Lunisolar Calculator

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The lunisolar calendar is based on first quarter moons beginning with the one before Yule. Times are given in Coordinated Universal Time, and local time using your system’s time zone and daylight saving time settings.

When there are 13 first quarter moons between the two Yules, the month of Middle Litha is added between the other two Lithas.

The other moon phases and solar holidays in each month are included for general interest; one might use this information to have a cross-quarter festival on the second full moon after a solstice or equinox, for example. The cross-quarters are calculated astronomically at the times when the earth is at the 45° points in its elliptical orbit between solstices and equinoxes.

The dates in parentheses are the “universal” first days of the month based on sunset at Greenwich as described below.

What do we know about the Old English Celtic and Anglo-Saxon calendar? Here are the historical sources.

According to Pliny the Elder (AD 23–79), Gaulish Druids began the month on the sixth day of the moon (basically the first quarter); no other source specifies the start date.

The mistletoe, however, is but rarely found upon the robur; and when found, is gathered with rites replete with religious awe. This is done more particularly on the fifth [see below] day of the moon, the day which is the beginning of their months and years, as also of their ages, which, with them, are but thirty years. This day they select because the moon, though not yet in the middle of her course, has already considerable power and influence; and they call her by a name which signifies, in their language, the all-healing.

Pliny the Elder, The Natural History
John Bostock, M.D., F.R.S., H.T. Riley, Esq., B.A., Ed.
http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0137%3Abook%3D16%3Achapter%3D95

“Fifth day of the moon” appears to be an often-repeated mistranslation; the latin is sexta luna, not quinta luna:

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0138%3Abook%3D16%3Achapter%3D115

See also:

. . . on the sixth day of the moon (which for these tribes constitutes the beginning of the months and the years) . . . .

Pliny, Natural History, by H. Rackham, M.A.
https://archive.org/stream/naturalhistory04plinuoft#page/548/mode/2up

Tacitus (c. AD 56 – c. 120) says that the Germanic people assembled at new or full moon, and reckoned by nights.

They assemble, except in the case of a sudden emergency, on certain fixed days, either at new or at full moon; for this they consider the most auspicious season for the transaction of business. Instead of reckoning by days as we do, they reckon by nights, and in this manner fix both their ordinary and their legal appointments. Night they regard as bringing on day.

Cornelius Tacitus, Germany and its Tribes
Alfred John Church, William Jackson Brodribb, Ed.
http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0083%3Achapter%3D11

The Venerable Bede (672/3 – 735) described the Old English calendar in some detail.

In olden time the English people . . . calculated their months according to the course of the Moon.

Bede, The Reckoning of Time
Faith Wallis

The next several chapters describe the “course of the moon” through the zodiac, suggesting that he may be describing sidereal months, based on constellations; but the addition of a thirteenth month in embolismic years indicates that the months are in all likelihood synodic, based on phase.

The first month, which the Latins call January, is Giuli; February is called Solmonath; March Hrethmonath; April, Eosturmonath; May, Thrimilchi; June, Litha; July, also Litha; August, Weodmonath; September, Halegmonath; October, Winterfilleth; November, Blodmonath; December, Giuli, the same name by which January is called.

He begins by associating each month with a Latin equivalent, but then describes a lunisolar system of 12 or 13 months in four seasons, then mentions an older system of two seasons.

They began the year on the 8th kalends of January [25 December], when we celebrate the birth of the Lord.

Whenever it was a common year, they gave three lunar months to each season. When an embolismic year occurred (that is, one of 13 lunar months) they assigned the extra month to summer, so that three months together bore the name “Litha”; hence they called [the embolismic] year “Thrilithi”.

A solar year does not contain an even number of lunar months, so some years need an extra month to stay in synchronization with the seasons. He does not describe the details of when the extra month was added.

But originally, they divided the year as a whole into two seasons, summer and winter, assigning the six months in which the days are longer than the nights to summer, and the other six to winter. Hence they called the month in which the winter season began “Winterfilleth”, a name made up from “winter” and “full Moon”, because winter began on the full Moon of that month.

