Elf aging
Introduction
One of the issues Tolkien spent a great deal of time wrestling with, as most clearly evident in the Nature of Middle-earth, was the aging and lifecycle of the Elves.
The most story-critical issue he was looking to address was Maeglin: it was crucial that he be born in Middle-earth after the return of the Noldor, and yet grow to maturity quickly enough to become great among the Gondolindrim and desire his cousin Idril. Further issues of consideration, which needed to remain consistent with any proposed solution, included the following:
Man and Elf couples, such as Aragorn & Arwen or Tuor & Idril, should be of roughly similar bodily age
Finduilas was of sufficient maturity to be betrothed to Gwindor prior to the Battle of Unnumbered Tears
Galadriel was a young adult during the Flight of the Noldor, and considered an elder stateswoman by the end of the Third Age
Harmony with the overarching Elf lifecycle already established such as their being four generations in the House of Finwë in Valinor before the Death of the Trees (ex. Finwë, Fingolfin, Turgon, Idril), and the respective ages of Galadriel and Elrond when they had their children
And, lastly, Tolkien had several other self-imposed conditions he was looking to adhere to:
Elves aged analogously to Men; while the rate(s) were different they still grew from infancy to childhood to adulthood and eventually to an equivalent of old age (though not physically apparent)
The aging rate of Elves to Men was consistently declared in ratios of 12 and 144 (ex. in 144 years an Elf could age the equivalent of 1 year for Men)
My goal is to provide a solution which accomplishes the above criteria with minimal alterations to any other data provided in sources such as Laws and Customs of the Eldar or the Annals of Aman. This in turn will be a fundamental building block for later calculations such as the number of generations and population growth rate between the Awakening of the First 144 Elves and the ~ 30,000 present at the time of the Great Journey.
Terms & conventions
Tolkien provided several terms as he worked through this issue:
Coimendi ("life years"): The period of an Elf's life after ontavalië
Essecilmë (“name-choosing”): A coming-of-age ceremony where an Elf's self-chosen name is declared
Olmendi ("growth years"): The period of an Elf's life before ontavalië
Olmië ("growth")
Ontavalië ("having beget power"): The point at which an Elf can produce offspring (i.e. puberty); generally defined as 18 for females and 21 for males
Quantolië ("full grown"): The point at which an Elf is considered a mature adult and can wed; generally defined as 21 for females and 24 for males
Vinimetta ("end of youth"): The point at which an Elf starts to wane and Elf women can no longer beget children; held to be around 72 coimendi
Beyond those, there are several terms I am introducing or clarifying:
Hröamen ("body year"): the physiological age of bodily maturity, as measured relative to Men; for example, an Elf of 25 hröamendi is similar physically to that of a Man of 25 years of age
Year, Great (GY): 144 Solar Years, also known as a "long year" or yén
Year, Solar (SY): Duration of one calendar year; also known as löa (season, growth) or coranar (sun-round)
Year, Aman (AY): 10 Solar Years, the calendar system used by the Elves in Aman
The aging scheme
The primary principle is that the speed of aging starts similar to that of Men, but steadily decreases throughout an Elf's life, with a major change occurring at ontavalië. The rules, as relative against the aging of Men, are as follows:
Aging starts at an rate of ¹²/₁₂ which decreases by ¹/₁₂ per SY until reaching ¹/₁₂ where it then remains until ontavalië (i.e. ¹²/₁₂, ¹¹/₁₂, ¹⁰/₁₂ ... ²/₁₂, ¹/₁₂, ¹/₁₂)
Elf-women reach ontavalië at 144 SY, Elf-men at 180 SY
After ontavalië aging rate decreases again, this time by increasing the denominator by 1 until reaching ¹/₁₄₄ where it then remains; at that point the Elf is considered to have reached quantolië (i.e. ¹/₁₂, ¹/₁₃, ¹/₁₄ .. ¹/₁₄₃, ¹/₁₄₄, ¹/₁₄₄)
In Valinor, while under the Light of the Two Trees, after reaching quantolië aging is further slowed to a rate of 1 SY per AY (¹/₁₄₄ ÷ 10 ≈ ¹/₁₄₄₀; represented as "Ө")
An Elf "ages" with major expenditures (ex. begetting children) and traumatic experiences (ex. crossing the Helcaraxë, being held in thralldom in Angband, etc.)
Under that scheme we get the following example solar year -> hröamen for the first 144 SY:
After this point, the maturity rate changes depending on the gender, and further again on if the Elf is in Valinor or Middle-earth. Below are some sample rows for reference.
Alignment
Applying the above scheme, we have the following characters and hröamen at key events.
