Editing Metonic cycle (section)

==Application in traditional calendars==
In the [[Babylonian calendar|Babylonian]] and [[Hebrew calendar|Hebrew]] [[lunisolar calendar]]s, the years 3, 6, 8, 11, 14, 17, and 19 are the long (13-month) years of the Metonic cycle. This cycle forms the basis of the Greek and Hebrew calendars. A 19-year cycle is used for the [[Computus|computation of the date of Easter]] each year.

<!--'The [[Chaldea]]n astronomer [[Kidinnu]] (4th century BC) knew of the 19-year cycle' This is not surprising as he lived in Babylon c. 100 years after they had started using the cycle. If he had been born say 200 years earlier, I can see the point of mentioning him-->
The Babylonians applied the 19-year cycle from the late sixth century BC.<ref>{{Cite web |date=July 2021 |title=The Babylonian Calendar |url=https://webspace.science.uu.nl/~gent0113/babylon/babycal.htm |url-status=live |archive-url=https://web.archive.org/web/20230902103953/https://webspace.science.uu.nl/~gent0113/babylon/babycal.htm |archive-date=2 September 2023 |website=Mathematical Institute |publisher=Utrecht University}}</ref>

According to [[Livy]], the second king of Rome, [[Numa Pompilius]] (reigned 715–673 BC), inserted [[Intercalation (timekeeping)|intercalary]] months in such a way that "in the twentieth year the days should fall in with the same position of the sun from which they had started".<ref>Livy, [[Ab Urbe Condita]], I, XIX, 6.</ref> As "the twentieth year" takes place nineteen years after "the first year", this seems to indicate that the Metonic cycle was applied to Numa's calendar.

[[Diodorus Siculus]] reports that [[Apollo]] is said to have visited the [[Hyperborea]]ns once every 19 years.<ref>Diodorus Siculus, ''Bibl. Hist.'' [https://archive.org/details/diodorusofsicily02dioduoft/page/40/mode/2up II.47].</ref>

The Metonic cycle was implemented in the 2nd century BC [[Antikythera mechanism]], which offers unexpected evidence for the popularity of the calendar based on it.{{sfn|Freeth|Jones|Steele|Bitsakis|2008|pp=614-617}}

The (19-year) Metonic cycle is a '''lunisolar''' cycle, as is the (76-year) [[Callippic cycle]].{{sfn|Nothaft  | 2012 | p=168}} An important example of an application of the Metonic cycle in the [[Julian calendar]] is the 19-year '''lunar''' cycle insofar as provided with a Metonic structure.{{sfn| McCarthy | Breen |2003 | p= 17}} Meton introduced the 19 year cycle to the [[Attic calendar]] in 432 BC. In the following century, [[Callippus]] developed the Callippic cycle of four 19-year periods for a 76-year cycle with a mean year of exactly 365.25 days.

Around AD 260 the Alexandrian [[Computus|computist]] [[Anatolius of Laodicea|Anatolius]], who became bishop of Laodicea in AD 268, was the first to devise a method for determining the date of Easter Sunday.{{sfn| Declercq | 2000 | pp= 65–66}} However, it was some later, somewhat different, version of the Metonic 19-year lunar cycle which, as the basic structure of [[Dionysius Exiguus]]' and also of [[Bede]]'s Easter table, would ultimately prevail throughout [[Christendom]],{{sfn| Declercq | 2000 | p= 66}} at least until in the year 1582, when the [[Gregorian calendar]] was introduced.

The [[Coligny calendar]] is a Celtic lunisolar calendar using the Metonic cycle. The bronze plaque on which it was found dates from c. AD 200, but the internal evidence points to the calendar itself being several centuries older, created in the Iron Age or late Bronze Age.{{sfn|Olmsted|2001|pp=}}

The Metonic cycle is thought to be numerically encoded on the [[Berlin Gold Hat]] from central Europe, dating from c. 1000-800 BC.{{efn|name=LifeAndBelief}}{{efn|name=BerlinGoldHat}}{{sfn|Menghin|2008|pp=157-169}}{{sfn|Anon|2003|pp=220-237}}

The [[Runic calendar]] is a [[perpetual calendar]] based on the 19-year-long Metonic cycle. It is also known as a Rune staff or Runic Almanac. This calendar does not rely on knowledge of the duration of the tropical year or of the occurrence of leap years. It is set at the beginning of each year by observing the first full moon after the winter solstice. The oldest one known, and the only one from the Middle Ages, is the [[Nyköping staff]], which is believed to date from the 13th century.

The [[Bahá'í calendar]], established during the middle of the 19th century, is also based on cycles of 19 solar years.

===Hebrew calendar===
A '''Small Maḥzor''' ([[Hebrew language|Hebrew]] מחזור, {{IPA|he|maχˈzor|pron}}, meaning "cycle") is a 19-year cycle in the [[lunisolar calendar]] system used by the [[Jewish people]]. It is similar to, but slightly different in usage from, the Greek Metonic cycle (being based on a month of {{fraction|29|13753|25920}} days, giving a cycle of {{fraction|6939|3575|5184}}&nbsp;≈&nbsp;6939.69 days{{efn|name=Tondering}}), and likely derived from or alongside the much earlier [[Babylonian calendar|Babylonian]] calendar.<ref>{{Cite web|title=Jewish religious year {{!}} Cycle, Holidays, & Facts {{!}} Britannica|url=https://www.britannica.com/topic/Jewish-religious-year|access-date=14 November 2021|website=www.britannica.com|language=en}}</ref>

===Polynesia===
It is possible that the Polynesian kilo-hoku (astronomers) discovered the Metonic cycle in the same way Meton had, by trying to make the month fit the year.{{sfn | Johnson | 2001 | p= 238}}