Editing Metonic cycle (section)

{{Short description|19 solar year recurrence of lunar phases}}
{{Use dmy dates|date=March 2022}}
[[File:CLM 14456 70v71r.jpg|thumb|320px|right|Depiction of the 19 years of the Metonic cycle as a wheel, with the Julian date of the Easter New Moon, from a 9th-century computistic manuscript made in [[St. Emmeram's Abbey]] ([[Codex latinus monacensis|Clm]] 14456, fol. 71r)]]
[[File:Christmas_full_moons_1711-2300.gif|thumb|For example, by the 19-year Metonic cycle, the full moon repeats on or near [[Christmas]] between 1711 and 2300.<ref>{{cite web |date=17 December 2015 |title=Rare Full Moon on Christmas Day |url=https://www.nasa.gov/feature/goddard/rare-full-moon-on-christmas-day |url-status=live |archive-url=https://web.archive.org/web/20231108031712/https://www.nasa.gov/solar-system/rare-full-moon-on-christmas-day/ |archive-date=8 November 2023 |website=NASA}}</ref><ref>{{cite news |last1=Skilling |first1=Tom |date=20 December 2015 |title=Ask Tom: How unusual is a full moon on Christmas Day? |newspaper=[[Chicago Tribune]] |url=http://www.chicagotribune.com/news/weather/ct-wea-1221-asktom-20151220-column.html |url-status=live |access-date= |archive-url=https://web.archive.org/web/20151222054149/http://www.chicagotribune.com/news/weather/ct-wea-1221-asktom-20151220-column.html |archive-date=22 December 2015}}</ref> A small horizontal [[libration]] is visible comparing their appearances. A red color shows full moons that are also [[lunar eclipse]]s.]]

The '''Metonic cycle''' or '''enneadecaeteris''' (from {{langx|grc|ἐννεακαιδεκαετηρίς}}, from ἐννεακαίδεκα, "nineteen") is a period of almost exactly 19 years after which the [[lunar phases]] recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 [[synodic month]]s is just 2 hours, 4 minutes and 58 seconds longer than 19 [[tropical year|tropical years]]. [[Meton of Athens]], in the 5th century BC, judged the cycle to be a whole number of days, 6,940.<ref>{{cite encyclopedia |entry=Meton |title= Oxford Reference |url=https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100154128}}</ref> Using these whole numbers facilitates the construction of a [[lunisolar calendar]].

A tropical year (about 365.24 days) is longer than 12 lunar months (about 354.36 days) and shorter than 13 of them (about 383.90 days).  In a '''Metonic calendar''' (a type of [[lunisolar calendar]]), there are twelve years of 12 lunar months and seven years of 13 lunar months.