The Eldar divided their solar year (or loa ‘growth’) into six seasons of unequal [1] length. The lengths are unequal because the Quendi were more sensitive to and concerned with the transition of one season into another and the seasonal changes in vegetation as the wheel of the year turned.

The table below gives the names of these seasons in Quenya and Sindarin, as well as the length of each season in days:

Important Transition dates

(I did not include Mettarë because it is the day just before Yestarë, and thus is the equivalent of “New Year’s Eve”. It is important as a holiday, but not as a seasonal transition in itself.)

When does the loa start, and why?

Luckily, some Fellow Tolkienists have already done this part of our calendar work for us. I refer to the entry in the Encyclopedia of Arda, which has a JavaScript calculator to calculate any given date:

As you can see, Shire April 6th (6 Astron) is equivalent to the beginning of the Elven year (loa); which corresponds to our March 28th. This calculator takes into account fact #3 above, and applies the offset to the dates. (For further confirmation of this fact, I refer interested parties to the notes for this section of their web site.)

Translating the loa to the Modern Calendar

The question immediately arises: Why would the Quendi begin their solar year approximately a week after the vernal equinox, and not directly on the equinox itself? The explanation, I think, is that the loa was not strictly a rule based calendar, but neither was it precisely a lunisolar calendar, but something of a combination of both – with a strong stellar-calibration component. As we know, ‘Summer’ and ‘Winter’ each had 72 days, and the remaining seasons 54 each. It is significant that each of these numbers is evenly divisible by 6, as the Quendi used a six day ‘week’, which they called an enquië. [Much more information on the Elven view of Time is explained in the article directly following this one.]

Additionally, we know (from linguistic evidence associated with the Lost Tales), that both the Summer and Winter solstices were celebrated. Given these facts, we now look for evidence that the Quendi used some sort of astronomical calibration [2] for their calendar, much like the ancient builders of Stonehenge were said to do, or the ancient Mayans. Whatever the astronomical event was, it must have been something fairly obvious that could be noted and acted upon by a population that was at least semi-nomadic (references to Elvish “wandering”—to say nothing of the Great Journey—are scattered throughout the whole Legendarium). This would seem to rule out large edifices such as Stonehenge or pyramidal constructions for the population as a whole, though it is certain that the Noldor, in particular, attained and surpassed such technology. Using either of the solstices as a calibration point doesn’t seem to fit; as each solstice would occur 5 enquier after the start (or 7 enquier before the end) of ‘Summer’ or ‘Winter’, respectively. This doesn’t seem to make sense given the fact that both ‘Summer’ and ‘Winter’ contained 12 enquier, and thus are evenly divisible into two halves of 6 enquier each. And, since the seasons are of unequal length and none fall upon an equinoctial boundary, the equinoxes don’t seem to be likely points either.

Surprisingly (and serendipitously) I discovered that the Pleiades, called the Remmirath (‘Netted Stars’) by the Elves, appears overhead (culminates) at midnight on November 21st – the beginning of Hrivë (Winter). In addition, they rise with the Sun at the beginning of Lairë (Summer), which admittedly cannot be seen directly – were it not for the fact that another constellation, which we know as Corona Borealis, culminates at midnight at the beginning of Lairë, as it lies exactly opposite the Pleiades in the sky. [3] Both of these events are explained more fully in the The Pawnee Star Calendar. Thus, using the date of November 21st on the Gregorian Calendar as a calibration date, and applying the length of the seasons forward and around from this date, we arrive at exactly the points determined by calculation using the Encyclopedia of Arda’s calendar [4] .

I should also mention here that the stellar configuration at the end of Varda’s labors in Chapter 3 of the Silmarillion matches what is seen at midnight, November 21st; and I here attach an image produced by the astronomical program “Starry Night” to prove it:

“Of the Coming of the Elves” describes Varda’s labours and the resulting sky:

Then Varda went forth from the council, and she looked out from the height of Taniquetil, and beheld the darkness of Middle-earth beneath the innumerable stars, faint and far. Then she began a great labour, greatest of all the works of the Valar since their coming into Arda. She took the silver dews from the vats of Telperion, and therewith she made new stars and brighter against the coming of the Firstborn; wherefore she whose name out of the deeps of time and the labours of Eä was Tintallë, the Kindler, was called after by the Elves Elentári, Queen of the Stars. Carnil [Mars] and Luinil [Vega*], Nénar [Capella*] and Lumbar [Saturn], Alcarinquë [Jupiter] and Elemmírë [Mercury] she wrought in that time, and many other of the ancient stars she gathered together and set as signs in the heavens of Arda: Wilwarin [Cassiopeia], Telumendil [Gemini?], Soronúmë [Lyra*], and Anarríma [Leo*]; and Menelmacar [Orion] with his shining belt, that forebodes the Last Battle that shall be at the end of days. And high in the north as a challenge to Melkor she set the crown of seven mighty stars to swing, Valacirca, the Sickle of the Valar and sign of doom [Ursa Major—The Big Dipper].

