The sidereal month
The time the moon takes to travel from a position in the heavens (using the stars as markers) back to the same position is 27 days, 7 hours, 43 minutes, 11.5 seconds is called a sidereal month.
The sidereal month is not the time from new moon to new moon and it is not what ancient men (nor modern humans) would call a month.
It is the relationship of the moon to the sun that marks the month which is used by mankind not the relationship of the moon to the stars.
As the moon travels around the earth, once every revolution it gets between the earth and the sun.
Sometimes the moon comes exactly between the sun and the earth and partly, or entirely, "hides" the sun.
When the moon "covers" the sun, we have an eclipse of the sun, or a solar eclipse.
Most of the time, the moon is slightly above or slightly below the sun so it is not covered up entirely.
Naturally, when the moon is between the sun and the earth, we can not see the moon because its dark side faces the earth and this is called the "new moon."
As the moon moves eastward from the sun around the earth, a sliver of light on one edge can be seen.
As the moon continues to "drift" eastward from the sun, more and more of the sunlit half of the moon can be seen each night.
When the moon has completed one-fourth of its revolution, we can see exactly half the sunlit portion.
As the moon continues to move eastwasrd, it grows gibbous as more of the sunlit portion is visible.
When it is on the side of the earth almost directly opposite to the sun, it is usually a little above or just below the earth's shadow; however, when it is exactly opposite and is in the earth's shadow, we have an eclipse of the moon, or a lunar eclipse.
When the moon is on the side of the earth opposite to the sun, the face of the moon which is toward the earth is also toward the sun and, since is entirely lit up, we have a "full moon."
The full moon is at the eastern horizon when the sun is at the western horizon; therefore, the full moon "rises" at sunset and "sets" at sunrise.
There are two "half moons", one coming to the full moon and one on the way back to the new moon.
Calendars show the first half moon as the first quarter and the second half moon as the last (or third) quarter of the moon.
The half moons are called "quarters" because half the visible face of the moon is one quarter the entire surface of the moon, if the unseen face on the other side is counted.
The time from new moon to new moon is measured as 29 days, 12 hours, 44 minutes, 3 seconds.
New moon to new moon is how people have measured time for thousands of years.
Synodical month
The responsibility for keeping time was originally the responsibility of priests.
The meeting of priests and other religious officials is known as a synod and it was such a group that determined when the new moon had arrived.
The astronomical period from new moon to new moon is even today called the synodical month.
During Roman times, the Pontifex Maximus (high priest) would be responsible for proclaiming the beginning of a new month when he saw the crescent of the waxing moon.
The Latin word for "proclaim" or "announce" is kalare and that's why the Roman calendar always started with the Calends and that's where the English word for "calendar" comes from.
The Romans called the day which came at or near the middle of each month the Ides (usually the 13th of each month, except for March, May, July, and October which had their Ides on the 15th).
The 9th day before the Ides (including the Ides and the Nones) was the Nones, which in Latin means nine.
The Nones fell on the 7th day of some months (March, May, July, and October) and on the 5th day of the others.
The Babylonians broke the month into parts which is still used even to our present time: the new moon, the first quarter, the full moon, and the last quarter.
The so-called parts of the moon are known as phases from Greek meaning "appearance."
The time between any of the four phases of the moon is one-quarter of synodical month (seven days, nine hours, and eleven minutes).
The word "week" comes to us from Teutonic, or Old English wicu to Middle English weke, and means "change" or "alteration" [perhaps as a reference to the moon].
The Greeks and Romans did not have the seven-day week in pre-Christian times.
Time goes, you say? Ah, no!
Alas, Time stays, we go.
—Austin Dobson
Sources of information for Calendar, Moon Facts, Parts 1 to 6 are located at this Calendars Bibliography Unit.
Moon Facts, Part 3, is available.