| rdfs:comment | - 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. Nineteen 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
- For astronomy and calendar studies, the Metonic cycle or Enneadecaeteris (from Ancient Greek: εννεαδεκαετηρις, "nineteen years") is a period of very close to 19 years which is remarkable for being nearly a common multiple of the solar year and the synodic (lunar) month. The Greek astronomer Meton of Athens (fifth century BCE) 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.
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| abstract | - 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. Nineteen 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 Mercury, with its 3:2 spin-orbit resonance or other orbital resonance. A year of 12 synodic or lunar months is about 354 days on average, 11 days short of the 365 day solar year. Therefore in a lunisolar calendar every 3 years or so there is a difference of more than a full month between the lunar and solar years, and an extra (embolismic) month should be inserted (intercalation). The Athenians appear not to have had a regular means of intercalating a 13th month; instead, the question of when to add a month was decided by an official. The Greek astronomer Meton of Athens introduced a formula for intercalation in 432 BC. It was his observation that a period of 19 solar years is almost exactly 235 lunar months, and rounded to full days counts 6940 days. The error is only 2 hours between 19 years and 235 months. This rounded day count defines the length of the year to be 365 + 1/4 + 1/76 days (the unrounded cycle is much more accurate). Seven of the 19 years would have an intercalated month. Traditionally (in the ancient Attic and Babylonian calendars, as well as in the Hebrew calendar), the years: 3, 6, 8, 11, 14, 17, and 19, are the long (13-month) years of the Metonic cycle. This cycle can be used to predict eclipses, forms the basis of the Greek and Hebrew calendars, and is used in the computation of the date of Easter each year. In Antiquity the Metonic cycle was sometimes called the Great year. The {{WPlink|Chaldea|Chaldean}} astronomer Kidinnu (4th century BC) knew of the 19-year cycle, but the Babylonians may have learned of it earlier. They measured the Moon's motion against the stars, so the 235:19 relation may originally have referred to sidereal years, instead of tropical years as it has been used in various calendars; however, ancient astronomers did not make a clear distinction between sidereal and tropical years before Hipparchus discovered precession of the equinoxes c. 130 BC. It is possible that Homer knew about the cycle some centuries before Meton. In the Odyssey, after Odysseus leaves Ithaca, he returns to secretly meet Penelope at the exact moment when one Metonic cycle has passed. The Metonic cycle incorporates two less accurate subcycles, for which 8 years = 99 lunations (an Octaeteris) to within 1.5 days, i.e. an error of one day in 5 years; and 11 years = 136 lunations within 1.5 days, i.e. an error of one day in 7.3 years. The Metonic cycle itself is a subcycle of the next more correct approximation: 334 years = 4131 lunations (see lunisolar calendar for more details). 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. In the following century Callippus developed the Callippic cycle. This 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. Later the solar Julian calendar was designed to have a year of this length by using leap 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.
- For astronomy and calendar studies, the Metonic cycle or Enneadecaeteris (from Ancient Greek: εννεαδεκαετηρις, "nineteen years") is a period of very close to 19 years which is remarkable for being nearly a common multiple of the solar year and the synodic (lunar) month. The Greek astronomer Meton of Athens (fifth century BCE) 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. Considering 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 BCE, but it was actually known earlier by Babylonian astronomers. 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), the medieval computus (i.e. the calculation of the date of Easter) and still regulates the 19-year cycle of intercalary months of the Hebrew calendar.
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