Does the ceiling fan affect the sound?

no kiddin' either:
was recently in Pour House where bunch of fans turned on and AC too Neither fans or AC stopped me from enjoying live music. No distortion heard due to the multiple ceiling fans and AC.
Noted that musicians often placed bottles of spring water on top of  PA speakers or instrument amps. Isn't that sounding "tweaky"?

If you try to tune adjacent stings of a guitar to the same pitch using harmonics you do it by gradually tuning one string up to match the other. In the process you hear increasingly slower "beats" as you move closer to the actual pitch of the other string. If a fan is on you can’t do this because the "beats" never go away. So fans are affecting musical sounds in a subtle but strange way. My wife had the ceiling fan removed from her (piano) teaching area for this reason. It drove her bats. I don’t notice it much when I’m not tuning an instrument by ear (I don’t use electronic tuners).

If I understand the question correctly (and I'm a newbie, so you can take all this into consideration), but if you're asking if the fan breeze alters speaker output, if it were a solid breeze (at whatever normal speed), I don't think so, the "pulses" of a speaker push back against whatever is against it, whether zero or .1 feet per second. I would think (again, presuming constant), it might change the frequency a fraction, much in the order of a train coming toward you, then going away. But if the train (or music) keeps coming toward you, you'll never notice. In JEA48's post, that sound that we've all heard, I believe requires you to be that close, where the relative chopped sound distances are significant: Two feet back from that same fan, and you don't hear that. Just my thoughts.

I am amazed and astounded by this thread. I have a large , 3 story house, The third story is my recital hall, if you like. When I have the fan on, any speed, it screws with the music in a big way. Sound is a wave of compression and decompression, and and factor that  changes that will change the music. I cannot run the fan and hear the music  accurately . This is an observation, supported by science. What is this discussion about?

rowe 1951 ...you are correct.  That's exactly what I experience.