It is told that even as Varda ended her labours, and they were long, when first Menelmacar [Orion] strode up the sky and the blue fire of Helluin [Sirius] flickered in the mists above the borders of the world, in that hour the Children of the Earth awoke, the Firstborn of Ilúvatar. By the starlit mere of Cuiviénen, Water of Awakening, they rose from the sleep of Ilúvatar; and while they dwelt yet silent by Cuiviénen their eyes beheld first of all things the stars of heaven. Therefore they have ever loved the starlight, and have revered Varda Elentári above all the Valar. [5]

The Seasons and their Festivals in Detail

March 28th: Vinya Loa(‘New Year’). Yestarë is the first day of the Elven Year (loa) and the eve of Spring (Tuilë). Though no specific festival is detailed, this is probably something like Ostara. First Spring flowers (snowdrops and crocuses) are blooming, snow is disappearing, and the new life which appeared in ‘Stirring’ (Coirë ) is beginning to burgeon. Also it is the New Year, and so probably had a something of a New Year's feel to it, but probably amplified because of the vernal energies. A possible alternative name for this time is Gwirith (‘Young, youthful’–this word was certainly also applied to new leaves/plant life). [6]

It is said that Lúthien danced on this day when long ago she first met Beren in the forest of Doriath:

A night there was when winter died;

then all alone she sang and cried

and danced until the dawn of spring,

and chanted some wild magic thing... [7]

May 21st: Nost-na-Lothion, the `Birth of Flowers' festival. Beginning of Summer (Lairë). This festival appears both within the text of “The Fall of Gondolin”:

[...] In these ways that bitter winter passed, and the snows lay deeper than ever before on the Encircling Hills; yet in its time a spring of wondrous glory melted the skirts of those white mantles and the valley drank the waters and burst into flowers.

So came and passed with revelry of children the festival of Nost-na-Lothion or the Birth of Flowers, and the hearts of the Gondothlim were uplifted for the good promise of the year... [8]

And in the linguistic information from the “elfling” Elvish Linguistics List we find:

SPRING - Tuilere, tuile

March - Lunde susuulima

April - tuileris, (month of Vana)

Lunde timpinea

May - Lotession, Kalainis Lunde lootea

Nost-na-Lothion `Birth of Flowers' a spring festival celebrated in

Gondolin (I place it on May Day, May 1st, because May Day was trad. Celebrated when the hawthorn bloomed, with a May pole and a May Queen, etc.)

A glance at the Quendian calendar, though, would show that this festival cannot have been celebrated on May 1st as that author supposes, because that date is an uneven fraction of an enquië from the beginning of Spring (34 days if the start-date is assumed to be Yestarë, 33 days if it is assumed to be the first day of Tuilë). So the only possible date for the Nost-na-Lothion given the structure of the Quendian calendar and the fact that it is a festival of flowers is May 22nd, the start of Summer (Lairë).

The Pleiades rise with the sun on this date.

June 21st (Solstice): The 'Gates of Summer' (Tarnin Austa) [9] festival which starts the following night and anticipates the rising of the sun. The fullest description is from the Lost Tales:

[…] and now at length is that great feast Tarnin Austa or the Gates of Summer near at hand. For know that on a night it was their custom to begin a solemn ceremony at midnight, continuing it even till the dawn of Tarnin Austa broke, and no voice was uttered in the city from midnight till the break of day, but the dawn they hailed with ancient songs.

For years uncounted had the coming of summer thus been greeted with music of choirs, standing upon their gleaming eastern wall; and now comes even the night of vigil and the city is filled with silver lamps, while in the groves upon the new-leaved trees lights of jewelled colours swing, and low musics go along the ways, but no voice sings until the dawn.

The sun has sunk beyond the hills and folk array them for the festival very gladly and eagerly -- glancing in expectation to the East. [10]

August 1st: Yávië, Elven Lammas (probably with a very similar focus to the current one) [11] . End of Summer/Beginning of Autumn (First Harvest).

NOTE: It may seem strange to say summer has ended at the beginning of August, but they meant that the time of growth had ended, and the time of maturation was at hand. Also, I have placed this festival on August 1st rather than the mathematically calculated date of August 2nd, because Lammas is traditionally celebrated on August 1st and it seemed silly to be off by one day. In addition, this day and February 1st are the two dates that coincide with the neo-Pagan cross-Quarter calendar in common use – and I do not think that this is a coincidence.

September 25-27th: The 3 Middle-Days (Enderi). End of the "warm weather" period. Beginning of later (sometimes called ‘Second’) Autumn and feeling of yearning/sailing/traveling, falling leaves, waning daylight, etc. Beginning of Fading (Quellë). This season is what everyone thinks of when they hear the word ‘Autumn’.

For the description of the festival on these days, we have a slight problem in that all sources I can find mention them as "holidays", but no specific details are given anywhere I can find – either on the 'net or off of it using authentic sources. So, what we have here are 3 days set aside at a time when leaves are falling from the trees, the Harvest Moon shines in the sky, and Elven thought (even in early times) must have turned towards Valinor -- or at least of traveling. I think even this excerpt from the Narn i Hîn Húrin may prove illustrative:

[...] But it chanced in the third summer, when Túrin was twenty years old, that desiring rest and needing smith-work for the repair of his arms he came unlooked for to Menegroth in the evening; and he went into the hall. Thingol was not there, for he was abroad in the greenwood with Melian, as was his delight at times in the high summer. (This was probably sometime after midsummer, probably stretching through First Autumn)

[...] Soon afterwards Thingol and Melian came back to their halls, for the summer was waning; and when the King heard report of what had passed he sat upon his throne in the great hall of Menegroth, and about him were all the lords and counsellors of Doriath. (This had to have been near the time of the enderi, as likely Thingol and Melian would be returning from their 'vacation' to attend the festivities.)

It seems reasonable to assume that this festival took the place of Samhain, though being earlier, was probably more associated with the change of the season itself rather than a harvest and without the “thinning of the veil” aspect emphasized by today’s Neo-Pagans. [See also Turuhalme below for more about this difference.] That Elves were more hunters than agriculturalists is pretty clear; probably their encounter with humans benefited them as much as the humans, as they were then freer to focus upon cultural pursuits.

November 21st: Cuivérë Quendiva [12] , “The Awakening of the Quendi”. On this night, the Pleiades culminate at midnight and Hrivë (Winter) begins. This is the only transition day in the loa for which no reference for a festival can be found. Given this fact, and the fact that the night sky on this date resembles that under which the Quendi first awoke in Arda (see picture above), I believe that it was a day for meditation and reflection rather than of festival as such.

