When I attended workshops in my diocese about this, the Director of Worship suggested repeating the Alleluia (or Lenten Gospel Acclamation as the case may be). I'm not sure I agree with that. In any case, whenever I do wedding worship aids or help couples making their own, I just include that text after the reception of consent. Of course around here priests and deacons just seem content to skip over it altogether.
We are wont to drop a hymn there. Those on our wedding music list are all of a primarily doxological character (Praise to the Lord, the almighty; Praise, my soul, the king of heaven, etc.), and in today’s times where few know what comes after Benedicamus Domino, and the married couples don’t want to print more than a half-page program and tend to misprint whatever they are sent. Thus I think it may be justifiable and fulfills the command for those present to praise God.
At weddings outside Mass, without a cantor, the celebrant just reads “Let us bless the Lord”, and whoever knows the drill makes the response.
At most parishes in my diocese, the priests look at you funny if you suggest the Gloria should be sung at a wedding Mass...so adding something else they didn't do "in the past" that adds to the time....well, it just doesn't happen.
It would presumably be licit to use the Alleluia from GS, Ps 20(19V) 1,4. The text in By Flowing Waters is : Alleluia iij The Lord answer you in the day of trouble! ; The name of the god of Jacob protect you! Alleluia iij May he grant you your hearts desire, and fulfill all your plans. Alleluia iij
or the Alleluia Psalm, Ps 20(19V):1-6, with response Alleluia, alleluia.
At the Cathedral in Memphis, the practice ever since the study texts of the new wedding rite came out in the 90s was to use an Alleluia there (and nothing if during Lent). As it wasn’t officially in the rite yet (unless done in Latin), the couple was given then option to not have it done, but that was a rare occurance.
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