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I thought that some of you might appreciate the information on the Calendars JRRT came up with for Middle-earth that one of the posters, Oddyseus, at Chapter of the Week came up with. With his permission, I am pasting his article here:

Appendix D: The Calendars

(I have followed the precedent of marking particular discussion
points as footnotes to the summary. These are a little sparse, so
please interject any comments or queries you may have regardless of
whether or not I've thought of something to say about any specific issue.)

In this essay J.R.R. Tolkien describes the calendar used by the
hobbits of the Shire, including an outline of its historical
antecedents among Men and Eldar. After introducing the Shire Calendar
he describes the quite different Elvish scheme, taking the calendar
of Imladris (Rivendell) for an exemplar, then provides accounts of
the Númenorean system, known as the Kings' Reckoning, and the later
reforms in Gondor and the Shire that led respectively to the
Stewards' Reckoning and the Shire Reckoning. A discussion of
pertinent terms from Quenya, Sindarin, and Westron follows. The
Appendix concludes with notes concerning the relations of the Shire
calendar, as used throughout the _LotR_ text, with the Gregorian
calendar we use today and with the New Reckoning that was adopted by
the Dúnedain at the beginning of the Fourth Age.

We are first presented with a convenient table displaying the "Shire
Calendar for use in all years". This calendar bears a sufficient
resemblance to ours that Tolkien was able to use modern terms for
nearly all the dates in _LotR_, more or less including them with the
Westron words and names that he renders into English in his authorial
persona as editor/translator of the _Red Book of Westmarch_. Beside
encountering occasional discrepancies concerning the number of days
in each month, and the slightly different relation between the dates
and the seasons (which are offset by a few days from ours), a reader
could take the story's dating of events at face value without
significant consequences [1].

However, for those who enjoy such minutiae there are several
interesting differences in detail. The most salient are that the
weekday corresponding to a given date is the same every year, and
that there are special days that belong to none of the months, which
all have exactly thirty days. Together these features give the Shire
calendar a degree regularity exceeding ours, quite reminiscent of two
modern reformed calendars: that officially established during the
French Revolution [2], but receiving little popular acceptance and
(unlike the metric system introduced around the same time) lasting no
longer than the revolutionary regime, and the "World Day" calendar
proposed somewhat over half a century ago.

In _PoME_ (_The History of Middle-earth_, vol. XII) Christopher
Tolkien notes that the only typescript of Appendix D began with a
typeset proof of the tabulated calendar (but including a column
showing the weekdays that was omitted from the printed editions,
apparently to save space), which JRRT had already received from the
publishers while finishing the text, suggestive of the haste with
which the appendices were prepared. This also implies that although
the Shire calendar was story-internally the newest, being a
descendant of the Elvish calendar _via_ that of the Dúnedain, it was
the first to be invented; story-externally its historical antecedents
were apparently developed retrospectively.

Before getting into the calendar descriptions a brief mention of the
problems facing calendar-designers seems _à propos_ (despite being
OT!) in order to help those who aren't astronomers to appreciate the
motivation for some of the details they'll encounter. Fortunately all
of Tolkien's calendars are solar, _i.e._ maintaining a fairly
constant correspondence between dates and seasons; these present far
fewer complications than do lunar calendars like the Jewish and
Islamic ones. The most inconvenient fact one has to deal with is that
the basic units of days and years are incompatible, causing any
reckoning that has the same number of days in every year to drift
rapidly out of synchronization with the seasons. The tropical year is
about 365.2422 days long [3]; the idea is to approximate this figure
with a reasonably convenient fraction. The Julian calendar alternates
three years of 365 days with one of 366 for an average of 365.25; its
successor, the Gregorian calendar, skips three leap-years every four
centuries, refining the approximation to 365.2425, gaining only three
days on the Sun every ten thousand years. All of Tolkien's calendars
described in this appendix start with the same approximation as that
of the Julian calendar, averaging 365.25 days per year over the short
term, but their methods for improving on this rather inaccurate
reckoning differ.

The Elvish calendar was quite unlike ours in several respects. Since
the Eldar counted in duodecimal, they grouped days and years by
multiples of six or twelve wherever possible. The Elvish version of a
week (_enquië_) had six days. Their long year or _yén_ comprised
52,596 days or 144 solar years; in Rivendell the latter was divided
into six periods or seasons, four of 54 days each and two of 72, with
five additional days to make 365 [4]. Two of these extra days, the
last (_mettarë_) of one year and the first (_yestarë_) of the next,
fell at the vernal equinox; the other three, called Middle-days
(_enderi_) were inserted around the autumnal equinox. Instead of
having a leap-year one day longer than usual every four years, the
Elves doubled the _enderi_ every twelfth year, to the same net
effect. The last triple-leap-year of every third _yén_ was replaced
with an ordinary year to eliminate most of the excess, bringing the
average down to about 365.2431 days per year, only a minute and a
quarter longer than the true value. It's implied that further
(unspecified) corrections were made, but even without them this
calendar would have accumulated an excess of just a few days over the
33 _yéni_ that had elapsed since the founding of Imladris.