It is also quite cold at this time of year, which would tend to discourage large outdoor gatherings. Though, given the importance of the night sky on this date, I am sure that many Quendi did incorporate viewing the stars into their meditations.

December 21st (Solstice): Turuhalmë, (“The Logdrawing”). Tale-telling before the Tale-fire. Remembering one's ancestors. Kind of like Yule but 'deeper'.

While it may be tempting to gloss over this holiday, saying it's like the rebirthing of the sun holiday of Yule celebrations, it's definitely deeper with its tale telling of "war stories." Two different ancient northern cultures have left us Neolithic evidence that they linked the winter solstice with their dead by lighting tomb constructions with the sunrise light of the solstice morning. One is in Ireland and another is in the Orkney Islands off the coast of Scotland:

Newgrange Passage Tomb

Maeshowe chambered cairn

The closest reasoning in current pagan practices that I can see relating to this is in the reference on an Asatru site saying that Winter Solstice is a time,

[...] for contact with those who had gone before. With the dead ancestors of the celebrant. Maybe its extreme length of darkness each night, maybe it's the cold, death-like grip of Winter. Maybe it's the fact that “death” reins supreme at this time of year, as all the plant of summer have either died or become dormant. Whatever the reason, those who follow the old religion know, from personal experience, that it is a time of magic, and contact with the spirits of our ancestors and even the gods and goddesses themselves. It is a good time to cast the runes for the coming year. It is an end, like the end of life. And it is at this same time a beginning, like birth. A magical time!

[from "YULE: The significance of the Yuletide Festival within the Religion of Asatru/Odinism" By Godi Edred Wodanson (E. Max Hyatt) ]

The Book of Lost Tales gives this description:

[...] The day of Turuhalme was come, and the company from Mar Vanwa Tyalieva went into the snowy woods to bring back firewood on sleighs. Never was the Tale-fire allowed to go out or to die into grey ash, but on the eve of Turuhalme it sank always to a smaller blaze until Turuhalme itself, when great logs were brought into the Room of the Tale-fire and being blessed by Lindo with ancient magic roared and flared anew upon the hearth. Vaire blessed the door and lintel of the hall and gave the key to Rumil, making him once again the Door-ward, and to Littleheart was given the hammer of his gong. Then Lindo said, as he said each year: ‘Lift up your voices, O Pipers of the Shore, and ye Elves of Kor sing aloud; and all ye Noldoli and hidden fairies of the world dance ye and sing, sing and dance O little children of Men that the House of Memory resound with your voices ...’

Then was sung a song of ancient days that the Eldar made when they dwelt beneath the wing of Manwe and sang on the great road from Kor to the city of the Gods… [13]

So it seems that memories and Tale-telling was a major feature of this holiday. In fact, the Silmarillion was designed to be told in just such a fashion—it was this archetypal idea that Tolkien had in mind.

February 1st: Sovalwaris, Beginning of 'Stirring' (Coirë) and new Life.

There is rather scant specific information on this holiday, but the reference from the “elfling” list says:

February - Amillion (month of Amillo), Sovalwaris

i Sovalle `the Purification' is some sort of purification ceremony that should involve `washing' or `bathing'. I have placed it in February because of the name Sovalwaris.

This leads us to this entry in the Appendix to The Lost Tales I:

Amillo This appears in QL but with no indication of meaning; Amillion is Amillo's month, February (one of the most 'primitive' entries). {That is, one of the earliest ever set down by Tolkien; before the narrative Legends were written.}

It seems, given this, that this ceremony had much in common with Imbolc, and is held on the same day.

These make for great evenings! In autumn, the full moon rises just after sunset and crops are flooded with moonlight. This lasts for days. But as the year moves onward, the angle at which the moon orbits the earth changes so that the angle at which the moon seems to climb up the sky grows steeper. By spring the moon rises so sharply that there is a much longer "waiting period" each successive night before the moon comes over the hill.

In spring, around the time of the vernal equinox, the angle at which the moon's orbit intersects the horizon is at its greatest, and you don't see the round, full moon as often. Is it any wonder that Halloween isn't observed in March?

Usually, the vernal equinox begins on March 21st, whereas (when translated to our calendar) the Elven New Year begins on March 28th. That is, one quarter orbital period of the moon later -- as near was we can judge given that all days are given as whole number values.

So, if the moon is new on the equinox, one quarter orbital period brings us to a first quarter (half illuminated) moon. Also, at this time of year, "A first-quarter Moon follows a daily path in the sky corresponding to that of the Sun after three months. Hence it comes at the highest altitude — or "runs high" — at or near the vernal equinox. "

Leaving aside the inherent variability of the moon's orbit now (and evidence from the Sil that it was even more so when it first appeared (according to the myth it rose in the West)), I think what is important here is the archetypal image: a dark sky sprinkled with stars and hosting a half-illuminated or crescent moon.

[4] Save in the few cases where we in Tië eldaliéva have chosen to shift them by a day to bring them into nodal alignment with the Neo-Pagan Wheel of the Year in common use (i.e. coinciding at some points, but not at every point).

[5] Those who are non-Tolkienists may be unaware that the assignment of these celestial bodies mentioned in this paragraph was a matter of debate at one time, and the matter was left unresolved. I believe that this was due to many being unfamiliar with the deeper and more obscure material found within the volumes of HOME, and too many modern people being basically unfamiliar with the night sky and astronomical information in general. I am familiar with both: I have studied Tolkien since I was 12 and have been a sky-watcher just as long, so I believe that I am qualified to solve this puzzle.

