Levítico 23:4 Halacá: Mishneh Torah, Prayer and the Priestly Blessing, Mishneh Torah, Sanctification, Abudarham & Sefer HaChinukh

On Sabbaths and Festivals, seven blessings are recited in each of the four Services for the day; namely, the usual first three blessings, and last three blessings, and an intermediate blessing appropriate to the particular day. On Sabbaths, the intermediate blessing concludes with the formula, "Who hallowest the Sabbath." On the Festivals it concludes, "Who hallowest Israel and the Seasons." And on a Sabbath which is at the same time a festival, the concluding formula is, "Who hallowest the Sabbath, Israel and the Seasons." On New Year, the conclusion is, "King over all the earth, who hallowest Israel and the Day of Memorial." When the New Year falls on a Sabbath, the concluding formula is, "King over all the earth, who hallowest the Sabbath, Israel and the Day of Memorial."

Witnesses that saw the month go to the court to testify, even on Shabbat, as it is said (Leviticus 23:4) "that you call them at their appointed time" and anywhere it is said "appointed time" the Shabbat is pushed off. Thus, we only violate the Shabbat for the first of the month of Nissan which contains the festival of Passover and for the first of the month of Tishrei which contains the festivals of the Day of Atonement and Tabernacles in order to fix the festivals which are described with the term "appointed time". And in a time when the Holy Temple exists, we violate the Shabbat for all the months because of the additional sacrifice of every first of the month which pushes off the Shabbat.

And according to the words of our Rabbis, may their memory be blessed, that is the moment that the sun and the moon attach themselves to each other in their median path in one of the parts of the sky; and this is the same in all of the world. So that is the beginning of the next month and the end of the past month. And it would have been fitting to designate this as the start of the month, according to the path of the luminaries, were it not that the [precise] time of this birth is not visible to people, such that the only way to arrive at is by way of calculation and reasoning. But both of these are difficult for most of the world and questions come about them, such that the thoughts of people do not come to a single opinion. And because of that, the Holy One, blessed be He, was not stringent and did not command us to observe the start of the months from their beginning in the sky, which is the time of the [moon's] birth. Rather, He granted us leeway about the thing and give us permission to set the month according to the counsel of the sages, since we have no sign that testifies to us about its beginning in the sky, whereas its beginning according to our eyesight - which is what is revealed to us - is not the same in every person's eyes. And because of that, it requires assistance and control. So the Holy One, blessed be He, gave the right and the power over this to the hands of our sages, so that they could control it according to their opinion and their wisdom. And that is why the verse made the festivals depend on proclamation, in its stating (Leviticus 23:4), "These are the festivals of the Lord, holy gatherings, which you shall proclaim in their seasons." That is to show that we have permission to set the festivals [by way of proclaiming the new months].