Sefer HaChinukh's 4th Mitzvah: Calendars

(1) And the LORD spoke unto Moses and Aaron in the land of Egypt, saying: (2) ’This month shall be unto you the beginning of months; it shall be the first month of the year to you.

(1) The commandment of sanctifying the new month—to sanctify months and intercalate [months into] years in the Court [whose members are the] greatest in wisdom and ordained in the Land of Israel, and to establish the year's holidays according to that sanctification, as it says, "This month shall be to you the first of months." (Exodus 12:2)

This means, when you see the renewal of the moon, establish for yourselves the new month, or even if you do not see it, since it is appropriate for [the moon] to appear according to the accepted calculation.

Likewise, this commandment includes the commandment of intercalation, since the basis of the commandment to sanctify the month is for Israel to observe God's holidays at their appointed times. And the commandment of intercalation has the same basis. However, beyond this verse are more Torah passages concerning the commandment of intercalation, as it is written, "You shall observe this commandment in its proper time" (Exodus 13:10); and likewise, "Observe the month of Aviv." (Deuteronomy 16:11)

(2) The procedure of the commandment: Two Jews fit to testify come before the court and testify before them that they saw the renewed moon. They establish the new month on the basis of their [testimony] and say, "Today has been sanctified." The reason why this commandment applies only with ordained judges is because of the interpretation [of the verse], "This month shall be for you," i.e. great [in Torah] and ordained, like you (Rosh Hashanah 22a), since [this verse] was said to Moses and Aaron. This matter was further expounded, as it is juxtaposed to "speak to the entire congregation of the children of Israel," meaning that they who sanctify the month must have the assent of all Israel, meaning the wisest men of Israel, such as the Great Court (the Sanhedrin). ..And if you ask: If so, how do we conduct ourselves today, when we lack ordained wise men? Know that thus we have received [our calendar], since R. Hillel the Prince, son of R. Judah the Prince, who was the greatest of his generation and ordained in the Land of Israel—he was the wise man who fixed for us the calculation of intercalation, sanctified future months, and intercalated future [months into] years until the coming of Elijah (i.e. until the Messianic Era), and it is upon this that we rely today....

(3) Of the roots of this commandment: so that Israel shall make God's holidays in their (proper) times, as God commanded that we make Passover in the time of produce, the spring, as is written, "Observe the month of Aviv, and you shall offer the Passover sacrifice." (Deuteronomy 16:1) And the holiday of Sukkot is [to fall] at the time of the [fruit] harvest, as is written, "And the Festival of the Harvest at the turn of the year." (Exodus 34:22) And were it not for intercalation, the holidays would come not at these times, since Israel calculates their months and festivals according to the lunar year, which has 354 days, 8 hours, and 876 halakim , which is less than the solar year by 10 days, 21 hours, and 204 halakim, (a mnemonic: 10, 21, 204). Due to the ripening of the produce and fruit from the power of the sun, it turns out that but for intercalation, by which we align the lunar and solar years, Passover would not come in spring, nor Sukkot at the time of the [fruit] harvest. And this matter is to be fixed by the greatest [scholars] of the generation, since it is a matter requiring great wisdom, and since it is also said that from this [calculation one comes to know] the agricultural happenings of the year, it is appropriate to give [this task] only to great and pious men.

(4) ...And furthermore did they expound on this verse: From where do we know that we only intercalate the month during daytime? [We learn this from the] verse, [which] says, "from year to year" (yamim yemima, a play on yom, day) (Sanhedrin 10b);

(5) [This commandment] applies in all places and at all times when we have ordained wise men, according to the aforementioned conditions. One who transgresses and does not [sanctify the new month or intercalate the month], if he be a wise man for whom it is appropriate, has neglected a positive commandment, and his punishment is very great since he causes the ruining of the holidays. And now, when in our sins we no longer have intercalation by ordained [scholars], our calculation relies on the accepted calculation from R. Hillel, as we have said.