TheMetonic cycle orenneadecaeteris (fromAncient Greek:ἐννεακαιδεκαετηρίς, from ἐννεακαίδεκα, "nineteen") is a period of almost exactly 19 years after which thelunar phases recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235synodic months is just 2 hours, 4 minutes and 58 seconds longer than 19tropical years.Meton of Athens, in the 5th century BC, judged the cycle to be a whole number of days, 6,940.[3] Using these whole numbers facilitates the construction of alunisolar 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 aMetonic calendar (a type oflunisolar calendar), there are twelve years of 12 lunar months and seven years of 13 lunar months.
In theBabylonian andHebrewlunisolar calendars, 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 thecomputation of the date of Easter each year.
The Babylonians applied the 19-year cycle from the late sixth century BC.[4]
According toLivy, the second king of Rome,Numa Pompilius (reigned 715–673 BC), insertedintercalary 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".[5] 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 thatApollo is said to have visited theHyperboreans once every 19 years.[6]
The Metonic cycle has been implemented in theAntikythera mechanism which offers unexpected evidence for the popularity of the calendar based on it.[7]
The (19-year) Metonic cycle is alunisolar cycle, as is the (76-year)Callippic cycle.[8] An important example of an application of the Metonic cycle in theJulian calendar is the 19-yearlunar cycle insofar as provided with a Metonic structure.[9] Meton introduced the 19 year cycle to theAttic 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 AlexandriancomputistAnatolius, who became bishop of Laodicea in AD 268, was the first to devise a method for determining the date of Easter Sunday.[10] However, it was some later, somewhat different, version of the Metonic 19-year lunar cycle which, as the basic structure ofDionysius Exiguus' and also ofBede's Easter table, would ultimately prevail throughoutChristendom,[11] at least until in the year 1582, when theGregorian calendar was introduced.
TheColigny 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.[12]
The Metonic cycle is thought to be numerically encoded on theBerlin Gold Hat from central Europe, dating from c. 1000-800 BC.[13][14][15][16]
TheRunic calendar is aperpetual 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 theNyköping staff, which is believed to date from the 13th century.
TheBahá'í calendar, established during the middle of the 19th century, is also based on cycles of 19 solar years.
ASmall Maḥzor (Hebrew מחזור,pronounced[maχˈzor], meaning "cycle") is a 19-year cycle in thelunisolar calendar system used by theJewish people. It is similar to, but slightly different in usage from, the Greek Metonic cycle (being based on a month of29+13753⁄25920 days, giving a cycle of6939+3575⁄5184 ≈ 6939.69 days[17]), and likely derived from or alongside the much earlierBabylonian calendar.[18]
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.[19]
The Metonic cycle is the most accurate cycle of time (in a timespan of less than 100 years) for synchronizing thetropical year and the lunar month (synodic month), when the method of synchronizing is theintercalation of a thirteenth lunar month in a calendar year from time to time.[20] The traditional lunar year of 12 synodic months is about 354 days, approximately eleven days short of the solar year. Thus, every 2 to 3 years there is a discrepancy of 22 to 33 days, or a full synodic month. For example, if the winter solstice and the new moon coincide, it takes 19 tropical years for the coincidence to recur. The mathematical logic is this:
That duration is almost the same as 235 synodic months:
Thus the algorithm is correct to 0.087 days (2 hours, 5 minutes and 16 seconds).
For alunisolar calendar to 'catch up' to this discrepancy and thus maintain seasonal consistency, sevenintercalary months are added (one at a time), at intervals of every 2–3 years during the course of 19 solar years. Thus twelve of those years have 12 lunar months and seven have 13 months.
What is especially fascinating is the ornamentation on the [Berlin gold hat] in which a complex counting system is encoded, enabling calendar calculations, especially the 19-year cycle of the sun and the moon. ... The star at the tip symbolises the sun, with the sickles and eye patterns representing the moon and Venus, while the circular ornaments can equally be interpreted as depictions of the sun or the moon. … The cycle of the sun determines day and nigh and the seasons, while the moon determines the division of the year into months and days. But the lunar year is eleven days shorter than the solar year. Even as early as the 2nd millennium BC intercalary days were inserted to bring the solar and lunar cycles into alignment. This knowledge is reflected in the ornamentation of the Gold Hat. The stamped patterns should be read as a calendar. For instance, the number of circles in certain decorative areas equals the twelve lunar periods of 354 days. If the patterns in other decorative areas are added, this gives the 365 days of the solar year. It takes 19 years for the solar year and the lunar year to align again. In the ornamentation of the hat the fact is encoded that seven lunar months need to be inserted into the 19-year cycle. Other calculations can be made as well, such as the dates of eclipses of the moon. (…) The golden hats show that astronomical knowledge was combined with cult activities… They were apparently worn over several generation and at some point buried in the ground in a sacred act to protect them from desecration and to place them in the realm of the gods. It seems that Bronze Age rulers combined worldly and spiritual power.
One particularly impressive piece of evidence for early man's astronomical knowledge is the Bronze Age Berlin gold hat, unique in its size and preservation. The sun, evoked by the gold coloration and the pattern of rays at the top of the hat, creates day, night and the seasons by apparently circling the earth. The moon, represented several times on the hat, marks out months and weeks. The number and arrangement of the ornaments is not random; it allows a nineteen-year lunisolar cycle of 228 solar months and 235 lunar months to be calculated. Someone who knew how to read these ornaments would be able to calculate the shifts between the solar year and the lunar year, predict lunar eclipses, and set fixed dates for significant events. … Over half a millennium before the astronomer and mathematician Meton in 432 BC calculated the shifts in the lunisolar cycle, they were already known to the educated elite of the Bronze Age. The golden hat may have been worn by a ruler with a religious role on ceremonial occasions. Other Bronze Age items prove that astronomical knowledge was often preserved in coded form on valuable and sacred objects.
Media related toMetonic cycle at Wikimedia Commons
