Three ways to count a year

Every calendar has to solve one basic problem: the Sun and the Moon move on two independent tracks whose paths do not divide neatly into one another. Out of the different ways of handling this discrepancy, three calendar types emerged.

A solar calendar ignores the Moon and divides only the solar year, like today's Gregorian calendar, whose "months" have long had nothing to do with the Moon. A pure lunar calendar follows only the phases of the Moon; its year of twelve lunar months is about eleven days shorter than the solar year. The best-known example is the Islamic calendar: because it never makes up the shortfall, the fasting month of Ramadan drifts backward through the entire solar year over roughly 32 years (33 Islamic lunar years).

The third type is the lunisolar calendar – the author Andreas E. Zautner aptly calls it the "bound" lunar calendar. It keeps the lunar months but binds them to the solar year, so that the festivals do not slip out of their seasonal anchoring. This is the type we are concerned with here.

The core problem: eleven missing days

To see why a lunisolar calendar needs a trick at all, a little arithmetic helps. A month in the sense of the Moon's phases – from new moon to new moon – is called a synodic month and lasts on average 29.53 days. In practice, a lunar calendar therefore alternates "hollow" months of 29 days with "full" months of 30 days.

Twelve such months add up to about 354 days. But the solar year – the time from one spring equinox to the next – runs a little over 365 days. That leaves a gap of roughly 11¼ days, often expressed in tradition as "twelve nights" (eleven days, framed by twelve nights).

If you ignored this gap, every lunar month would slide about eleven days against the seasons each year – within a few years a "harvest month" would land in midwinter. A pure lunar calendar accepts that; a lunisolar calendar corrects for it.

The solution: the leap month

You let the missing days accumulate, and as soon as they add up to a whole lunar month, you insert a thirteenth month, the leap month. For practical as well as mythical reasons a lunar cycle could not be cut in half, so a whole lunar month was always added, never single days.

For this correction not to become arbitrary, it needs a fixed solar point as an anchor. The two solstices and the two equinoxes are the natural candidates. At such a fixed date you can read off, year by year, whether the Moon has fallen so far behind the Sun that a leap month is due. That keeps the calendar permanently in step with sowing, harvest, and the seasons – without giving up the Moon.

Which fixed point was chosen, and whether the Moon "hurried after" the Sun or the Sun "waited" for the Moon, depended on each culture and its cults. That is where the many lunisolar systems of the world differ from one another – yet in principle they are close relatives.

A worldwide principle

For long stretches of history, the lunisolar calendar was the norm. Before Gaius Julius Caesar introduced a pure, originally Hellenistic-Egyptian solar calendar into the Roman Empire in 45 BC, it was "customary, especially on the Eurasian continent, to reckon the years (also) by the Moon." Romans, Greeks, Celts, Balts, and the Germanic peoples all initially used lunisolar calendars, in which a leap month reconciled Sun and Moon.

The evidence is tangible. The early Roman calendar was a lunar year of 354 days, into which a mensis intercalaris was inserted every two years. The Gallo-Roman bronze calendar found in 1897 at Coligny in south-eastern France shows a Celtic lunar year of twelve months, bound to the Sun by a thirty-day leap month roughly every two and a half years. The Jewish calendar is lunisolar too: the Crucifixion fell on the spring full moon of the month Nisan, which is why the Christian calculation of Easter still hangs on a moving lunar date to this day.

Out of this practice grew the classic intercalation cycles. The Greek astronomer Meton observed in the 5th century BC that 19 solar years correspond almost exactly to 235 lunar months: the famous Metonic cycle, by which the Moon's phases fall on the same date again every 19 years. It still underlies the calculation of Easter. An even shorter rhythm, the octaeteris, reconciles eight solar years with about 99 lunar months. Both are refined answers to the same eleven-day question.

Equally widespread was the simplest variant of all: empirical intercalation. Rather than following a rigid cycle, a month was simply inserted – or "forgotten" – when observation demanded it. In his foundational work Primitive Time-Reckoning (1920), Martin P. Nilsson shows that this practice is nearly universal, from the Inuit through the Babylonians to the Germanic peoples. The full sweep of these calendars, from the earliest evidence to Japan, is traced in the article on lunar calendars through history.

The Germanic case

The Germanic-speaking peoples reckoned lunisolar as well. Around 725 the monk Bede describes the Anglo-Saxon calendar as exactly such a system: twelve lunar months in an ordinary year, thirteen in a leap year, with the extra month – a third Lida – inserted in summer, and the year divided into two halves of summer and winter. Nilsson and others confirm this and show that the leap month typically fell in the summer half among Icelanders and others too.

The Germanic case has its own particular subtleties: the first visible crescent as the start of the month, the winter solstice as the sole solar anchor, the Yule-Moon rule for the start of the year, and the famous twelve-nights leap rule. If that interests you, the detailed, source-based account is in the article on the Germanic lunar calendar. It is a lunisolar calendar like many others, built on the same underlying principle of Moon, Sun, and leap month.

From principle to date

As clear as the principle is, in everyday use a lunisolar calendar quickly becomes unwieldy. Whether a given year is a leap year, which evening the first crescent falls on, and exactly when a festival occurs all depend on astronomical observations that once had to be tracked laboriously by hand. A festival does not sit on a fixed date, but rather "around the full moon of the winter month."

That is precisely the computation the Ártala app takes off your hands. It calculates the moon phases astronomically correctly and even without an internet connection, shows the months with the inserted leap month, and reminds you of the festival days of the Germanic lunisolar calendar – source-based and ad-free. If you want to know which lunar month you are currently living in, or when the next festival falls, you can find it for web, Android, and iOS on the Ártala home page.

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