This sounds like the old insular Celtic calendar which would have preceded the Anglo-Saxon one. The phrase “full moon of that month” seems to imply that months in Bede’s time did not start on the full moon. But he does not come out and say when months actually started.

The months of Giuli derive their name from the day when the Sun turns back [and begins] to increase, because one of [these months] precedes [this day] and the other follows.

Guili is Yule, described as the solstice; it appears to be a pivotal date. The calendar is evidently lunisolar: lunar months anchored to a solar event like the solstice.

Solmonath can be called “month of cakes”, which they offered to their gods in that month.

Hrethmonath is named for their goddess Hretha, to whom they sacrificed at this time.

Eosturmonath has a name which is now translated “Paschal month”, and which was once called after a goddess of theirs named Eostre, in whose honour feasts were celebrated in that month.

Thrimilchi was so called because in that month the cattle were milked three times a day; such, at one time, was the fertility of Britain or Germany, from whence the English nation came to Britain.

Litha means “gentle” or “navigable”, because in both these months the calm breezes are gentle, and they were wont to sail upon the smooth sea.

Weodmonath means “month of tares”, for they are very plentiful then.

Halegmonath means “month of sacred rites”.

Winterfilleth can be called by the invented composite name “winter-full”.

Blodmonath is “month of immolations”, for then the cattle which were to be slaughtered were consecrated to their gods.

So months are lunar; what about solar holidays, the solstices, equinoxes, and cross-quarter days?

The solstices and equinoxes have been known since antiquity; Bede has already mentioned the winter solstice.

Most of what we know about their observation in Celtic or Anglo-Saxon times is based on tradition and “cultural fossils.”

The English quarter days (also observed in Wales and the Channel Islands) are close to the solstices and equinoxes:

Lady Day (25 March)
Midsummer Day (24 June)
Michaelmas (29 September)
Christmas (25 December)

The cross-quarter days are four holidays falling in between the quarter days: Candlemas (2 February), May Day (1 May), Lammas (1 August), and All Hallows (1 November).

https://en.wikipedia.org/wiki/Quarter_days

The Old Scottish Term and Quarter Days (Julian to Gregorian), prior to 1886, are close to the cross-quarter days:

Candlemas (2 February)
Whitsunday (15 May)
Lammas (1 August)
Martinmas (11 November)

https://en.wikipedia.org/wiki/Scottish_term_days

More about celebrations:

Historical and archaeological evidence suggests ancient pagan and polytheist peoples varied in their cultural observations; Anglo-Saxons celebrated the solstices and equinoxes, while Celts celebrated the seasonal divisions with various fire festivals.[3] In the 10th century Cormac Mac Cárthaigh wrote about “four great fires . . . lighted up on the four great festivals of the Druids . . . in February, May, August, and November.”[4]
3 Hutton, Ronald (8 December 1993), The Pagan Religions of the Ancient British Isles, Oxford, Blackwell, pp. 337–341, ISBN 0-631-18946-7
4 Murray, Margaret. 1931. The God of the Witches.

Murray reports a 1661 trial record from Forfar, Scotland, where the accused witch (Issobell Smyth) is connected with meetings held “every quarter at Candlemas, Rud−day, Lambemas, and Hallomas.”[5]
5 Kinloch, George Ritchie. Reliquiae Antiquae Scoticae. Edinburgh, 1848.

https://en.wikipedia.org/wiki/Wheel_of_the_Year

Note also that the solstices are “midwinter’s day” and “midsummer’s day,” implying that the seasons begin on cross-quarters.

Discussion

People who begin their months with the moon tend to begin their days at the same time, at sunset. Hence terms like fortnight (fourteen nights), and holidays that start on an “eve.” In antiquity, the “new” moon usually meant the first visible crescent (which appears after the dark of the moon, our astronomical new moon). But without an official observer in an official location, this reckoning is hard to standardize, much less predict. Pliny says that the Druids began their month on the sixth day of the moon. This is notable because the first quarter moon is very easy to recognize. The sighting of the first crescent depends on one’s vision and the atmospheric conditions, and even the full moon is not always easy to identify as it may look full three nights in a row. The sixth image below is the first quarter moon, and the preceding ones are each one day apart; you can see that the sequence begins with the “new” moon.

