For a Mass with music, the singing of propers is widely considered optional. Less widely, but often enough, the singing of the ordinary is also considered optional. Hymns--which, except for a couple of sequences and Holy Week chants, are always optional at Mass--are widely considered mandatory. If nothing else, we will sing 4 hymns! Thus we will have fulfilled our obligation to have music at our Mass.
As has often been discussed, this completely inside-out liturgical music ethic derives from the long-standing custom of the "Low Mass," which is not a sung Mass, but at which, at certain points, singing is permitted. The singing is not part of the Mass itself.
As a relative newcomer to the 1962 Missal, I've often wondered why the Low Mass's avoidance of propers and ordinary has to be absolute. A Missa cantata and a Low Mass are at opposite ends of the sung-Mass spectrum: the Low Mass sings nothing of the Mass, and the Missa cantata sings the entire Mass.
I can't help but wonder why there could never be anything in between. At a parish that might not be able to manage the sung Latin propers, why could there not be a Kyrie and a Sanctus instead of O Lord, I Am Not Worthy and Holy God, We Praise Thy Name? Was the Low Mass legislated? When, and where, and what could the reason have been? Would it have had to do with the anomaly of repeating in song some of the priest's spoken words, but not repeating others? Or to avoid the choir's singing, while the priest only spoke?
Imagine how different liturgical music would have been in the postconciliar period, and would be today, if the singing at the Low Mass had not been hymns, but a simple ordinary.