Reckoning of Rivendell
The Reckoning of Rivendell or Imladris is the only recorded Elvish calendar. It contained six 'months' (more akin to seasons), rather than twelve, and its arrangement reflects the Elvish preference for counting in sixes and twelves. Because of their long lifespan, the Elves tended to divide time into Yéni of 144 years each, but they also had a period equivalent to a year, called a Loa or Coranar.
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Rather than adding one day every four years, as with the modern leap year, the Elves instead added three days every twelve years. In these years, the Enderi ('middle-days') of each year were doubled from the usual three to six. For precision, the last year of every third yén was shortened by three days, rather than lengthened (the last year of a yén was always a 'leap' year). This was a rare occurrence, happening only once every 432 years.
According to Jim Allan in An Introduction to Elvish, each of the elvish month names has a correspondence to the months of the French Republican Calendar. (cf. Nénimë/Pluviôse mean 'Rainy', Súlìmë/Ventôse mean 'Windy' etc). Jim Allan suggests that Tolkien used this similarity because the French Republican Calendar was based on earlier unrecorded Germanic month names.