As a preliminary observation I wish you to make note that these Days are MEMORIALS,--every one of them!  Now God instituted some memorials just for the Israelites only, as Circumcision, for that  rite memorializes a Covenant between Him and the Israelites only.  BUT THE DAYS WE NOW CONSIDER MEMORIALIZE GOD'S GREAT CONTACTS WITH ALL MANKIND, AND THEREFORE ARE TO BE OBSERVED BY ALL RACES, THE WORLD OVER.  These Days memorialize some tremendous contact of God with all mankind and so are to be observed by all races, everywhere.
The Trumpets and Atonement Sabbaths memorialize GOD'S MESSAGES TO MANKIND--TO ALL RACES--as the Bible; The Divine or real message on Repentance, on Regeneration, so forth and so on, on the one hand, and OUR DIRE NEED OF REDEMPTION on the other (Atonement)....While the Feast of Tabernacles the Scriptures show plainly is an eight-day THANKSGIVING SEASON, the first and last days of which are Sabbaths regardless of on what days of the week they may fall.  Is gratitude merely a Jewish virtue?  Then this Thanksgiving Week is of worldwide significance.  We now pass to a more detailed study of these last three, which three constitute the autumnal cluster.

This is a one-day Sabbath.  Read of it in Lev. 23:24-25 and Num. 29:1-6.  It is first in the    autumnal cluster.
In the Scriptures, trumpets are associated with Messages--be they messages of alarm, or redemption, or of whatnot.  A whole "feast" of such then, and an entire day turned Divinely into a Sabbath for such then, would be a day for the recalling to memory and refreshment every Message that God has given mankind lest any one of them be lost!
It is a TIME FOR TESTIMONY.  The minister or some leader may in address call attention to some one Message from God that is very apt to our times; or to one that is about to be lost; or to some group of Messages, even a half-dozen or so.  People in the congregation stand and give testimony of one Divine Message after another, all day long.
One stands to set forth God's Message on the Weekly Sabbath; another His Message on the Special Sabbaths, or, on any one of the Special Sabbaths.
Yet another rejoices to refreshen minds on God's message about motor power at the Age-End, to which subject the Holy Spirit gives one entire book in the Bible, from first to last!  A half-dozen folks (or even more) may testify on the same subject or Message, each calling attention to some further phase of the subject.