Reckoning of Rivendell
The Eldar measured time on two scales:
- Long periods of time were reckoned in yéni, which corresponded to 144 solar years[note 1] containing 8,766 enquier (six-day weeks) or 52,596 days.
- A single solar year was called a Coranar ("sun-round") or Loa ("growth"); this was divided into six long "months", or rather short "seasons", of irregular length.
In addition to the six seasons, a coranar had additional days inserted into the calendar to bring the total to 365 days. The first day of the year was yestarë, which preceded Tuilë, and the last day of the year was mettarë, which followed Coirë. Between yávië and quellë were three enderi ("middle-days") which were doubled every twelve years as leap days.
The names of the six seasons and additional days of the coranar were:
|Quenya name||Sindarin name||English Translation||Length in Days||Relationship to the Shire Calendar, more or less[note 2]|
|Yestarë||First Day||1||6 April|
|Tuilë||Ethuil||Spring||54||7 April through 30 May|
|Lairë||Laer||Summer||72||1 June through 9 August|
|Yávië||Iavas||Autumn||54||10 August through 3 October|
|Enderi||Middle Days||3 or 6||4 October through 6 October|
|Quellë||Firith||Fading||54||7 October through 30 November|
|Hrívë||Rhîw||Winter||72||1 December through 10 February|
|Coirë||Echuir||Stirring||54||11 February through 4 April|
|Mettarë||Last Day||1||5 April|
A yén would be over 1 day too long when compared to the length of 144 solar years.[note 3] There is a note in the Red Book on the Reckoning of Rivendell that the last year of every third yén omitted the doubling of its enderi; in other words, every 432nd year only had 3 enderi and omitted the 3 leap days due in that year (see: haranyë). The note also mentions that the omission of the 3 leap days every 432 years 'has not happened in our time' (the time of the writing of the Red Book). Any further methods of adjustment are unknown.
 Days of the week
The number of days in a leap year cycle of the Calendar of Imladris is very close to number of days in a leap year cycle of the modern Gregorian calendar, since 3 leap days every 12 years in the Calendar of Imladris is the same average as 1 leap day every 4 years in the Gregorian calendar. The Gregorian calendar, however, omits 3 leap days every 400 years (the last year of a century except in centuries divisible by 400), whereas the Calendar of Imladris omits 3 leap days every 432 years.
The only correlation between this calendar and any other is a statement in Appendix D that Yestarë in the Calendar of Imladris "corresponded more or less with Shire April 6", and The Tale of Years lists the "Meeting of Celeborn and Thranduil" on 6 April in T.A. 3019, which is said to have taken place on the "New Year of the Elves".
Note that due to the differences in the leap year rules between the Calendar of Imladris and the Shire Calendar, even if the Yestarë of the Calendar of Imladris fell on a Shire April 6 in one year, that does not mean it would fall on Shire April 6 in every year. Within 4 years, after the Shire Calendar adds its leap day, Yestarë would start falling a day earlier in the Shire Calendar (April 5). This continues every 4 years until the Calendar of Imladris has a leap year and adds its 3 leap days. This would cause Yestarë to re-sync with with Shire April 6 once again; or, depending on when the Calendar of Imladris started reckoning, it could actually start falling on a day or more after Shire April 6. So Yestarë could fall anywhere from Shire April 4, 5, and 6, or April 5, 6, and 7, or April 6, 7, and 8; and if the leap years in these calendars are not in sync, that adds the possibility of Yestarë falling on a Shire April 3 or 9 in leap years of the Calendar of Imladris. Any of these may be possible, with the only known restriction that Yestarë of the Calendar of Imladris should fall on 6 April in T.A. 3019.
Although it's not stated when the Calendar of Imladris was established or from what year it started reckoning, Paul Sarando suggests one possibility in the Shire Reckoning project's "Rivendell Reckoning Notes", which seems to fit the restrictions listed above: if the Calendar of Imladris started reckoning from the first Year of the Sun in the First Age (F.A. 1), then it would have started a new 432-year cycle just before the birth of Bilbo Baggins, and its next would not be due until well after the Red Book was copied in Gondor. Also, since the Yestarë of the Calendar of Imladris should fall on 6 April in T.A. 3019, then reckoning from F.A. 1 means its Yestarë would generally fall on Shire April 5, 6, or 7 around the end of the Third Age, which appears to fit nicely with Tolkien's statement that it "corresponded more or less with Shire April 6". Note that reckoning from F.A. 1 does not necessarily mean that the calendar was already invented and in use in that year. It could have been invented anytime later, but it may have calculated its rules and leap days retroactively starting with F.A. 1.
- ↑ The number 144 (12x12) is 100 in the duodecimal system; in other words a yén is a duodecimal century.
- ↑ Based on the statement in Appendix D that Yestarë in the Calendar of Imladris "corresponded more or less with Shire April 6". Since The Tale of Years lists the "Meeting of Celeborn and Thranduil" on 6 April in T.A. 3019, which is said to have taken place on the "New Year of the Elves", this relationship applies to the years around the end of the Third Age.
- ↑ 144 years multiplied by the length of a solar year (given in Appendix D as 365 days, 5 hours, 48 minutes, 46 seconds) results in approximately 52594.8767 days.
- ↑ 1.0 1.1 J.R.R. Tolkien, The Lord of the Rings, Appendix D, "The Calendars"
- ↑ 2.0 2.1 2.2 Paul Sarando, "Rivendell Reckoning Notes", Shire Reckoning: A visualization of the calendars described in J.R.R. Tolkien's The Lord of the Rings Appendix D (accessed 15 May 2018)
- ↑ J.R.R. Tolkien, The Lord of the Rings, Appendix B, "The Chief Days from the Fall of Barad-dûr to the End of the Third Age"