The first day of the biblical month is called Rosh Chodesh (×¨××© ×—×“×©), which literally means 'a new head' and is understood to mean the 'first of the New Month.' A Rosh Chodesh occurs when the first crescent of the New Moon appears in the sky. Note that the biblical Rosh Chodesh is not the same as the English "New Moon." Rather the Rosh Chodesh moon is ordinarily the first visible crescent of the new lunar cycle.
The middle of the biblical month is a full moon. The end of the biblical month occurs when the moon disappears completely from the sky.
Most of the Ancient Near East determined their calendars according to the lunar phases. In that regard, Israel was not unique.
In the Torah, the commandment of identifying and declaring the new moon was addressed only to Moses and Aaron (Exodus 12). Were it addressed to the entire community, the determination of the calendar would be arbitrary and subject to all sorts of discrepancies. For that reason, this commandment has always been regarded as a function of the Sanhedrin, i.e. the leadership of Israel.1
However, in the Fourth Century, the Roman government officially forbade the Sanhedrin from convening and determining the New Moon. The Jewish community throughout the diaspora was left to their own devices for determining the calendar. The result was uncertainty over festival days, discord between communities and general chaos. A cloudy day could change the day one celebrates Passover! As a result, the method of determining the moon by observation alone fell into disuse. Astronomical projections were made to fix the calendar in advance. Rabbi Hillel II created a fixed calendar that all Israel could use.
The advent of the Rosh Chodesh is customarily announced in the synagogue on the Shabbat before it occurs. This tradition arose in ancient times as a means of keeping the community informed about the biblical calendar. A special congregational prayer, petitioning God for a good month, accompanies the announcement of the day on which the New Moon will occur.
May it be Your will, LORD, our God and the God of our fathers that You make new this month upon us for goodness and for blessing. May You give us a long life--a life of peace; a life of goodness; a life of blessing; a life of sustenance; a life of physical health; a life in which there is fear of heaven and fear of sin; a life in which there is no shame nor humiliation; a life of wealth and honor; a life in which we will have love of Torah, fear of God; a life in which the LORD fulfills our heartfelt requests for the good. Amen, Selah. (Shabbat Petition of the coming New Month)
Although the New Moon is an appointed time, it is not a Sabbath, nor is there a commandment to assemble on it for a 'holy convocation.' We know from the book of 1 Samuel that King Saul used to hold a two-day banquet on the New Moon.2 We know that the prophets taught on the Sabbaths and New Moons.3 Shofars were sounded on the New Moon.4 In the Messianic kingdom to come, "it shall be from new moon to new moon and from Sabbath to Sabbath, all mankind will come to bow down before Me," says the LORD. (Isaiah 66:23)
According to some traditions, the New Moon is a holiday for women. The Jerusalem Talmud reports that women are given the extra holiday on which they are to be free from their usual duties as a reward for not contributing their jewelry to the golden calf project.5 Fathers and husbands may be wise to take on an extra load of duties on the New Moon to give their daughters and wives a break.
For believers, the celebration of the new moons carries great significance. Not only are they calendar events, but also the cycle of the moons speaks to the new birth and recreation which is ours in Messiah. Just as the moon is born again, we are renewed in Messiah. It is the festival of the born again.
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