A brother priest, who knows what this antiphon in the EF Breviary Common of the BVM means, confesses that he does not know what it means. Neither do I.
Its oddity has left a variant form in the Tradition: In odorem huius virginis frequentate nobis dulcia cantica dragmatis. This does pinpoint where the problems lie.
S Antony of Padua had obviously been thinking about this when he observed, obiter, in one of his sermons that dragma is a form of drachma, while drama means a rather active form of music, with gesticulatio and repraesentatio. I suspect that this is what the composer of the antiphon meant it to mean; the problem is that drama is very uncommon in Latin. Presumably it comes from the Greek verb drao, I do; and means a doing. It is the word which we know as Drama. Perhaps it means dramatic choral lyric. But why should the author choose such an (almost) hapax legomenon to appear in an antiphon to be sung before and after a Mattins psalm? My suspicion is that it came from some already much older source and thus already had the status of a venerable quotation. But from where?
Frequentare did sometimes mean to repeat. No problem. But why nobis? Who is it that is being addressed and asked to sing nice songs for us before our Lady? An echo conceivably of the psalm Super flumina?
Ante torum remains as a problem. Torus is a couch or bed. You might recline on one at a banquet or consummate your marriage on one or be carried to burial on one. We might be tempted to emend to ad thronum if it were not for the text-critical principle of difficilior lectio potior: a reading hard to understand is more likely to have been 'corrected' to a commonplace and problem-free reading than vice versa. Would the torus be that on which the Mother of God gave birth to our Redeemer ... that on which she was carried to burial, according to some apocryphal account, before her Glorious Assumption ... or what?
It's the sort of thing that one of those erudite 1930s Benedictine liturgists, or someone like Edmund Bishop, might have already sussed out. Does anybody know?