A correspondent (Peter from Boston) sent me an interesting point I hadn't known. In the Carmelite Rite, from the 1959 Antiphonale, the Sprinkling chant is change from Asperges to a chant that is unique to this order: the Sancte Deus (Trisagion of the Eastern Rite). And look at the tune. It begins very much like Vidi Aquam and then it begins to sound like Asperges, though with a completely different text. How glorious this is!
By the way, our own schola is singing a setting of this text by Thomas Tallis during Lent, and Good Friday in particular.