If you want to move air quietly you need to move a large volume slowly.
Buy it for life: Durable, Quality, Practical
For practical, durable and quality made products that are made to last.
I've been looking for a fan that literally mechanically raises and lowers a large leaf-like thing (think Anthony&Cleo) in a pleasant wafting fashion. How does no such device exist?
I've seen that done. But only in commercial contexts, like restaurants, or in Thailand and India
YEP this guy gets it. Large diameter & low velocity. Vornado is nice.
Vornado makes powerful fans. I think they're pretty quiet on low and medium, less so on high, but YMMV depending on your noise tolerance. I haven't tried Dyson but they are outrageously expensive (and I think I've seen a video on them not moving much air, I'll come back with the link if I can find it).
Edit: video
How about a 20" box fan on low? Too loud? Put together several computer case fans, they're made to be quiet.
Either of these fans can also be used to make a Corsi-Rosenthal box to filter air. So you could do both...assuming it's not too loud...