Metonic calendar
For astronomy and calendar studies, the Metonic cycle or Enneadecaeteris (from Ancient Greek: ἐννεακαιδεκαετηρίς, "nineteen years") is a period of very close to 19 years that is nearly a common multiple of the solar year and the synodic (lunar) month. The Greek astronomer Meton of Athens (fifth century BC) observed that a period of 19 years is almost exactly equal to 235 synodic months and, rounded to full days, counts 6,940 days. The difference between the two periods (of 19 years and 235 synodic months) is only a few hours, depending on the definition of the year.
Considering a year to be 1⁄19 of this 6,940-day cycle gives a year length of 365 + 1⁄4 + 1⁄76 days (the unrounded cycle is much more accurate), which is about 11 days more than 12 synodic months. To keep a 12-month lunar year in pace with the solar year, an intercalary 13th month would have to be added on seven occasions during the nineteen-year period (235 = 19 × 12 + 7). When Meton introduced the cycle around 432 BC, it was already known by Babylonian astronomers.
A mechanical computation of the cycle is built into the Antikythera mechanism.
The cycle was used in the Babylonian calendar, ancient Chinese calendar systems (the 'Rule Cycle' 章) and the medieval computus (i.e. the calculation of the date of Easter). It regulates the 19-year cycle of intercalary months of the modern Hebrew calendar. The start of the Metonic cycle depends on which of these systems is being used; for Easter, the first year of the current Metonic cycle is 2014.
...
Wikipedia