Metonic cycle

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The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the year (specifically, the seasonal i.e. tropical year) and the synodic month. 19 tropical years differ from 235 synodic months by about 2 hours. The Metonic cycle's error is one full day every 219 years, or 12.4 parts per million.

19 tropical years  = 6939.602 days
235 synodic months = 6939.688 days

It is helpful to recognize that this is an approximation of reality. The period of the Moon's orbit around the Earth and the Earth's orbit around the Sun (ignoring also exact definition of the year) are independent and have no known physical resonance. Examples of a real harmonic lock would be the Mercury, with its 3:2 spin-orbit resonance or other orbital resonance

The cycle was known to the Greek astronomer Meton, who introduced it about 432 BC, and the Chaldean astronomer Kidinnu (4^th century BC). The Babylonians may have known it earlier, and originally they may have measured the Moon's motion against the stars (sidereal year); however, ancient astronomers did not make a clear distinction between sidereal and tropical years before Hipparchus discovered precession of the equinox ca. 130 B.C.

This cycle is used by the Hebrew calendar. It is also used in the computation of the date of Easter.

It is possible that Homer knew about the cycle some centuries before Meton, and used it in the Odyssey. Homer makes Odysseus leave Ithaca, and then return and secretly meet Penelope at just the exact moment when one cycle has passed Gilbert Murray. The Rise of the Greek Epic. Oxford, (1907) Joseph Campbell. The Masks of God: Occidental Mythology, vol III, (1964) J.F. del Giorgio. The Oldest Europeans. A.J. Place (2006).

In a typical lunisolar calendar, most years are lunar years of 12 months, but some years have an extra month, known as an intercalary or embolismic month. There are 7 of these intercalary months in the 19 years of a Metonic cycle. Traditionally (in the ancient Babylonian, Hebrew, and Attic calendars), the years: 3, 6, 8, 11, 14, 17, and 19, are the long (13-month) years of the Metonic cycle.

The Cycle incorporates two less accurate subcycles, for which 8 years = 99 lunations to within 1.5 days, with an error of one day every 5 years (an Octaeteris), and 11 years = 136 lunations within 1.5 days, with an error of one day every 7.3 years. The Metonic cycle itself is a subcycle of the next more correct 334 years = 4131 lunations to within 41 minutes, with an error of one day every 11598 years.

Meton approximated the cycle to a whole number (6940) of days, obtained by 125 long months of 30 days and 110 short months of 29 days. The Callippic cycle was a more accurate approximation, obtained by taking one day away from every fourth of Meton's cycles, so creating a 76-year cycle with a mean year of exactly 365.25 days.

The 19-year cycle is also close (to somewhat more than half a day) to 255 draconic months, so it is also an eclipse cycle, which lasts only for about 4 or 5 recurrences of eclipses.

Metonic cycle

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See also