A year by the Sun alone

A calendar has to reconcile two celestial bodies whose motions do not divide neatly into one another: the Sun, which sets the beat of the seasons, and the Moon, which counts the months. Out of the ways of handling this discrepancy, three calendar types emerged. A lunisolar calendar keeps both; a pure lunar calendar follows the Moon alone.

The solar calendar takes the third path. It follows the solar year exclusively and leaves the Moon out of the division of the year. What matters to it is the tropical year, the time from one spring equinox to the next. That comes to exactly 365.242190 days, or 365 days, 5 hours, 48 minutes, and 45 seconds. Every solar calendar has to follow this figure, because it describes the seasonal year. Our present Gregorian calendar is such a pure solar calendar, one in which the course of the Moon plays no part in dividing the year.

The Egyptian wandering year

The solar calendar has its origin in ancient Egypt. The early Egyptians first used a lunisolar calendar, whose months followed the Moon and which was bound to the solar year by a leap month. But for running a state with great building projects, taxation, and record-keeping, a year of shifting length was inconvenient. For that reason the Egyptian bureaucrats invented a more regular calendar.

This civil year rested on the observation that some 365 days usually separated two heliacal risings of Sirius. It ran to twelve months of 30 days each, plus five extra days at the end that the Greeks later called epagomenal days. There was no leap day and no leap month. Because 365 days is about a quarter-day shorter than the tropical year, this year began one day earlier against the seasons every four years. After roughly 1500 years it had drifted once all the way through the solar year. The Latin name for it is annus vagus, the wandering year.

The wandering year shows the basic trait of every solar calendar in its purest form, and its exposed flank as well: round the year off to whole days and ignore the remainder, and the calendar slowly walks out of the seasons. Closing that gap was the task.

Caesar and the leap day

In 47 BC Gaius Julius Caesar travelled to Alexandria, then probably the greatest centre of learning in the world. There the astronomers Acoreus, Sosigenes, and others taught him the mathematics of the solar calendar. Two years later, in 45 BC, he introduced an originally Hellenistic-Egyptian solar calendar across the whole Roman Empire. Before that it had been customary on the Eurasian continent to reckon the years by the Moon; Romans, Greeks, Celts, Balts, and the Germanic peoples all used lunisolar calendars.

Caesar's reform solved the problem of the wandering year with one simple device. Instead of letting the remainder of about a quarter-day lapse, you collect it over four years and insert it as a leap day. That brings the mean calendar year to 365.25 days and keeps it bound to the seasons. The Julian calendar thereby turned the wandering year into a fixed solar calendar.

The fine correction of 1582

A quarter-day, though, is not quite exact. The tropical year measures 365.242190 days, but the Julian year measures 365.25. The difference comes to eleven minutes and fourteen seconds. Small as it is, it accumulates over long spans: every 128 years the shortfall grows by a whole day. By the sixteenth century the spring equinox had drifted far from its established calendar place, which above all disturbed the calculation of Easter.

Pope Gregory XIII corrected this in 1582. The mean year was shortened from 365.25 to 365.2425 days. This is done by an added leap rule: years divisible by 100 are leap years only if they are also divisible by 400. The years 1700, 1800, and 1900 dropped out as leap years, while 1600 and 2000 remained. To catch up the shortfall already accrued, the reform dropped ten calendar days: 4 October was immediately followed by 15 October 1582. This Gregorian calendar is the solar calendar that almost the whole world now uses for administration and trade. The offset between the Julian and Gregorian reckonings, which began with this ten-day jump, is still visible today: the Ártala app carries both datings and shows the Julian date as a secondary date alongside the Gregorian.

What the solar calendar gives up

The pure solar calendar is practical. It keeps the seasons fixed, every year has nearly the same number of days, and the interval between two dates can be worked out without observation. For a large empire with taxes, administration, and long-distance trade, that is a solid advantage, and it is no accident that Egypt's bureaucrats and Caesar's administration alike chose exactly this path.

The advantage comes at a price: the solar calendar gives up the Moon. Its "months" are divided-off stretches of the solar year that no longer have anything to do with the lunar phases. A glance at the Gregorian calendar does not tell you whether the Moon in the sky is full or new. The short, directly observable beat of the Moon, which structured time for thousands of years, drops out of the reckoning.

The bridge back to the Moon

If you want to keep both, the seasonal reliability of the Sun and the living beat of the Moon, you arrive at the third type. A lunisolar calendar keeps the lunar months and binds them to the solar year through a leap month. It thus joins the best of both sides, and pays for it with a little more computation. A pure lunar calendar goes the other way and accepts that its festivals drift through the seasons.

The Germanic-speaking peoples reckoned lunisolar. How their calendar brings together the first crescent, the winter solstice as its sole solar anchor, and the leap month is set out in the article on the Germanic lunar calendar. 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. You can find it for web, Android, and iOS on the Ártala home page.

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