The (updated) GIRM allows for an appropriate hymn after the congregation has received communion (see Art. 88 on p 17 of the linked, scanned document).
Otherwise, there really should not be any place for it within the Mass. Before you complain, though, think about the tremendous patrimony of music we have that is appropriate. In other words, there really is not a huge NEED for it.
See post #10 for more. Also, I would refer you to an address made by Bishop Slattery of Tulsa last August at the Matriculation Ceremony for Thomas Aquinas College:
I know that for two generations now, Catholics have been expected to sing an opening hymn at Mass and in many parishes the faithful are regularly browbeaten to stand up and greet this mornings celebrant with hymn #so-and-so which, depending upon the parish, might be taken from the red hymnbook, or the blue hymnbook, or the nicely disposable paperback missalette. So deeply has this opening hymn mentality shaped our consciousness that most Catholics would be astounded to hear me say that hymns have no real place in Mass.
Hymns belong in the Liturgy of the Hours and in the common devotions of the faithful, but the idea that the parish liturgy committee should sit down sometime early in the month and look through a hymn book, trying to find pretty hymns which havent been overdone in the past three or four months, which explore the themes of the Sunday Masses and which brings the people together as a singing community is an idea completely alien to the spirit of the Catholic liturgy.
It is alien first of all because the singing of hymns as Sunday worship was a Protestant innovation, better suited to their non-Sacramental worship than to the Mass, and alien secondly because an opening hymn introduces - at the very inception of the sacred action - that element of creative busy-ness, which is, as we have seen, antithetical to the nature of salvation as a gift we receive from God.
What belongs at the beginning of Mass is the sung introit, that is a sung antiphon and psalm. In the Catholic liturgical tradition, these are unique compositions in which a scriptural cento is set to a singular piece of music. The melody explores and interprets the text of the cento, while the composition as a whole illuminates the meaning to be discovered later in the readings of the day.
Maybe I should say this better, but what I meant was that by a traditonal hymm, it is one that stood the test of time, not one of those “happy-clappy” type of songs. A traditional hymm is acceptable.