Metonic cycle

The Metonic cycle is a special pattern that happens about every 19 years. After this time, the Moon’s phases, like when it is full or new, happen on the same dates each year. This idea was discovered by a person named Meton of Athens a long time ago, in the 5th century BC.

Even though the Metonic cycle is very close, it is not perfect. If you measure it very carefully, it is a little bit longer than 19 years. But using whole numbers makes it easier to create a special kind of calendar called a lunisolar calendar.

In a Metonic calendar, some years have 12 lunar months and others have 13. This helps match up the Moon's phases with the seasons of the year.

Application in traditional calendars

The Metonic cycle is a pattern that happens every 19 years. It helps match the lunar calendar, which follows the Moon, with the solar calendar, which follows the Sun. Ancient Babylonians and Hebrews used this cycle in their calendars. In these calendars, some years have an extra month to keep everything in sync.

This 19-year cycle was also used to decide the date of Easter each year. The Greeks and Hebrews used it, and the Antikythera mechanism from ancient times showed knowledge of this cycle. The Metonic cycle was also used in other calendars, like the Celtic Coligny calendar and the Runic calendar.

Mathematical basis

The Metonic cycle is a way to match the time it takes for the Earth to go around the Sun (tropical year) with the time it takes for the Moon to go around the Earth (synodic month).

A normal year based on the Moon is about 354 days. This is about eleven days shorter than a year based on the Sun. Over time, this difference adds up. It takes 19 years for the same moon phases to happen again at the same time of year.

This works because 19 years based on the Sun are almost the same as 235 months based on the Moon. To keep the calendar matching the seasons, seven extra months are added over 19 years. Some years have 12 months and some have 13. This keeps the calendar in line with the seasons.