Metonic cycle

The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 synodic months is just 2 hours, 4 minutes and 58 seconds longer than 19 tropical years.

[4] According to Livy, the second king of Rome, Numa Pompilius (reigned 715–673 BC), inserted 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".

[6] The Metonic cycle has been implemented in the Antikythera mechanism which offers unexpected evidence for the popularity of the calendar based on it.

[10] 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,[11] at least until in the year 1582, when the Gregorian calendar was introduced.

[12] The Metonic cycle is thought to be numerically encoded on the Berlin Gold Hat from central Europe, dating from c. 1000-800 BC.

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

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).

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 ( Clm 14456, fol. 71r)
For example, by the 19-year Metonic cycle, the full moon repeats on or near Christmas between 1711 and 2300. [ 1 ] [ 2 ] A small horizontal libration is visible comparing their appearances. A red color shows full moons that are also lunar eclipses .