Small Mahzor
A Small Mahzor (Hebrew מחזור, pronounced [maχˈzor], 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 with, the Greek Metonic cycle.
Because a tropical year is 365.24219879 days, and a synodic month is 29.53058868 days, the difference between nineteen solar years and 235 lunar months is only about two hours. Thus by adding seven intercalary months in nineteen years, the solar years and the lunar years basically synchronize.
Three ancient civilizations (Babylonia, China and Israel) used lunisolar calendars and knew of the rule of the intercalation from as early as 2000 BC, about the time of the biblical Tower of Babel, the confusion of language, and dispersion of nations. Whether or not the correlation indicates cause-and-effect relationship is an open question.[1][2]
The Greek astronomer Meton in the fifth century BC discovered the same principle, and the western civilization named the cycle after him. The west later applied the Metonic cycle on the solar Roman years (Julian and Gregorian years) in the Era of the Lord (Anno Domini), a.k.a. the Common Era. The golden number is the remaining number of dividing the year in the Common Era by nineteen, plus one.
The Babylonians and the Israelites used Nisan-years, and the Jews used Tishri-years, their years were lunar in nature, different in length, and the beginning of the Jewish cycle is by making the day of creation according to the Rabbinical Chronology (3761 BC) Thus the Golden Number value in the Small Mahzor is different from that in the Metonic cycle, although the principles are the same.