I read Tolkien’s works years ago, and for a while I was very interested in various aspects of the fictional world, such as languages, geography, and calendars; then, as often happens, I moved on to other interests. I recently discovered that, over the millennia, our planet’s rotational speed has been slowing down, and therefore the length of the tropical year is decreasing (while the orbital period remains more or less unchanged). I recalled having done some calculations on the length of year across various calendars, and I had seen that in the Elven calendar, the average length of the year was:

365 days x 11 times + 368 days (the 12° year doubles the three enderi) = 4383 days in 12 years

4383 days x 12 times = 52596 days in 144 years (1 normal yén)

52596 days x 2 times + 52593 g (in the 144° year of the third of three yéni the enderi aren’t doubled) = 157785 days in 3 yéni (432 years cycle)

The average length of a year in this system is therefore 157,785/432 = 365.2430556 days

In addition to this, I recalled reading something about what Tolkien said regarding the setting of his stories in a distant imaginary past:

Letter to Rhona Beare (1958) - 3019 T.A. is 6,000 years before 1958, so 1 F.A. would be 11,091 B.C.

The Awakening of the Quendi (1960) - 310 F.A. is 16,000 years before 1960, so 1 F.A. is 14,349 B.C.

BBC interview (1964) - 3019 T.A. is 7,000–8,000 years before 1964, so 1 F.A. is 12,085 / 13,085 B.C.

Why did I specifically mention the hypothetical correspondences with 1 F.A.? Because that would be the period when the Elvish solar calendar began to be used as the Sun began it’s cycle. And guess what? The year duration was 365.2430556 days… approximately around 11,000-12,000 B.C. !