A Metonic cycle aka Enneadecaeteris is a period of 19 years or 235 lunar months. It was named after the mathematician and astronomer Meton of Athens (most mathematicians were astronomers way back when) who is credited with its discovery. This Greek mathematician/astronomer introduced this cycle to the Greeks in 432BCE.
A lunar month or lunation is the time it takes for the Moon to return to the same phase, for example new moon to new moon, it’s about 29.5 days. The Metonic cycle is very close to a whole number of lunar months that roughly corresponds to a whole number of solar years.
This is important in the study of calendars and astronomy because it’s an effective way to synchronize lunar and solar calendars since it’s close to both 19 solar years and 236 lunar months.
This is important because it makes celestial predictions easier. Using the Metonic cycle we alternate between 12 years of 12 months and 7 leap years of 13 months in each cycle of 19 years. Doing this keeps both the lunar and solar calendars aligned -well reasonably aligned.
This cycle was used by various ancient civilizations to create a more accurate calendar and its principles are still used in some modern calendar systems. These civilizations recognized the importance of reconciling lunar and solar calendars to accurately track time, religious festivals, agricultural cycles, and significant events. The Metonic cycle allowed them to create calendars that aligned better with natural astronomical cycles.
The ancient Greeks used this method to synchronize their lunar and solar calendars. It was invented by a Greek man. Babylonians used it to refine their lunar calendars. We can’t forget that they were renowned astronomers and mathematicians. The Hebrew calendar was also influenced by the Metonic cycle. The Jewish lunisolar calendar incorporates aspects of Metonic cycle to align its lunar months with solar years. This helps determine the dates of Jewish holidays. The Mayans incorporated similar concepts into their lunar-solar calendar. Their calendar was highly sophisticated and had different cycles that tracked both lunar and solar movements.
What about in our modern age?
A lunar month consists of 29.5 days and a solar year/calendar consists of 635.25 days. These are not whole multiples of each other and create challenges when trying to merge lunar and solar calendars. We depend on our lunar months and yearly calendars to track time, agricultural cycles, religious observances, and other important dates.
Without adjustments a purely lunar calendar would gradually shift out of alignment with the solar year. Over time the lunar months would move through the seasons causes holidays and agricultural activities to occur at different times in relation to the solar year, and a purely solar calendar wouldn’t accurately reflect the lunar phases used for religious or cultural purposes.