Hebrew Calendar. The Israelites used such a lunisolar, or bound solar, calendar. This is evident from the fact that Jehovah God established the beginning of their sacred year with the month Abib in the spring and specified the celebration of certain festivals on fixed dates, festivals that were related to harvest seasons. For these dates to have coincided with the particular harvests, there had to be a calendar arrangement that would synchronize with the seasons by compensating for the difference between the lunar and solar years.​—Ex 12:1-14; 23:15, 16; Le 23:4-16.

The Bible does not indicate what method was originally used to determine when additional days or an additional, or intercalary, month should be inserted. It is logical, however, that either the vernal or the autumnal equinox served as a guide to indicate when the seasons were falling behind sufficiently to require calendar adjustment. Though not specifically mentioned in the Bible, a 13th month that was added by the Israelites to accomplish this adjustment was called, in postexilic times, Veadar, or the second Adar.

We do not find record of a definitely fixed or standardized form of Jewish calendar until the fourth century of our Common Era (c. 359 C.E.), when Hillel II specified that the leap years of 13 months should be the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th of each 19 years. Such a 19-year cycle is commonly called the Metonic cycle, after the Greek mathematician Meton (of the fifth century B.C.E.), although there is also evidence that such a cycle was perfected before him by the Babylonians. (See Babylonian Chronology, 626 B.C.–A.D. 75, by R. A. Parker and W. H. Dubberstein, 1971, pp. 1, 3, 6.) This cycle takes into account that every 19 years the new and the full moons fall again on the same days of the solar year.