The Kings' Reckoning of the Númenoreans, in use from the beginning of
the Second Age, had a more familiar arrangement. There were twelve
months, ten of 30 days and two (June and July) of 31, with three
additional days inserted at the beginning, middle, and end of the
year; in leap-years there were two mid-year days instead of one. The
last leap-year of each century was replaced with an ordinary year,
except that the last year of each millennium was a leap-year
augmented by an additional day [5], for an average of 365.242 days
per year. The Númenorean year began at the winter solstice instead of
the vernal equinox [6] and their weeks had seven days.

Early in the second millennium of the Third Age a calendar reform was
undertaken in Gondor by Mardil the Steward. Beside making a one-time
correction that added two days to the year T.A. 2059 [7], he made all
the months equal in length, the days that were taken from June and
July being inserted near the spring and fall equinoxes. We may
probably safely assume that the extra day in leap-years was still
inserted at midsummer. This produced a very tidy arrangement, as follows:

New Year's Day (Winter Solstice or just after)
January, February, March - 30 days each
Spring-day (Vernal Equinox)
April, May, June - 30 days each
Mid-year's Day (Summer Solstice)
or, in a leap-year, two Middle-days
July, August, September - 30 days each
Harvest-day (Autumnal Equinox)
October, November, December - 30 days each
New Year's Eve (Winter Solstice or just before)

A form of the Kings' Reckoning remained in use in the Shire, despite
being superseded in other Westron-speaking lands; for quite some time
the only difference was that the Hobbits had three "Lithedays" at
midsummer instead of one, accordingly giving June and July only
thirty days each like the other months. In the time of Thain Isengrim
II (Took), fl. c. T.A. 2700, the Shire-reform removed Mid-Year's Day
(and the "Overlithe" of leap-years) from the cycle of weekdays so
that there were exactly 52 weeks in every year. From then on 2 Yule
(New Year's Day) was always a Saturday and every other date likewise
fell on the same weekday each year. It is unclear how (if at all) the
Shire Reckoning made corrections to the 'Julian' year averaging
365.25 days; in Gondor the usual Kings' Reckoning addition was made
to the year T.A. 2000, but in the Shire this year was numbered 400
and the Hobbits might well have postponed the adjustment until S.R.
1000 -- or neglected it altogether [5,7].

A fairly detailed survey of calendar-related nomenclature and
etymology is given [8]. Particularly interesting is the 'arranged
coincidence' whereby the names of the weekdays used by the Hobbits,
translated from Quenya of the Númenoreans', turn out to be similar in
sound to our English terms -- a sort of extended pun that one can
imagine Tolkien's pleasure in devising. Saturday corresponded to
"Sterday" < _Sterrendei_ (Star-day), but Sunday < _Sunnendei_ and
Monday < _Monendei_ were derived just as in English. The rest are all
ostensibly happy accidents like "Sterday": Tuesday was "Trewsday" <
_Trewesdei_ (Tree's-day), Wednesday was "He(ve)nsday" < _Hevenesdei_
(Heavens-day), Thursday was "Mersday" < _Meresdei_ (Sea-day), and
Friday was "Highday" < _Highdei_.

WIth the advent of the Fourth Age a new calendar was inaugurated,
although in the Shire the traditional system remained in use. The
year now began on the anniversary of the destruction of the RIng,
with three Middle-days between September and October. Including the
first and last days of the year, the five 'epagomenal' days now
corresponded quite closely to those of the Elvish calendar, with two
in the spring and three in the fall.

COMMENTS & QUESTIONS

1. Those who don't care for the fine details of world-building may be
grateful for not having to deal with an 'alien' calendar on top of
the imagined geography, names and languages. Is it likely that
Tolkien made the Shire Reckoning mostly comparable with our calendar
out of consideration for such readers, or did he perhaps devise it as
something of an afterthought, keeping it similar enough in structure
that it could be 'patched in' without requiring extensive revisions
of the text beyond small adjustments to some of the dates?

