Molad (מולד, plural Moladot, מולדות) is a Hebrew word meaning "birth" that also generically refers to the time at which the New Moon is "born". The word is ambiguous, however, because depending on the context, it could refer to the actual or mean astronomical lunar conjunction (calculated by a specified method, for a specified time zone), or the molad of the traditional Hebrew calendar (or another specified calendar), or at a specified locale the first visibility of the new lunar crescent after a lunar conjunction.
Other than its usage connected with the lunar cycle, מולד is also the word used in the Hebrew term for Christmas, חג המולד (literally “Holiday of the Birth” or “Holiday of the Nativity”).
The Traditional Molad Interval
The molad emtza'i (מולד אמצעי, average molad, used for the traditional Hebrew calendar) is based on a constant interval cycle that is widely but incorrectly regarded as an approximation of the time in Jerusalem of the mean lunar conjunction. Each molad moment occurs exactly 29 days 12 hours 44 minutes and 3+1/3 seconds (or, equivalently, 29 days 12 hours and 44+1/18 minutes) after the previous molad moment. This interval is numerically exactly the same as the length of the mean synodic month that was published by Ptolemy in the Almagest, who cited Hipparchus as its source. Although in the era of Hipparchus (2nd century BC) this interval was equal to the average time between lunar conjunctions, mean lunation intervals get progressively shorter due to tidal transfer of angular momentum from Earth to Moon, consequently in the present era the molad interval is about 3/5 of a second too long.
The molad interval as an exact improper fraction = 29+12/24+44/1440+(10/3)/86400 = 765433/25920 days, where the denominator 25920 is the number of parts per day (each part equals 1/18 minute or 10/3 seconds) and one can alternatively write the numerator in the interesting descending sequence 765432+1. As a mixed fraction this reduces to 29+13753/25920 days, which implies an underlying fixed arithmetic lunar cycle of 25920 months in which 13753 months have 30 days and the remaining 25920 – 13753 = 12167 months have 29 days, spread as smoothly as possible. In any such lunar cycle, which must have an integer number of days, 30-day months must occur slightly more frequently than 29-day months, such that 2 consecutive 30-day months occur at intervals of either 17 or 15 months, where the 17-month interval is approximately twice as common as the 15-month interval.
This typical mean lunar cycle pattern becomes clearly evident if one computes the molad moment, adds 1/4 day to account for the molad zakein postponement rule, keeps only the integer part of the result to compute the molad day, calculates the difference from the previous molad day (will be either 30 days = "F" for full, or 29 days = "D" for deficient), and then lists the sequence with the insertion of one space in the middle of every FF pair and starting a new line at the end of every 15-month interval. For example, for the period from the molad of Nisan 5726 until the molad of Elul 5818 inclusive the pattern obtained is: