Notice something about the Five Glorious Mysteries?
Jesus rises from the dead.
Jesus ascends into heaven.
The Holy Spirit descends at Pentecost.
Mary is assumed into heaven.
Mary is crowned Queen of Heaven and Earth.
You'll have to work with me on that last one, that a coronation is a sort of raising up to a throne. But Pentecost is the only one of these that involves a downward movement, from higher to lower, away from the Throne of Glory.
"Glory" is one of those slippery concepts; St. Augustine's formula, "brilliant celebrity with praise," contains the keynotes of brightness (and hence evident and attractive) and of praise (the proper response to glory, so much so that the response of praise is also called "glory").
Pentecost is certainly something worth praising, but what makes it brilliant? Not merely the tongues of light (if it were just that, it might better be a luminous mystery). It wasn't just that the Holy Spirit descended, the way your aged relative who sucks all the air out of the room does, but that He descended upon the disciples. The disciples themselves are what became brilliant, attractive evidence of God's praiseworthiness.
And how did they become this way? Is it, we might even ask, a way that we may follow today? 1 Peter 4:10-11 might be relevant:
As each one has received a gift, use it to serve one another as good stewards of God's varied grace. Whoever preaches, let it be with the words of God; whoever serves, let it be with the strength that God supplies, so that in all things God may be glorified through Jesus Christ, to whom belong glory and dominion forever and ever. Amen.
"Gift," as we all know, is the proper name of the Holy Spirit, and the charisms He gives to each of us are given, not for our own sake, not even for the sake of the Church, but to be used to build up the Church so that God may be glorified through Jesus Christ.
Had the Holy Spirit led the disciples out into the desert for a time of fasting and prayer, Pentecost would not have been glorious. Instead, He made the disciples, St. Peter foremost, shine before the crowds in Jerusalem, testifying to Jesus, to the glory of God the Father.