Depending on conditions, the first crescent moon tends to be visible by the first sunset 24-36 hours after the astronomical new moon; if you have good eyes and clear skies, it may be a number of hours sooner. If you are keeping track of the moon phases, the delay in sighting the first crescent would throw off the intervals between phases; someone who realized that the dark of the moon was actually the new moon might want to start the month on a more-identifiable phase.

It appears that months/moons were the basis of short-term periodic events such as community meetings and the mistletoe ceremony. They were synodic, with a thirteenth month added when needed, and began after the winter solstice. The big annual holidays were either solstices/equinoxes or cross-quarters, probably not both, although remnants of both still exist. (The eightfold wheel of the year is cool, but it is actually a modern syncretism.)

Bede says that when a thirteenth month was addd to the year, they called the year “Thrilithi” (three Lithas). But he does not give the month an actual name, other than to say that three months together bore the name “Litha”. Similarly, he calls the Yules “the months of Giuli.” At some point, possibly fairly recently, the double months were distinguished as Ærra Gēola (Ere Yule) and Æfterra Gēola (After Yule), Ærra Līþa (Ere Litha) and Æftera Līþa (After Litha). It so happens that if a third Litha is added after the first two, the month of After Litha may begin before Litha, the summer solstice. This doesn’t sound right, even though it is actually not a contradiction if “ere” is interpreted as “early” or “former,” and “after” similarly as “late” or “latter,” as in afterthought or afterburner. Be that as it may, I have named the thirteenth month “Middle Litha” (Middel Līþa ?) and placed it between the other two.

Making a “modern” Old English calendar

Should the calendar be based on observation, or mathematics? Sunset is fairly easy to recognize as long a you have a clear horizon. The first quarter moon is also easy to identify as described above. If it’s overcast, a mean synodic month is 29 days, 12 hours, 44 minutes, 2.8016 seconds; simple math may be used with this interval with fairly good long-term accuracy. Something like this plus the Metonic cycle also makes a lunar calendar that is reproducible over long intervals without the use of computers.

The ancients determined when to add months in embolismic years using the Metonic cycle or similar means; observational rules having to do with fixed events such as the summer solstice may also be used. Observational rules are inherently a little inaccurate because lunar months are not all the same length. But if you want a rule, here’s one. The winter solstice is 183.51 days after the summer solstice, and the mean synodic month is 29.53 days long. That means that there are about 183.51 / 29.53 = 6.214 lunar months between the summer and winter solstices. After Litha through Ere Yule is 6 lunar months. So if Ere Litha ends less than 6.214 - 6 = 0.214 months, or about 6 days and 8 hours, after the summer solstice, or before it, you will need a 13^th month; add Middle Litha.

The solstices and equinoxes may be determined using observatories like Stonehenge, or instruments like equatorial rings that the ancient Greeks used; it takes a degree of doing and know-how.

Of course, if you want to generate an entire calendar ahead of time, you will need to use mathematics. High-tech computer algorithms may be used to determine any moon phase, solstices, equinoxes, cross-quarter days, and even sunsets anywhere in the world without difficulty. It is also easy to determine when there are thirteen moons of a given phase in a solar year. In short, you can do a much better job with computers, but some people like a hands-on approach. And they are not mutually exclusive; even though we now have cruise missiles, some people still attend revolutionary war re-enactments.

Should a lunisolar calendar be local, with everyone making their own observations and “doing their own thing,” or should there be a global standard? Mondern days are based on midnight at Greenwich, England. Lunar months could be based on sunset at Greenwich. Define “day” as sunset-to-sunset; the month would begin at local sunset on the Gregorian calendar date that begins a sunset-to-sunset day in Greenwich that includes the first quarter moon. That way, everyone everywhere on earth would start their month on the same date. These are actually the dates in parentheses in the calendar above. If you want to completely immerse yourself in the lunar calendar, you might even celebrate the holidays based on sunset days as well.

If you are curious, here are the sunset dates and times in Greenwich for the seleted calendar year:

Get your own local sunset times

Calculations are based on the “higher accuracy” equations in Astronomical Algorithms, second edition, by Jean Meeus, and the full VSOP87 data set.