Calendar Structures

There are dozens of different calendars in use throughout the world. Most of them can be assigned to one of three basic types, each of which is based upon apparent motion of the moon and/or sun. Those that are based only on the moon’s phases are termed “lunar” after Luna, the Roman moon goddess. The Muslim Calendar  is strictly lunar.

Calendars whose year length is based upon the sun’s motion are termed “solar” after the Roman sun-god Sol. As the name suggests, calendars that model apparent motions of both the moon and sun are termed “lunisolar.”
Because the time that passes between new or full moons averages just over 29.53 days, it is obvious that there is a good match between natural and calendar months if the latter alternate between 29 and 30 days in length. This is the case for most modern lunar and lunisolar calendars. If based on the sighting of a new moon, two or three months of either 29 or 30 days might occur in a row.

Twelve sequential lunar phases total just over 354.367 days, almost eleven short of a tropical year. That’s why extra months are usually added to lunisolar calendars on a scheduled basis. An example is the Hebrew Calendar. One unfortunate result is that those calendars in some years are thirteen months in length rather than twelve. An unusual superstition grew out of this practice as used in the Chinese Calendar.
Oddly enough, Babylonians and other ancient peoples of Western Asia inserted extra months irregularly, sometimes two or three times a year early in the first millennium B.C.—Near and Middle Eastern people continued irregular intercalation until at least the sixth century B.C. ( Bickerman, Elias Joseph. Chronology of the Ancient World. Ithica, N.Y.: Cornell University Press, 1968. pp. 22-23. )

Babylonians eventually worked out a 19-year cycle in which there were twelve years with twelve months each and seven years with thirteen months each. The thirteenth month was inserted in a fixed pattern that kept cycles of the moon and sun even. Similar calendars were then adopted in many places near Babylon.
Between the 8th and 4th centuries B.C., permanent alterations were made to almost all calendars, regardless of their structure. See 8th to 4th Century B.C. Calendar Changes for details.