Metonic cycle

The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the 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.

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

This approximation is used by the Hebrew calendar. It was known to the Greek astronomer Meton, who introduced it about 432 BC, and the Chaldean astronomer Kidinnu (4th cent. BC). It is also used in the computation of the date of Easter.

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

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