Molad Emtza'i (Average Molad)
The molad emtza'i (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 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, so that in the present era the molad interval is about 3/5 of a second too long.
The traditional epoch of the cycle was 5 hours 11 minutes and 20 seconds after the mean sunset (considered to be 6 hours before midnight) at the epoch of the Hebrew calendar (first eve of Tishrei of Hebrew year 1).
Historically, the original molad reference meridian of longitude was halfway between the Nile river and the end of the Euphrates river, but the excess length of the molad interval causes it to drift progressively eastward at an accelerating rate — in the present era it is at a meridian that passes near Qandahar, Afghanistan!
The molad interval as an exact fraction is 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, so 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.
Although the moment of the traditional Hebrew calendar molad is announced in synagogues on the Shabbat prior to each month (except before Tishrei), its only relevance to the present day fixed arithmetic lunisolar Hebrew calendar is that the molad of the month of Tishrei determines the date of the New Year Day (Rosh Hashanah), subject to possible postponements of 0, 1 or 2 days (depending on certain postponement rules, also see external link).
Traditionally the announced or printed molad moment is quoted in terms of the hours, minutes, and 18ths of a minute elapsed from mean sunset, because Hebrew calendar days begin at sunset. Some printed sources subtract 6 hours to convert the molad moment to "civil" time, but doing so causes the Hebrew weekday to be wrong 25% of the time (whenever the molad moment is between sunset and midnight). Also, some printed sources even add an hour during the summertime for "daylight saving", or attempt to apply conversions to the local time zone, but those are also mistakes because they would affect the molad of Tishrei and thus could imply an erroneous date for Rosh Hashanah.
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