The Metonic Cycle
Posted by Byron Pendason on , in Heathenry, Reconstruction, Anglo-saxon calendar
As per my Reconstructed Anglo-Saxon Calendar page, my method for determining if a year is a leap year is to count how many new moons there are between the previous year's winter solstice and the current years winter solstice. If there are thirteen new moons, it is a leap year. If there are only twelve new moons, it's a regular year. In leap years, you add the extra month in between Ærra Liðe and Æfterra Liðe. This keeps Ġēola (Yule, which Bede identifies as the winter solstice) in its proper place in the final month of the year.
This isn't the only way of determining leap years though. Most lunisolar calendars of the ancient world used what's known as the Metonic Cycle. It's named after the Greek mathematician that discovered it, but it was also discovered by the Babylonians centuries before, and independently discovered by the Romans as well. The Jewish calendar uses the Metonic Cycle, and the Celtic peoples that once inhabited present day Germany were aware of it, according to artifacts found dating to around 1000 to 800 B.C.E.
The Metonic Cycle uses a nineteen year cycle to designate years 3, 6, 8, 11, 14, 17, and 19 as leap years. Beofeld from Wind in the Worldtree uses the Metonic Cycle to determine leap years for his Anglo-Saxon Calendar, with 2018 being year 1 of the current cycle. That makes the current year as of this being written (2021) year 4 in the current cycle.
Deciding to compare the results of our different methods of determining leap years, I decided to compare the years 2020 to 2050. The results? They lined up exactly. I tried several more random years as test cases, with the same results.
So the Metonic Cycle works. The next question I wanted to resolve was whether the Anglo-Saxons would have been aware of the Metonic Cycle. If the answer is no, than I have no justification for using the Metonic Cycle. If they did though, then I have no justification for not using it. As it turns out though, they had to have known about it; they had a word for it. The Old English word for the Metonic Cycle is getæl-circul.
So, I think I will be switching to using the Metonic Cycle myself. But you may be wondering, how does one use the Metonic Cycle to determine if it's a leap year or not?
As stated above, 2018 began the current cycle that keeps Yule in it's proper place. To determine whether it's a leap year, subtract the 3 from the current calendar year (according to the Gregorian calendar, which is almost universally used throughout the world today) and get the remainder of dividing this number by 19. A result of 0 means it's year 19. If the result is 0, 3, 6, 8, 11, 14, or 17, it's a leap year. This would be expressed mathematically as:
M = (Y-3) % 19
Let's take the year of my birth as an example, 1987. Subtracting 3 from this, we get 1984. Dividing this by 19 gives us a result of 8. This means that the year of my birth would have been a leap year.