I see the 7th of each set of sevens as containers - the 7th seal containing the 7 trumpets, the 7th trumpet containing the 7 bowls. Thus at the 7th trumpet, the voices in heaven can say "the kingdoms of this world are become the kingdoms of our Lord" even though the nations aren't gathered and defeated until the 7th bowl.
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7th Seal:
And when he had opened the seventh seal, there was silence in heaven about the space of half an hour. And I saw the seven angels which stood before God; and to them were given seven trumpets. Revelation 8:1-2
7th Trumpet:
And the seventh angel sounded; and there were great voices in heaven, saying, The kingdoms of this world are become the kingdoms of our Lord, and of his Christ; and he shall reign for ever and ever. Revelation 11:15
And after that I looked, and, behold, the temple of the tabernacle of the testimony in heaven was opened: And the seven angels came out of the temple, having the seven plagues, clothed in pure and white linen, and having their breasts girded with golden girdles. And one of the four beasts gave unto the seven angels seven golden vials full of the wrath of God, who liveth for ever and ever. Revelation 15:5-7
7th Bowl:
And the sixth angel poured out his vial upon the great river Euphrates; and the water thereof was dried up, that the way of the kings of the east might be prepared. And I saw three unclean spirits like frogs come out of the mouth of the dragon, and out of the mouth of the beast, and out of the mouth of the false prophet. For they are the spirits of devils, working miracles, which go forth unto the kings of the earth and of the whole world, to gather them to the battle of that great day of God Almighty. Behold, I come as a thief. Blessed is he that watcheth, and keepeth his garments, lest he walk naked, and they see his shame. And he gathered them together into a place called in the Hebrew tongue Armageddon.And the seventh angel poured out his vial into the air; and there came a great voice out of the temple of heaven, from the throne, saying, It is done. And there were voices, and thunders, and lightnings; and there was a great earthquake, such as was not since men were upon the earth, so mighty an earthquake, and so great. And the great city was divided into three parts, and the cities of the nations fell: and great Babylon came in remembrance before God, to give unto her the cup of the wine of the fierceness of his wrath. And every island fled away, and the mountains were not found. Revelation 16:12-20