Notes on the Bible, by Albert Barnes, [1834], at sacred-texts.com
Numbers Chapter 29
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 Lev 23:23 ff). The special offering for the day anticipated that of the great Day of Atonement.
The offering on the great Day of Atonement was the same with that just specified. The great ceremonies of the day are described in Lev. 16.
Feast of tabernacles: compare Lev 23:33 ff. The offerings required at this feast were the largest of all. It was especially one of thankfulness to God for the gift of the fruits of the earth; and the quantity and the nature of the offerings (see Num 29:7-11) were determined accordingly.
Stress is laid on the number seven, the holy symbolic covenant number, by way of intimation that the mercies of the harvest accrued by virtue of God's covenant. The diminishing number of bullocks sacrificed on the preceding days of the Feast (compare Num 29:13, Num 29:17, etc.), is adjusted simply to obtain the coincidence before us on the seventh day; but some have thought that the gradual evanescence of the Law until the time of its absorption in the Gospel is here presignified in the Law itself.
The offerings prescribed for the closing day of the Feast of tabernacles were the same with those appointed for the Feast of Trumpets and the Day of Atonement. The solemnities of the month thus terminated, as
A whole, with the same sacrifices with which, three weeks before, they had been introduced; and the Day of Atonement, even though succeeded by the rejoicings of the Feast of tabernacles, thus left its impress on the whole month.