Jewish Calendar

Rosh Hodesh is the beginning of the new month. The length of a month in the Jewish calendar is determined by the time it takes for the moon to make one revolution around the earth as determined by the conjunction of the sun, moon, and earth in a line. This is called the molad, i.e., the "birth" of the "new" moon. Such a revolution is completed in 29 days, 12 hours, 44 minutes and 3.5 second….

Since a calendar month does not begin in the middle of the day because months are counted by days, not hours (B. Meg 5a), it is necessary to add half a day to one month or subtract half a day from the next. As a result, the months alternate between twenty-nine and thirty days in length. The thirty-day month is malei, i.e. full or long; the twenty-nine day month is haser, i.e. defective or short. There are some variations, however, due to considerations [related to the scheduling of certain holidays]. Nisan, Sivan, Av, Tishrei, Shevat and Adar I (in a leap year) are always full. Iyar, Tamuz, Elul, Tevet, Adar II (in a leap year) and Adar (in a nonleap year) are always defective. Heshvan and Kislev are sometimes full and sometimes defective. When a month is thirty days, the Rosh Hodesh of the next month is celebrated for two days because the thirtieth day of the month that has just passed is counted as the first day of Rosh Hodesh, and the first day of the next month, as the second day. Consequently Nisan, Sivan, Av and Tishrei (only the first day of Rosh Hashanah is counted as Rosh Hodesh) always begin with one day of Rosh Hodesh; Iyar, Tamuz, Elul, Tevet, Adar I and Adar II always begin with two days.

These variations result from the solar-lunar structure of the Jewish calendar. The year in the Jewish calendar consists of twelve lunar months, but the festivals follow the solar year, since several of them (Passover, Shavu'ot and Sukkot) must take place in certain seasons, and the seasons are determined by the earth annual revolution around the sun. Since the lunar years is roughly 354.3 days in length, while the solar year is roughly 365.5, or roughly eleven days longer, the festival would eventually fall in the wrong seasons if their occurrence followed the cycle of lunar months. For example, Passover would be celebrated eleven days earlier in each succeeding year, and as a result would eventually be celebrated in the winter, and then in the autumn and summer, in violation of the biblical prescription that Passover must take in the month of Aviv, i.e., in the spring (Deut. 16:1). Similarly, Shavu'ot must occur at the time of the early harvest and Sukkot in the fall.

To prevent this difficulty, the lunar calendar is regularly adjusted to keep it in conformity with the solar year. This is done through the periodic additional, or intercalculation, of a thirteenth month, known as Second Adar or Adar II, immediately after the normal month of Adar, which in leap years is known as First Adar or Adar I. Since the discrepancy between the solar and lunar years amounts 207 every nineteen years, the "leap month" of Adar II is added to the third, sixth, eight, eleventh, fourteenth and nineteenth year of every nineteen year period.

	From: Isaac Klein, A Guide to Jewish Religious Practice Jewish Theological Seminary of America, 1992
	History of the Jewish calendar Zodiac in the Jewish tradition