More in-depth calculation with respect to the Imladris calendar, and its relation to the week-days, shows that the habit of the Eldar of reckoning "in sixes and twelves as far as possible" has stood them in good stead in simplifying what would be their universal calendar. You may have seen some of the 'universal calendars' for the Julian-Gregorian year; they consist of some fourteen calendars (seven for ordinary years, seven for leap years, each starting on a different day of the week) with a table for determining which calendar answers to which year. The sequence of the table is extremely complex, with a very long cycle before it repeats. The Rivendell cycle is also very long (864 years, or 6 yeni) but the internal structure of the cycle is very simple, unlike that of the Julian-Gregorian.

If we suppose (arbitrarily) the first year of the cycle to be a 365-day year starting on Orgilion, then the normal cycle of years will be:

Yestare Mettare
Year 1: Gilion Menel
Year 2: Belain Galadhad
Year 3: Menel Ithil
Year 4: Galadhad Anor
Year 5: Ithil Gilion
Year 6: Anor Belain

And back around to one.

There should theoretically be six possible "leap years" (368-day years) but - surprise - there are only two that will actually exist in the system. These are:

Year A: Anor Ithil
Year B: Menel Belain

The Imladris universal calendar only has eight different calendars. Leap-years fall on every twelfth year, so in the first twelve-year cycle of a yen, the calendars will progress as follows:

Cycle I: 1 2 3 4 5 6 1 2 3 4 5 A
Cycle II: 4 5 6 1 2 3 4 5 6 1 2 B

And this pattern will simply repeat, over and over, throughout all but the last cycle of a three-yen period: that is, for 420 years.

The last cycle (in which the leap year is omitted) will look like this:

Cycle XXXVI: 4 5 6 1 2 3 4 5 6 1 2 3 and the 1st year of the next _yen_ is:
Cycle I: 4 5 6 1 2 3 4 5 6 1 2 B and then
Cycle II: 1 2 3 4 5 6 1 2 3 4 5 A and so on for another 3 yeni until:
Cycle XXXVI: 1 2 3 4 5 6 1 2 3 4 5 6

And then we go right back to the cycle used in the previous three-yen period. So there is a 12-year pattern for odd and even years, which switches odds and evens every 432 years. Simple!

If we suppose this system to have started with Year 1 of the Sun, in TA 3009, the sixteenth three-yen period having been completed in TA 2881, we are now following the first pattern (odd A, even B). TA 3009 is in the 11th (odd) cycle of this pattern (TA 3002-TA 3013), which runs 1 2 3 4 5 6 1 2 3 4 5 A, and is the eighth year of the cycle, and therefore follows Calendar 2: its yestare should therefore be Orbelain, and its mettare Orgaladhad; TA 3008's yestare should have been Orgilion, if this system is followed.