Because the length of the lunar month is not an even fraction of the length of the tropical year, a purely lunar calendar quickly drifts relative to the seasons.
Such months average 29.5 days, but the length of the true lunar month is, as I've pointed out, 29.5306 days.
The average length of the month is further corrected by adding a day to Nayon at irregular intervals-a little more than seven times in two cycles (39 years).
However, the calendar will already have to have been adjusted after some millennia because of changes in the length of the vernal equinox year, the synodic month, and the day.
The average length of the synodic month is 29.530589 days.
In Temple times, the length of the month depended on witnesses who had seen the new moon coming to the Temple in Jerusalem.
Thus, estimation of the length of the month was ensured to have relative accuracy of 1 part in millions.
The length of the lunar month is 29.53059 days so if you count the number of days in a lunation it will be either 29 or 30 days.
Rounded approximations to π, the length of the year, and the length of the month are also ancient-see base 60.
Rounded approximations to π, the length of the year, and the length of the month are also ancient.
