The Imladris calendar was that used by the People of the Stars (Eldar) of Rivendell, Middle Earth, through the first three Ages and not discontinued by Elf-friends (Elendillion) in the Fourth, which began with the final departing of the Eldar, March 25, 6417 BC.
In it one sunset-to-sunset day is a ré, 6 ré make an enquië. The six are respectively named: Elenya ("stars-day"), Anarya ("sun-day"), Isilya ("moon-day"), Aldúya ("tree's-day"), Menelya ("heaven's-day") and Valarya ("Valar-day"). 365 ré make a loa ("growth") and 144 loa make a yén ("long year"). Every twelfth loa the loëndë was doubled to make a 368-ré atendëa (double-middle (loa)).
This is still however 1 ré short from the astronomical year, the coranar (sun-round), every 1800 loa or 2 ré every 25 yén, but was adjusted however at the end of the Second and Third Ages. Since the beginning of the Fourth Age 58 yén ago however this now amounts to a 4.7-ré deficit, and 5 by AD 2584.
The loa is divided into nine parts now beginning on our Mar. 25:
Yestarë ("first-day", 1 ré), Tuilë ("spring", 9 enquië), Lairë (12 enquië), Yávië (9 enquië), enderi (3 or in leapyear 6 "middle-days"), Quellë ("fading" or Lasselanta "leaf-fall", 9 enquië), Hrívë ("winter", 12 enquië), Coirë ("stirring", 9 enquië), metarë ("last-day", 1 ré).
This was adapted by the Edain into the King's Reckoning having a loa with a 7-ré enquië (the same as above except Aldúya = Aldëa, and Eärenya was between Menelya and Valarya), 12 astari (Narvinyë, Nénimë, Súlimë, Víressë, Lótessë, Úrimë, Yavannië, Narquelië, Hísimë, Ringarë with 30 ré and Nárië and Cermië, either side of loéndé with 31 ré) and 3 (or 4) non-enquië ré (yestarë [Dec. 23], loëndë and mettarë or 2-ré enderi) used until 10,900 BC.
It was replaced everywhere but the Shire by Stewards' Reckoning in which all astari were 30 ré, tuilérë (spring-day) came after Súlimë 30 and yáviérë (autumn-day) after Yavannië 30.
It was further adapted even in the Shire in 7837 BC (SR 1) and 6736 BC (SR 1100) with Shire Reckoning. Like King's Reckoning it had 7 days in a week, Sterday [Sterrendei], Sunday [Sunnendei], Monday [Monendei], Trewsday [Trewesdei], Hevensday or Hensday [Hevenesdei], Mersday [Meresdei], Highday [Highdei], and 12 30-day astari, Afteryule, --, Foreastron, Astron, Afterastron, Forelithe, Lithe, Afterlithe, --, --, Foreyule, Yule. Overlithe was added every fourth year and after the reform of 6736 BC the Yuledays, the Lithedays, Midyear's Day and Overlithe or leapday were excluded from the year's 52 weeks so that the days of the week did not change from year to year. Yuletide was a 6-day holiday from 29 Foreyule to 2 Afteryule.
New Reckoning replaced Stewards' Reckoning in Mar. 17, 6420 BC (FA 3) by King Elessar of the Reunited Kingdom. It had a yestarë, Víressë, Lótessë, Nárië, Cermië, Úrimë, Yavannië, 3 enderi (middle one, Loëndë, Narquelië, Hísimë, Ringarë, Narvinyë, Nénimë, Súlimë and mettarë. Cormarë ("ring-day"), Frodo's birthday, Yavannië 30, is doubled in leapyears.