All electrical machines have the potential to make a noise. Every coil is going to have a pulsating force acting on it and there will be forces reflected on the magnets. Even dc machines ( dynamos) make a noise.
With a single phase winding the torque pulsation is additive from all coils . Any polyphase machine will balance most of the total torque variation and be much smoother. Beyond 3 phase there will be virtually no improvement in total torque variation ( even 2 phase is almost there).
What sometimes happens is that a mechanical resonance picks up and amplifies a certain frequency and that is almost certainly what you have in your case. Finding the resonance is a more difficult problem. Usually the noise can be lived with, I have always got noise from my machines at some speed. If you had a fast commercial machine with noisy blades you would be unlikely to even hear the alternator noise.
If you have potted the magnets then my immediate suspicion would be bell mode resonance on the return disc with no magnets although I have never experienced significant noise with this type of construction.Casting a layer of epoxy or vinyl ester on the back of the blank disc may be enough to damp it ( it would at least eliminate that as a possible source). Stator mountings may not be rigid enough and if you beef them up and shift the noise to another speed then you have a clue that that is causing a problem.
I suspect you have a strong resonance if you are exciting it near cut in where the magnetic forces are small. You may even be able to excite it mechanically by tapping things with a small hammer and looking for the same note. Even bearing tightness may be a factor is you have taper rollers.
No point in doing any electrical redesign with different number of phases, you may accidentally get an improvement but the potential to excite resonance will still be there and you could hit things even worse at another speed.
If you have such a thing try a large inductance (choke) in the dc line, it works wonders with single phase, I have never seen any advantage for polyphase but lengthening the conduction period may reduce the exciting forces. Unfortunately a decent very low resistance choke will cost the earth so if you don't have one dismiss this option.
Flux