How the Biblical Law of Rosh Chodesh Explains the Rabbinic Understanding of Rosh Ha-Shana

You have given new moons to your people as a time of atonement for all their offspring. They would bring You offerings of goodwill, and goats as sin offerings for atonement. It served as a remembrance for them all, and a deliverance of their lives from the hand of the enemy...

Our God and God of our fathers, may these rise, come, reach, be seen, be favored, be heard, be visited, and be remembered, our remembrance and our consideration, the memorial of our fathers and the memorial of Messiah the son of David Your servant, the memorial of Jerusalem Your holy city, and in memorial of all the people of the house of Israel... Remember us today, Lord our God, for good...

(23) The LORD spoke to Moses, saying: (24) Speak to the Israelite people thus: In the seventh month, on the first day of the month, you shall observe complete rest, a sacred occasion commemorated with loud blasts.

(11) On your new moons you shall present a burnt offering to the LORD: two bulls of the herd, one ram, and seven yearling lambs, without blemish. ... (15) And there shall be one goat as a sin offering to the LORD, to be offered in addition to the regular burnt offering and its libation.

(1) In the seventh month, on the first day of the month, you shall observe a sacred occasion: you shall not work at your occupations. You shall observe it as a day when the horn is sounded. (2) You shall present a burnt offering of pleasing odor to the LORD: one bull of the herd, one ram, and seven yearling lambs, without blemish. (3) The meal offering with them—choice flour with oil mixed in—shall be: three-tenths of a measure for a bull, two-tenths for a ram, ... (5) And there shall be one goat for a sin offering, to make expiation in your behalf— (6) in addition to the burnt offering of the new moon with its meal offering and the regular burnt offering with its meal offering, each with its libation as prescribed, offerings by fire of pleasing odor to the LORD.

(10) For the land that you are about to enter and possess is not like the land of Egypt from which you have come. There the grain you sowed had to be watered by your own labors, like a vegetable garden; (11) but the land you are about to cross into and possess, a land of hills and valleys, soaks up its water from the rains of heaven. (12) It is a land which the LORD your God looks after, on which the LORD your God always keeps His eye, from year’s beginning to year’s end.

(13) When Abraham looked up, his eye fell upon a ram, caught in the thicket by its horns. So Abraham went and took the ram and offered it up as a burnt offering in place of his son.

(22) At that time Abimelech and Phicol, chief of his troops, said to Abraham, “God is with you in everything that you do. (23) Therefore swear to me... (28) Abraham then set seven ewes of the flock by themselves, (29) and Abimelech said to Abraham, “What mean these seven ewes which you have set apart?” ... (32) When they had concluded the pact at Beer-sheba... (33) [Abraham] planted a tamarisk at Beer-sheba, and invoked there the name of the LORD, the Everlasting God.

(31) Then they took Joseph’s tunic, slaughtered a kid, and dipped the tunic in the blood. (32) They had the ornamented tunic taken to their father, and they said, “We found this. Please examine it; is it your son’s tunic or not?”

(4) Moses then wrote down all the commands of the LORD. Early in the morning, he set up an altar at the foot of the mountain, with twelve pillars for the twelve tribes of Israel. (5) He designated some young men among the Israelites, and they offered burnt offerings and sacrificed bulls as offerings of well-being to the LORD. (6) Moses took one part of the blood and put it in basins, and the other part of the blood he dashed against the altar. (7) Then he took the record of the covenant and read it aloud to the people. And they said, “All that the LORD has spoken we will faithfully do!”