הזרעים והוא דאיתליד לבנה או בלבנה או בצדק

And Shmuel said: There is no Tekufat Nissan that falls in Tzedek that doesn’t break trees, and there is no Tekufat Tevet that falls in Tzedek that doesn’t dry out the seeds. And this is one that the moon is renewed (i.e. the Molad falls in) Levanah or Tzedek.

We see from here that Shmuel attaches significance to two events on the calendar which occur in 7 year intervals. Then, there is a condition limiting the scope, depending on the accompanying Molad. It should be noted, for those that can’t read the original text above, that the extra stipulation uses an Aramaic word, wherein the main statement uses only Hebrew.

Looking at the 84 Year Cycle, we see that when Tekufat Nissan falls in Tzedek, Molad Nissan falls in Chamah. This occurs once in 7 years, therefore the condition of the Baraita never occurs. However, that is not the case: the column I have labeled Molad Nissan is really only Molad Nissan once in a while. That is to say each year advances 12 months, with no leap years.

This cannot be directly demonstrated from Tevet (as above for Nissan) due to the intentional inaccuracies in the Lunar calculations.