The offertory Ave Maria

This is a piece I've always been curious about but never had the occasion to look at closely: it is the offertory proper for the Votive Mass of the Blessed Virgin Mary, with the text Ave Maria. It is an 8th mode chant but somehow doesn't strike me as typical in any way. It never really rests on its final. I'm sure a chant scholar could tell me more.

Here is a recording.