Albert Barnes Commentary Numbers 29:1-6

"And in the seventh month, on the first day of the month, ye shall have a holy convocation; ye shall do no servile work: it is a day of blowing of trumpets unto you. And ye shall offer a burnt-offering for a sweet savor unto Jehovah: one young bullock, one ram, seven he-lambs a year old without blemish; and their meal-offering, fine flour mingled with oil, three tenth parts for the bullock, two tenth parts for the ram, and one tenth part for every lamb of the seven lambs; and one he-goat for a sin-offering, to make atonement for you; besides the burnt-offering of the new moon, and the meal-offering thereof, and the continual burnt-offering and the meal-offering thereof, and their drink-offerings, according unto their ordinance, for a sweet savor, an offering made by fire unto Jehovah." — Numbers 29:1-6 (ASV)

The ordinance of the Feast of Trumpets was to be observed on the opening day of that month within which the great Day of Atonement and the Feast of Tabernacles fell (compare Leviticus 23:23 and following). The special offering for the day anticipated that of the great Day of Atonement.