The names followed by an asterisk are not directly identified by Christopher Tolkien in his analysis of his father’s notes. Most of this information is to be found in the prefatory note to the index of Morgoth’s Ring (HOME volume X). One will note in the description of Varda’s Star Making that it is in two parts: the first deals with her making “new stars and brighter”. Since planets and bright stars are mentioned in the same category here, we can postulate that it was the relative brightness of the objects that lead to their being important enough to receive names, not whether they moved against the background stars or not. In fact, the only star-like objects that do not fit here with regard to the quality of marked brightness are the assignments that most Tolkien scholars give to Nénar and Luinil as Uranus and Neptune—an assignment which Christopher Tolkien himself discounts (see the Index to Morgoth’s Ring for the full discussion).

The second period of Star Making was when Varda formed the constellations: “many other of the ancient stars she gathered together and set as signs in the heavens of Arda.” In the names which follow, some clues can be found from the meaning of the Quenya names themselves.

I will now present all of the hitherto unidentified names, and my reasons for making their assignments:

Luinil [Vega]: The note for Luinil says “The name of a bright star”. It also contains the element luin, meaning blue. Since these Legends are North-centric, this means a bright blue star somewhere on the Northern celestial sphere is a candidate, and that this star should be especially bright to deserve special mention (as explained above and supported by Christopher’s interpretation). Now Capella, Vega, and Arcturus are the brightest stars on the Northern celestial sphere.† Of these, only Vega is noticeably blue, so this, and the fact that it is on the opposite side of the celestial sphere from Capella and thus does a sort of ‘dance’ with it as the seasons turn† was my reason for selecting it.

Nénar [Capella]: The note for Nénar also indicates that this is a bright star. Its name contains the element nén, which means “Water”. It is also almost directly overhead at the beginning of Coirë (Stirring) in the early evening after sunset†. This would be February on our Calendar, and is called Nénimë in Quenya. This month-name also contains the “water” element, nén, and is indeed very wet in many Northern locations. Hence, my choice.

Soronúmë [Lyra]: This constellation was not always thought of as a Lyre, but in fact had an ancient association with birds, particularly birds of prey and Eagles.‡ Since it’s name means something very like “Eagle of the West”, and the fact that Lyra is more prominent in the Northern hemisphere than Aquila, the modern Eagle constellation, and rises more truly East (this particular fact has to do with the directional assignments in our Spiritual system, which is not a public matter for now), we have chosen Lyra as the best fit for Soronúmë.

Anarríma [Leo]: The Encyclopedia of Arda says of Anarríma “It has not been certainly identified, but its name apparently means 'Sun-edge' or 'Sun-border', so it perhaps lies to the side of the Ecliptic, the Sun's path through the sky.” . Given this clue the question then becomes: “What constellation is of a configuration that most of it lies on one side or the other of the ecliptic, with perhaps part of it touching so as to “border” the Sun’s path?” The constellation that most nearly fits these requirements is Leo. In fact, its brightest star Regulus lies very near the path of the Sun: “Leo's mane looks like a backward question mark. Regulus, the ‘dot’ at the bottom of the mark, lies nearly on the ecliptic.” Regarding this, Mrs. Martin says:

The constellation Leo is one of those that the Sun passes through in its apparent annual path across the heavens. The Sun stays in this constellation a little more than five weeks, entering it at the beginning of the second week in August. Two weeks later, the Sun passes Regulus, and as this star lies almost exactly in the path of the Sun, they would seem to an observer on the Earth to almost touch each other. But at this time the light of Regulus is lost in the Sun's rays, and we do not see this interesting meeting.

† See “The Friendly Stars” by Martha Evans Martin. This is a wonderful Naturalistic look at astronomy, and I recommend it to everyone. It is not ‘technical’ at all. It is no longer in copyright and can be downloaded here.

‡ "Ancient records tell us that Lyra's association with birds goes back over two thousand years. In ancient India Lyra was seen as a heavenly vulture. And in Babylon as a great mythological storm bird named Urakkhga. Some desert peoples of ancient Arabia saw it as two birds, the desert eagle and would you believe a cosmic goose? Lyra was also once known as an osprey and a wood falcon. [...] At any rate only in the past couple hundred years or so have we in the west seen Lyra exclusively as a lyre. In fact at the time of the American Revolution these stars were still seen as a bird, an eagle but holding a lyre in its beak. But since then the eagle has flown away and only the lyre remains."

[6] From the Addendum to A Gateway To Sindarin by David Salo.

[7] The “Lay of Leithian”, The Lays of Beleriand, lines 717-720

[8] The Book of Lost Tales II, “The Fall of Gondolin”.

[9] From the “elfling” list:

Solstice - austalende '[mid]summer day' < *austakalenda. (The fact that this word includes the element kalenda means that they had a festival. It was probably Tarnin Austa `Gates of Summer', a festival described for Gondolin with singing all night.)

[10] The Book of Lost Tales II, “The Fall of Gondolin”.

[11] Again, from the “elfling” list:

August - **Lunde sarea `fiery' or **Lunde saiwa `hot' Lammas, said to have been celebrated in Gondolin. This is `formerly in England the festival of the wheat harvest or loaf mass, held on the 1st day of August, when bread baked from the first crop of wheat was consecrated at Mass' according to Webster's dictionary.

[12] Thanks to Cyllwen, for reconstructing this term for me.

[13] “Gilfanon’s Tale”, The Book of Lost Tales I.

© 2007 by Dave Woosley, All rights reserved

The Quendian (Elven) Calendar and the Six Seasons, Part II—the Venus Connection

The Elven Century and the Venus Rose

It is known from the information in Appendix ‘D’ of The Lord of the Rings that the Quendi reckoned time in two related periods: the first, a ‘week’ of 6 days known as an enquië, and the second much longer period known as a yén, or “elven century” of 144 years.