Arwen (born TA 241)
Celebrían waylaid (TA 2509): 33.78
First meeting Aragorn (TA 2952): 36.86
Engagement to Aragorn (TA 2980): 37.05
Finarfin (born YT 1230)
Wedding of Finarfin and Eärwen (YT 1280): 23.22
Birth of Finrod (YT 1300): 24.33 (includes +1 for begetting of child)
Birth of Galadriel (YT 1362): 27.69 (includes +3 for begetting of Angrod, Aegnor, and Galadriel)
Finduilas (born FA 272)
Bëor comes to Nargothrond (FA 311): 8.75
Death of Bëor (FA 355): 12.50
Nirnaeth Arnoediad (FA 472): 19.37
Túrin arrives in Nargothrond (FA 490): 19.58
Galadriel (born YT 1362)
Fëanor draws sword on Fingolfin (YT 1490): 20.52
Death of the Trees (YT 1495): 20.55
Fingolfin's host crosses the Helcaraxë (YT 1500): 23.91 (includes +3 for ordeal)
End of the First Age (FA 590): 28.00
Birth of Celebrían (SA 300): 32.08 (includes +2 for begetting of child)
End of the Second Age (SA 3441): 53.89
End of the Third Age (TA 3021): 74.86
Maeglin (born FA 320)
Maeglin named by Eöl (FA 332): 6.50
Aredhel & Maeglin enter Gondolin (FA 400): 12.50
Húrin and Huor brought to Gondolin (FA 458): 17.42
Nirnaeth Arnoediad (FA 472): 18.67
Tuor comes to Gondolin (FA 495): 20.67
Wedding of Tuor and Idril (FA 502): 21.16
Birth of Eärendil (FA 503): 21.25
Fall of Gondolin (FA 510): 21.54
Further, we can check against specific statements:
For at the end of the third year mortal children began to outstrip the Elves, hastening on to a full stature while the Elves lingered in the first spring of childhood. — Laws and Customs Among the Eldar
By the end of the 3rd year, an Elf-child and Man-child would look fairly similar, only a few months difference. By the end of the 4th year however, the difference would be noticeable, with the Elf-child looking ~ 6 months younger. Assuming that "first spring of childhood" can refer to the ages 6 - 11, from a mortal perspective they would certainly linger there, staying in that period from their 12th coranar until their 78th.
Children of Men might reach their full height while Eldar of the same age were still in body like to mortals of no more than seven years. — Laws and Customs Among the Eldar
Assuming that full height for Men is reached by 18, that matches up exactly to when an Elf-child would appear seven.
The Eldar wedded for the most part in their youth and soon after their fiftieth year. — Laws and Customs Among the Eldar
This points to a switch in the use of "year" from "solar year" to "Aman year", and refers to Elves in Valinor. As a case in point, Finarfin was born in YT 1230, and married fifty 'years' later in YT 1280.
Not until the fiftieth year did the Eldar attain the stature and shape in which their lives would afterwards endure, and for some a hundred years would pass before they were full-grown. — Laws and Customs Among the Eldar
There are two possible explanations for the "hundred years" statement.
First, continuing with the assumption that this is speaking of the Elves in Valinor, this would be about 100 Aman years, or 1000 solar years. With the reduced aging rate post quantolië, an Elf-woman would be at 20.44 hröamen and an Elf-man at 23.41; reasonable that they might still be growing slightly at that point.
Second, it's also possible that, this could be "100" in dozenal (as the Noldor used), and thus actually 144 in decimal; in that case, this could be referring to Elf-women reaching ontavalië and thus being considered "full-grown".
Sources
NM.XII.01: The Eldar distinguished between olmië and coivië. The former was the period or process of their ‘growth’ from conception to maturity of body, and was achieved twelve times as rapidly as the coivië. This latter was the process of ‘living’ or “enduring in Arda”, and of acquiring skill, knowledge, and wisdom.
NM.XII.02: The olmië was achieved at a rate equalling 12 löar (or sun-years) to 1 löa of human life. An Elvish ‘growth-year’, or olmen, was therefore 12 sun-years. Thus from conception to birth they grew in the womb 9 löar. When born they continued to grow at this rate until maturity of body.
NM.XII.03: The coivië then proceeded at a rate 12 times as slow, so that 144 löar (or sun-years) may be more or less equated, so far as change or alteration are concerned, with 1 year of human adult life. This length of time was the yén or Elvish year, or coimen as a measure of age.
NM.XII.04: The arrival at maturity was recognized at once by individuals, and occurred with little variation. It was (in times of peace) recognized also by the Elvish families and communities and honoured with ceremony, part of which was the announcement of the essekilmë or personal “choice of name”.
NM.XII.05: In this, say the Eldar, more of their “youth” is expended than is the case with Men; and for Elf-men, they say that each child costs as much as 1 coimen or life-year; but for Elf-women as much as, or more than, 2 coimendi. So that for the parents of six children the “waning”, or passing of youth, might come 6 life-years sooner for the father, but for the mother 12 life-years sooner, or more.
NM.XII.06: Other special “expenditures”, such as grief, long and arduous travel, great craft-labours, and especially the bodily recovery from grave wounds and hurts, might also hasten the waning. It is said that the “dreadful year” (1 yén) of the journey of the Exiles from Valinor, over the Grinding Ice, to Beleriand, affected those of the Ñoldor who endured it as greatly as three normal life-years.
NM.XII.07: Six coimendi was in fact the longest interval found in the early histories; except in Aman where “waning” was retarded, and an interval of 12 coimendi occasionally recorded.
NM.XII.08: The only effect of residence in Aman upon the Eldar seems to have been this: in the bliss and health of Aman their bodies remained in vigour, and were able to support the great growth in knowledge and ardour of their spirits without any appreciable waning (except in very special cases: such as that of Míriel). Those who entered Aman, from without or by birth, would leave it in the same health and vigour as they had to begin with
NM.XVII.01: First Elves. Awoke at ontavalië [‘puberty’] ([males] 21/[females] 18). But they did not turn to marriage until maturity of the elf-man (24), the elf-woman then being 21. These ages were ever after held the earliest suitable ages for marriage, though elf-women were sometimes married earlier. (As soon as they were 18 they were sought in betrothal – a period which, whenever entered, usually lasted 3 years.)