The Moon must have made an incredible impression on the first members of the human race. Apart from being the brightest object in the night sky, its constantly and regularly changing shape may have led to the invention of the first calendars.
What could be more natural than to say: Lets meet again at the next full Moon. The Moons phases were there for everyone to see and their use would avoid the counting and recording of the number of days since the last meeting. It was thus inevitable that the month would become an inseparable part of our calendar along with the day, marked by the movement of the Sun, and the year which was marked by the passing of the seasons.
A natural next step would have been to link the lunar month with the year and this is where the difficulties began. Initially, twelve lunar months with four seasons of three lunar months would have seemed a good approximation to the year. Unfortunately, the lunar month is just over 29½ days long which means that twelve lunar months falls short of a year by about eleven days.
Starting a year eleven days early might not seem much, but after only three years the lunar year would be a calendar month out of step with the seasons which would certainly cause problems with the sowing of crops if you live in an agricultural community.
So, how about a year of 13 lunar months? Unfortunately, this would lead to a year that would be over 18 days too long.
In 433 B.C. Meton discovered that 19 years (6939.689 days) is almost exactly the same length as 235 lunar months (6939.602 days). This would produce a year that would be that a 19-year cycle consisting of 12 years that were 12 lunar months long and 7 years that were 13 lunar months long would keep the lunar months in step with the seasons. These dates were inscribed in gold lettering on public monuments and, for this reason, the number of a year in a Metonic cycle is called the Golden Number.
The first year of a cycle can be chosen arbitrarily but the cycles now in use can be traced back to 1 BC where the cycle begins at 1 when the New Moon occurs on 1 January (1995, 2014, 2033). You can also see whether a year is the beginning of a cycle by dividing it by 19 and checking whether the remainder is 0.
Predicting the phases of the Moon
Calculating the date of many religious festivals, including Easter, requires you to be able to predict the dates of the full Moon. As the mean time between the Moons phases is just over 29½ days, you could roughly predict the next few occurrences of the same phase by alternating gaps of 29 and 30 days. Unfortunately, this method will become inaccurate after a few months because the Moon is subject to over 1500 influences which can affect the date of the full Moon from month to month.