Two questions immediately arise: why a week of 6 days, and why a ‘century’ of 144 years? The answers to these questions are that the Quendi did not count using the decimal (base-10) system we are familiar with, but rather in a duodecimal (base-12) system. [1] In base-12, the first three-digit number, ‘100’, equals 144 in our familiar decimal system. [2] So, this was for them a ‘century’. [3] Thus it was natural for them to divide this period by some factor of 12, their counting base. Although I do not know their exact reason for choosing 6 days as their weekday period, I suspect that it was because 12 days seemed too long for a week, and three too short; especially when many of the days were intended to honor various celestial bodies and the Valar. [4]

According to the Information in Appendix ‘D’, the Quendi did not observe ‘months’ as we know them, but rather 6 “short seasons”; but for ritual purposes (which by their very nature connote time-keeping [5] ) they reckoned the enquier continuously throughout the yén. [6] They were thus using what today is called an ‘Integral Week’ [7] calendar. Now, one yén contains 8766 enquier, or 52,596 solar days; both equally divisible by 6. When we divide the total of enquier in a yén (8766) by 6, we obtain a very interesting number: 1461. [8] Why is this number interesting? Because it is exactly one half the number of days in the 8-year “Venus Rose”, which is the path Venus makes in the sky of Arda (Earth) during 8 years. If we could see the totality of these movements within the finite limits of our attention and perception (if one day were as one second, let’s say), it would look like this:

“That’s all very well”, some may say, “but exactly how is this related to Tolkien’s Legendarium?” Well, in addition to appearances of Venus playing a central role in the mythos [9] (where it is usually known as the Star of Eärendil), the shape of the Venus Rose itself closely matches the description of a Silmaril surrounded by its radiance (see note 11).

Venus and the Legendarium

Anyone who has done more than a cursory flip-through of Tolkien’s works must have noticed the central role that the Star of Eärendil plays in the mythos. It first rose to herald the decision of the Valar to intervene in the genocide Morgoth was perpetrating in Middle-earth (which culminated in the War of Wrath). In order to demonstrate this clearly, it is necessary to quote the following passage from the Silmarillion:

But [the Valar] took Vingilot [Eärendil’s ship; the metaphysical “vessel” of Venus], and hallowed it, and bore it away through Valinor to the uttermost rim of the world; and there it passed through the Door of Night and was lifted up even into the oceans of heaven.

Now fair and marvellous was that vessel made, and it was filled with a wavering flame, pure and bright; and Eärendil the Mariner sat at the helm, glistening with dust of elven-gems, and the Silmaril was bound upon his brow. Far he journeyed in that ship, even into the starless voids; but most often was he seen at morning or at evening, glimmering in sunrise or sunset, as he came back to Valinor from voyages beyond the confines of the world.

[…] Now when first Vingilot was set to sail in the seas of heaven, it rose unlocked for, glittering and bright; and the people of Middle-earth beheld it from afar and wondered, and they took it for a sign, and called it Gil-Estel, the Star of High Hope. And when this new star was seen at evening, Maedhros spoke to Maglor his brother, and he said: 'Surely that is a Silmaril that shines now in the West?'

And Maglor answered: 'If it be truly the Silmaril which we saw cast into the sea that rises again by the power of the Valar, then let us be glad; for its glory is seen now by many, and is yet secure from all evil.' Then the Elves looked up, and despaired no longer; but Morgoth was filled with doubt. [10]

There is here not only a mythical explanation for the cycles of Venus, but also an idea central in the Legendarium that each Silmaril captured the light of the Two Trees [11] (or as they were referred to in the earliest works, the “Magic Sun”). In fact, this idea of a bright star presaging a momentous event seems to be one of the earliest specific images of the Mythos, and goes back to Tolkien’s undergraduate days at Oxford:

"[…] He was particularly interested in extending his knowledge of the West Midland dialect in Middle English because of its associations with his childhood and ancestry; and he was reading a number of Old English works that he had not previously encountered.

Among these was the Crist of Cynewulf, a group of Anglo-Saxon religious poems. Two lines from it struck him forcibly:

Eala Earendel engla beorhtast ofer middangeard monnum sended.

‘Hail Earendel, brightest of angels/above the middle-earth sent unto men.’ Earendel is glossed by the Anglo-Saxon dictionary as ‘a shining light, ray’, but here it clearly has some special meaning. Tolkien himself interpreted it as referring to John the Baptist, but he believed that ‘Earendel’ had originally been the name for the star presaging the dawn, that is, Venus. He was strangely moved by its appearance in the Cynewulf lines. ‘I felt a curious thrill,’ he wrote long afterwards, ‘as if something had stirred in me, half wakened from sleep. There was something very remote and strange and beautiful behind those words, if I could grasp it, far beyond ancient English.’ [12]"

But how do these rather general references relate to the specific mathematics mentioned earlier? The answer comes from understanding how time is reckoned in Valinor, a period known as the Valian Year, which was synchronized to the rhythm of radiance of the Two Trees.

The Valian Year and the Reckoning of Time

The Valian Year is held to be 1000 Valian Days; a Valian Day being the length of time it took both Trees to achieve a state of full radiance and then wane, each in its turn, as is described in the Silmarillion. [13] In addition, one Valian Year is the unit of Time in which the Valar could just perceive the Ageing of the World—it was, so to speak, their ‘frame rate’. [14] There were thus 12 Valian hours in one Valian Day, 1000 Valian Days in one Valian Year, and 100 Valian Years in one Valian Age.

This elegant duodecimal system was thrown into disarray by the destruction of the Two Trees and the extinguishing of the primal Light. Although the Valar were able to create two new Lights from the remains of the Trees (the Sun and Moon) they did not have the same regular synchronicity nor periods as those that had gone before. [15] Through their inherent prescience, the Valar were able to tell that the destruction of the Trees had hastened the rate of “all change and withering”, what we no doubt would call 'entropy', of the Earth as a whole. Thus they designed that each “New” (Solar) hour should be one-seventh as long as an hour of the Trees as a good approximation of this new rate of entropy. According to their original plan for the new Lights, each Solar Year would equal exactly one tenth of a Valian year, or 1200 Valian hours; which given that Solar hours were to be one-seventh as long as Valian hours, yields 8400 Solar hours in one Solar Year.

