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Mr Milk said..
Summer nights I just need a soft kiss of breeze while I'm trying to sleep, but there are no fans on the market that turn down really low. All of them are noisy at minimum setting.
The technology for silent propellers is focused on drones.. Some tests mimicking the feather structure of an Owl's wing (silent stealthy flight specialists) has removed up to 85% of that incessant whine -- so there is hope it is all in the trailing edge design

Suggest if you are good for a ceiling fan (so big blades gives more blow at low speeds)

) check out the DC type and ask about getting a linear controller (= rheostat) so more settings than the 3 click wonder switches ( my old unit has a 5 position switch = ok).. I have used a remote control unit for fan which had a plus and a minus for speed control - that would nail it..
DC (opposed to A/C) fans I think, are better to control the revs on as less likely to setup electronic harmonic which can create a problem noise too when not run at one of the regulated switch power settings.
I suppose you must live away from any of nature's night time chirpers - we have a relative of a night jar which whoops not quite regularly most all nights sometimes here sometimes there over summer

- so fan's constant noise are off the radar - count your blessings -
White noise is another way can cover up a noisy blow - have you tried a talking book read by say Stephen Fry or equivalent.
cheers
AP