Metonic Cycle

In astronomy and calendar studies, the Metonic cycle or Enneadecaeteris (from Greek words for nineteen years) is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the solar year and the synodic (lunar) month. The Greek astronomer Meton of Athens observed that a period of 19 years is almost exactly equal to 235 synodic months, and rounded to full days counts 6940 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.

Taking a year to be 1⁄₁₉ of this 6940-day cycle gives a year length of 365 + 1⁄₄ + 1⁄₇₆ days (the unrounded cycle is much more accurate), which is slightly 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). Meton introduced the cycle in circa 432 BC but it was actually known earlier by Babylonian astronomers.

Mechanical calculation 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), the medieval computus (i.e. the calculation of the date of Easter) and still regulates the 19-year cycle of intercalary months in the Hebrew calendar.