More specifically, they purposed that each Solar Year should contain 700 times of Moonlight and Sunlight in total, each exactly twelve hours long, recalling the regular pulsating radiance of Telperion and Laurelin. Since the new Lights were intended to replicate the pattern of the Two Trees as closely as possible, each Solar Day was then to consist of two Light periods, one of Moonlight and one of Sunlight, thus making a Solar day of 24 hours duration. Since the total of Moonlight and Sunlight periods in one year was to equal 700, and there were to be two such periods in each Solar Day, this made a Solar Year of 350 days in length; or 8400 hours in a Solar Year (24 hours/day × 350 days/year), as mentioned above.

It soon became obvious, though, that the Sun and Moon did not adhere exactly to this new system after they were made and set in motion. Or, as the Loremasters said: “the Sun and Moon proved more wayward and slower in their passage than the Valar had intended”, and observationally one Solar Year equaled 8766 Solar hours (as is the case today).

The Valar were thus faced with a system which was already over 4% slower than they had intended and was probably in drift. How to rectify, or at least ameliorate, this situation? Although I do not know exactly how the Valar did what they did, I will show here mathematical evidence that the addition of the characteristic numbers associated with Eärendil’s Star (Venus) unifies and seems to stabilize the system.

How the mathematics of Venus preserves the Ancient Order

The new observational value of 8766 hours in a Solar Year is no longer in alignment with the intended 8400-hour Solar Year, which resonates with (is evenly divisible by) the factors 6 and 7, as the original Valian Year was also. However, it does resonate with 6 and a new factor: 487. Now, 6 is not itself a prime factor, but is the product of two primes, 2 × 3. It is also what is referred to as a “perfect number”. Perfect numbers are numbers that are equal to the sum of every (smaller) number that divides them. For example 6 is perfect because it is divisible by 1, 2 and 3; and 1 + 2 + 3 = 6. The new factor, 487, is the seventh number in row ten of a very interesting table of numbers called a “Wythoff Array”, as shown here:

				↙ Column number

Seed ↘			1	2	3	4	5	6	7	8	9	10	11

Row→	0	1	1	2	3	5	8	13	21	34	55	89	144
	1	3	4	7	11	18	29	47	76	123	199	322	521
	2	4	6	10	16	26	42	68	110	178	288	466	754
	3	6	9	15	24	39	63	102	165	267	432	699	1131
	4	8	12	20	32	52	84	136	220	356	576	932	1508
	5	9	14	23	37	60	97	157	254	411	665	1076	1741
	6	11	17	28	45	73	118	191	309	500	809	1309	2118
	7	12	19	31	50	81	131	212	343	555	898	1453	2351
	8	14	22	36	58	94	152	246	398	644	1042	1686	2728
	9	16	25	41	66	107	173	280	453	733	1186	1919	3105
	10	17	27	44	71	115	186	301	487	788	1275	2063	3338
	11	19	30	49	79	128	207	335	542	877	1419	2296	3715
	12	21	33	54	87	141	228	369	597	966	1563	2529	4092

In this table, the first column is the number of the row, starting at zero. The second column is equal to the whole number portion of (1 + the row number) × the “golden ratio”, a very important number in classical mathematics. These are our “seed” numbers and are separated from the main table by a vertical bar. The other numbers in each row are found by adding the last number found to the one before it. For example, in row zero, we have 0 and 1 as the first two numbers. So, we add those to obtain “1” for column 1 (that is, the first column to the right of the “seed numbers”), then add column 1 to the second “seed number” to get “2” for column 2, then add column 2 to column 1 to obtain “3”, and so on. A close examination of this table will show that row zero is the Fibonacci sequence, which is very important in Nature—in everything from plant growth to the arrangement of the Solar System (see “Final Thoughts” below). As mentioned, 487 is in column 7 of row 10. Seven being a primally important number in the Valian system, and ten being the number base we are all familiar with. You may also notice 52 in column 4 of row 4 (more about this important number later). The table also contains the three most important prime factors in the Valian system: 2, 3, and 7 (all in the first two rows).

Now, if one divides the observed hours in a Solar Year (8766) by 6 hours in each Tree’s “full radiance”, one obtains 1461 (which is equal to 3 × 487). You will remember that the number 1461 mentioned in the first section seems to have a special significance with regard to the Venus cycles. In fact, 1461 is one-half the number of Solar Days in the “Venus Rose” mentioned above, the full cycle being 2922 days (1461 × 2).

Similarly, dividing the “intended” 8400-hour Solar Year by 6 yields 1400, which has the prime factors: 2, 5, and 7. However, as the 8766-hour “observed” Solar Year has 3 and 487 as its prime factors, we cannot directly reconcile them. This is where the Star of Eärendil comes in…

Venus is Visible in the morning sky for about 260 days before it passes behind the Sun and is no longer visible from Earth (this is called Superior Conjunction), after 50-some days of invisibility, it then reappears in the evening sky and is visible for another 260 days until it is again lost in the Sun’s glare and passes between us and the Sun (this is called Inferior Conjunction). This time, it is invisible for a much shorter period: about 8 days. It then reappears in the morning sky and the cycle begins again. The total number of days it takes to complete one of these cycles (known as a synodic cycle) is 584 days. [16] (Incidentally, 584 = 2 × 2 × 2 × 73. The number 73 being in column 4 of row 6 in the table. See a pattern developing here?)