2. It strikes me that the motives of modern calendar-reformers would
be quite antithetical to Tolkien's world-view, reflecting a
rationalistic, even technocratic, attitude that would seem to suit
Saruman much better than e.g. the Elves. Indeed the French
revolutionaries were decidedly anticlerical, and many of their
reforms sought to get rid of what they perceived as 'religious
baggage' that didn't belong in an egalitarian, progressive society.
Against this, though, we can set Tolkien's hobbit-like fondness for
tidiness and thoroughness. There's a passage in _LotR_ that alludes
to this 'legalistic' side of the Hobbit character, mentioning their
appreciation for meticulous documentation of pedigrees and the like,
but I don't remember where it appears -- anyone?

3. In the first paragraph of the Appendix Tolkien writes, "The year
no doubt was of the same length [as ours], for long ago as those
times are now reckoned in years and lives of men, they were not very
remote according to the memory of the Earth." Measuring the length of
the year is a much more complicated matter than may appear on its
face; where great precision is required it even makes a difference
what point in the cycle one chooses as the beginning and end. I won't
go into the gory details, but suffice it to say that Tolkien's
assumption is quite reasonable, and the figure of 365 d 5 h 48 m 46 s
that he used, while differing by a second or so from the best modern
values, is perfectly adequate for all but the most rigorous calculations.

4. The earlier draughts reproduced in _PoME_ contain two very
different versions of the Elvish calendar; it seems that Tolkien's
ideas on the subject were developing quite rapidly. Had he more time
available to work on them, his final results may well have been quite
different again. Wasn't it during this period that he began thinking
about expanding the timescale of the First Age and 'inflating' the
length of the Valinorean and Eldarin years? At least a germ of this
development appears to be present in the 'great year' or _yén_ of 144
solar years. The citation of Galadriel's Farewell is noteworthy, as
where she sings of "long years numberless" we are to understand these
as lasting 144 years each. There seems to be some poetic licence at
work here: while the seven millennia she's been in Middle-Earth is
indeed a long time by human standards, that amounts to 'only' about
fifty _yéni_, scarcely "numberless"!

5. This is just my conjecture. The fine adjustments that were made to
keep the Númenorean and Gondorian calendars in synchronization with
the seasons over the long term present some difficulties. According
to my accounting there were 36,524 days to the century, so in a
millennium the uncorrected calendar would be running 365,242.2 -
365,240 = 2.2 days behind the Sun. Since we are told that the
"millennial deficit" *after* correction was about 0.2 day, this
implies that *two* days were added every thousand years; while one of
these could come from the restoration of the usually omitted
centennial leap-day, still another would have to be inserted. There's
no indication of where in the calendar this day would have been placed.

6. Could this be an echo of the shifting of New Year's Day in
XVIII-c. Britain from 25 March (Lady Day, or the Feast of the
Annunciation) to 1 January? Note that the beginning of the New
Reckoning year had been 25 March in the previous calendar: while of
course the story-internal explanation of commemorating the defeat of
Sauron is quite adequate, the significance of this date to Catholics
is worth consideration.

7. The confusion (mine at least!) over the adjustments deepens
considerably with Mardil's reform. These notes are already
overburdened with figures, so I won't reproduce my work here
(although if anyone else is interested in helping me get to the
bottom of the matter I'll be happy to follow up with some details),
but the short version is that the account, as I read it, doesn't add
up. AFAICT Mardil overcorrected by a day, creating an excess where
there had been a deficit. To make matters worse, in his discussion of
the dating of events in the _LotR_ text, near the end of this
appendix, Tolkien says that the fall of the Dark Tower occurred on
"March 25 in both Kings' and Stewards' Reckoning." If the latter
reformed the former by making 'unscheduled' corrections, how could
the two agree at any time from that point onward?

8. It's only natural that Tolkien would give considerable attention
to the linguistic matters pertaining to the calendars. Indeed it
wouldn't be out of character for him to have taken up the subject
primarily as a pretext to explore the aspects of his languages that
it leads into. However, in a broader view both timekeeping and
language can be considered part of a culture's 'infrastructure'; the
systems we devise for organizing time may be thought of as
paralleling or complementing, on a limited scale, the grammatical
structures that provide a framework for thinking and communication.
Just as a people's language reflects their culture and history, some
of their character might well be revealed through their approach to
counting the days.

--
Odysseus

I was somewhat disappointed at the lack of discussion generated at r.a.b.t./a.f.t by my own CotW summary on the Hobbit Family Trees last week, which many of you were kind enough to vet for me. However, I try to remember that in "Concerning Hobbits" JRRT said "all but Hobbits would find them exceedingly dull". The info got a lot more interest here, so, guess what, friends--we must be hobbits, LOL!

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