The ordinance of the Feast of Trumpets was to be observed on the opening day of that month within which the great Day of the Atonement and the Feast of Tabernacles fell (compare Leviticus 23:23 ff). The special offering for the day anticipated that of the great Day of Atonement.
Numbers 29:1-6
1 And in the seventh month, on the first day of the month, ye shall have an holy convocation; ye shall do no servile work: it is a day of blowing the trumpets unto you.
2 And ye shall offer a burnt offering for a sweet savour unto the LORD; one young bullock, one ram, and seven lambs of the first year without blemish:
3 And their meat offering shall be of flour mingled with oil, three tenth deals for a bullock, and two tenth deals for a ram,
4 And one tenth deal for one lamb, throughout the seven lambs:
5 And one kid of the goats for a sin offering, to make an atonement for you:
6 Beside the burnt offering of the month, and his meat offering, and the daily burnt offering, and his meat offering, and their drink offerings, according unto their manner, for a sweet savour, a sacrifice made by fire unto the LORD.