Given this, we know that Venus is visible in either the morning or evening sky for a total of 520 days in each cycle. Thus its total period of invisibility is 64 days. Subtracting the (quite accurate) 8 day period of invisibility at Inferior Conjunction gives us 56 days for the period of invisibility at Superior Conjunction. That may seem too long for some, as most sources list 50 days as the duration of invisibility at this time. However, there is some dispute about exactly what this interval was in ancient times, as the Mayan Calendar used a much longer figure. [17] For our purposes, since neither the total number of days in the Venus synodic cycle nor the duration of invisibility at Inferior Conjunction are in dispute, I think that it makes sense to accept 56 days as the duration of Venus’s invisibility at Superior Conjunction. Look at what happens when we do:

The prime factors of 56 are 2 and 7. That is 56 = 2 × 2 × 2 × 7. What of it, you may ask? Consider this:

i.    56 / 2 = 28; a good approximation of the lunar cycle (The Moon can be thought of as the “New Telperion”).

ii.    56 × 6.5 [18] = 364; a good approximation of the number of days in a Solar Year (The Sun can be considered the “New Laurelin”).

iii.   56 / 3 = 18 2/3; a good approximation of the Moon’s nodical period, which is important in predicting eclipses. [See this PowerPoint presentation on Archeoastronomy for a more thorough discussion of these divisors and factors. See especially pages 13-15.]

In addition (and perhaps more importantly) it is known from the work on the Mayan Calendar that the 365-day Solar year and the 260-day period of morning or evening visibility of Venus coincide every 52 years (44 years in duodecimal), if both start at the same point in Time.

Thus, through the introduction of the Star of Eärendil a new balance was restored to the trinary Earth-Moon-Sun system. Although it did not happen immediately after the creation of the Sun and Moon, it did happen because of the intercession of a descendant whose bloodline contained the combined essence of Men and Elves— Eärendil himself.

Finally, though it may seem that this entire discussion has been about “mere math”, and that “a calendar can mean whatever you want it to mean”, it is also true that the underlying patterns represented by these numbers are expressed within the very fabric of the Solar System [19] itself. The discussion of that topic lies far outside the scope of this essay, but I refer interested parties to SPIRA SOLARIS.

Final Thoughts

I hoped to show by providing specific examples that this is not just a numerological “playing with numbers”. And that, though these repeating numerical patterns do not, of themselves, prove my conjecture, they are rather striking. In fact, this idea of mathematical resonances having a basic and intricate link to the structure of Reality itself has, it seems, been noticed before. One striking example is this quote from Mathematical Physicist Geoffrey Dixon:

"My personal motivation is the notion of mathematical resonance. In experimental physics the presence of a new particle is often made apparent by a resonant response - a peak of activity rising above surrounding noise. The noise is a null result; the peak signifies existence. In mathematics there are also "resonances", algebraic and topological dimensions that explode with intricacy and depth compared with dimensions immediately above and below. I share a view with many others that the connection of mathematics to physics is not accidental, and I share an intuition with perhaps fewer that existence is attributable in part to mathematical resonance - that the rich and specific structure of our unique physical reality mirrors the rich and specific structure of the few mathematical resonances. "

With regard to the factor of 487 mentioned earlier, it has many other interesting properties. Among these are:

i.    6 × 487 = 2922, the number of days in the “Venus Rose”

ii.   There are exactly 1461 (3 × 487) days in 4 years.

iii.   The number 1461 (3 × 487) is the number of years in a much longer cycle than the one we have discussed thus far, the Sothic cycle, first mentioned in connection with ancient Egypt.

iv.   487 when expressed in duodecimal = 347. The numbers 3, 4, and 7 are the first three non-trivial Lucas Numbers. Lucas Numbers are related to the better known Fibonacci numbers (in fact, both are known as “Lucas sequences”), which occur frequently in the Natural world (such as the number of petals of flowers, the branches of trees, and in animal bodies ).

v.    The product of the first two Lucas numbers in the sequence {3, 4, 7} is 12–the base of the duodecimal system.

Thus, one can see that this “magic number”, 487, occurs again and again in different ‘modes’ and at different scales of time.

[1] […] “already in Common Eldarin the multiples of three, especially six and twelve, were considered specially important, for general arithmetical reasons; and eventually beside the decimal numeration a complete duodecimal system was devised for calculations, some of which, such as the special words for 12 (dozen), 18, and 144 (gross), were in general use.”—From Vinyar Tengwar #42

[2] That is 1 (12×12)’s + 0 12’s + 0 ones = 144. If this is not clear to you, then I refer you to this page on number base calculations.

[3] Even today, there is evidence of a 144-year cycle of calendrical reckoning. For example, in India there is a celebration known as the Kumbha Mela which goes back to Vedic times. Every 144 years, there is a “Great” Kumbha Mela, known as a Maha Kumbha Mela. Here is an article on the most recent one:

[4] “The six-day week of the Eldar had days dedicated to, or named after, the Stars, the Sun, the Moon, the Two Trees, the Heavens, and the Valar or Powers, in that order, the last day being the chief day of the week.”—Appendix ‘D’, The Lord of the Rings.

[5] “The common theme of calendar making is the desire to organize units of time to satisfy the needs and preoccupations of society. In addition to serving practical purposes, the process of organization provides a sense, however illusory, of understanding and controlling time itself. Thus calendars serve as a link between mankind and the cosmos. It is little wonder that calendars have held a sacred status and have served as a source of social order and cultural identity. Calendars have provided the basis for planning agricultural, hunting, and migration cycles, for divination and prognostication, and for maintaining cycles of religious and civil events. Whatever their scientific sophistication, calendars must ultimately be judged as social contracts, not as scientific treatises.” See this page, for a better explanation of the central role religion and ritual play in calendars.

[6] “For ritual rather than practical purposes the Eldar observed a week or enquië of six days; and the yén contained 8,766 of these enquier, reckoned continuously throughout the period.”—Appendix ‘D’, The Lord of the Rings

[7] An integral-week calendar is a calendar in which the years always have an integral number of weeks, where weeks consist of a certain fixed number of days, not necessarily seven. In an integral-week calendar all days are part of some week.

[8] Someone may object at this point that I have divided ‘weeks’ by days to arrive at a spurious number, which if one considers this particular example alone is true,

http://www.khaldea.com/planets/venus_type.shtml

then we see that this quotient also equals 1461 – and in this case the quotient is in solar days, beyond question.

[9] In addition to its first appearance mentioned below, it was also the Star that guided the descendants of Eärendil to their new land:

“That land the Valar called Andor, the Land of Gift; and the Star of Eärendil shone bright in the West as a token that all was made ready, and as a guide over the sea; and Men marvelled to see that silver flame in the paths of the Sun.

Then the Edain set sail upon the deep waters, following the Star; and the Valar laid a peace upon the sea for many days, and sent sunlight and a sailing wind, so that the waters glittered before the eyes of the Edain like rippling glass, and the foam flew like snow before the stems of their ships. But so bright was Rothinzil that even at morning Men could see it glimmering in the West, and in the cloudless night it shone alone, for no other star could stand beside it. And setting their course towards it the Edain came at last over leagues of sea and saw afar the land that was prepared for them, Andor, the Land of Gift, shimmering in a golden haze. Then they went up out of the sea and found a country fair and fruitful, and they were glad. And they called that land Elenna, which is Starwards; but also Anadûnë, which is Westernesse, Númenórë in the High Eldarin tongue.”—From the book Akallabêth in The Silmarillion.

Much later, it was also the Light that Queen Galadriel captured in the phial that she gave to Frodo, as described in The Fellowship of the Ring.

[10] The Silmarillion, Chapter 24, “Of the Voyage of Eärendil and the War of Wrath”.

[11] “As three great Jewels they were in form. But not until the End, when Fëanor shall return who perished ere the Sun was made, and sits now in the Halls of Awaiting and comes no more among his kin; not until the Sun passes and the Moon falls, shall it be known of what substance they were made. Like the crystal of diamonds it appeared, and yet was more strong than adamant, so that no violence could mar it or break it within the Kingdom of Arda. Yet that crystal was to the Silmarils but as is the body to the Children of Ilúvatar: the house of its inner fire, that is within it and yet in all parts of it, and is its life. And the inner fire of the Silmarils Fëanor made of the blended light of the Trees of Valinor, which lives in them yet, though the Trees have long withered and shine no more. Therefore even in the darkness of the deepest treasury the Silmarils of their own radiance shone like the stars of Varda; and yet, as were they indeed living things, they rejoiced in light and received it and gave it back in hues more marvellous than before.”—The Silmarillion, Chapter 7, “Of the Silmarils and the Unrest of the Noldor”

[12] J.R.R. Tolkien: A Biography, Humphrey Carpenter. The references are to a period sometime in 1913.

[13] The process is described most succinctly in Chapter 1, paragraph 14 of the Silmarillion, but in greater detail in “The Annals of Aman” (Morgoth’s Ring, HOME volume X), Commentary on §§5-10 in section 1. Here is a table which makes the relations clearer:

[14] “In Aman things were far otherwise than in Middle-earth. But they resembled the mode of Elvish life, just as the Elves more nearly resemble the Valar and Maiar than do Men.

In Aman the length of the unit of 'year' was the same as it was for the Quendi. But for a different reason. In Aman this length was assigned by the Valar for their own purposes, and was related to that process which may be called the 'Ageing of Arda'. For Aman was within Arda and therefore within the Time of Arda (which was not eternal, whether Unmarred or Marred). Therefore Arda and all things in it must age, however slowly, as it proceeds from beginning to end. This ageing could be perceived by the Valar in about that length of time (proportionate to the whole of Arda's appointed span) which they called a Year; but not in a less period.”—Morgoth’s Ring (HOME volume X), Text XI in “Myths Transformed”.

[15] For this and the following discussion, I refer you to “The Annals of Aman” (Morgoth’s Ring, HOME volume X), §8:

“It is recorded by the Lore-masters that this is not rightly as the Valar designed at the making and ordering of the Moon and Sun. For it was their intention that ten years of the Sun, no more and no less, should be in length as one Year of the Trees had been; and it was their first device that each year of the Sun should contain seven hundred times of sunlight and moonlight, and each of these times should contain twelve hours, each in duration one seventh of an hour of the Trees. By that reckoning each Sun-year would contain three hundred and fifty full days of divided moonlight and sunlight, that is eight thousand and four hundred hours, equaling twelve hundred hours of the Trees, or one tenth of a Valian Year. But the Moon and Sun proved more wayward and slower in their passage than the Valar had intended, as is hereafter told, and a year of the Sun is somewhat longer than was one tenth of a Year in the Days of the Trees.”

[16] See this discussion:

[17] See this page for a modern viewpoint; and this page for a discussion of the discrepancy noticed in ancient records in the Mayan and other cultural records.

[18] The Golden Ratio × 4 = 6.5 (to one decimal place).

[19] “Arda, or 'The Kingdom of Arda' (as being directly under the kingship of Eru's vice-regent Manwë) is not easy to translate, since neither 'earth' nor 'world' are entirely suitable. Physically Arda was what we should call the Solar System. […]It is certainly the case with the Elvish traditions that the principal part of Arda was the Earth (Imbar 'The Habitation'), as the scene of the Drama of the war of the Valar and the Children of Eru with Melkor: so that loosely used Arda often seems to mean the Earth: and that from this point of view the function of the Solar System was to make possible the existence of Imbar.”—Commentary to the “Athrabeth Finrod ah Andreth”, Morgoth’s Ring (HOME volume X).

© 2005,2007 by Dave Woosley, All rights reserved

The Quendian (Elven) Calendar and the Six Seasons