With 2 and 4 bladed systems, I could never understand where the 3-per-rev came from. Then I got a really good explanantion from a rotor dynamics guy... (I'm going to embarrass myself by trying to relay it as only an avionics puke can.) ....In forward flight when you have an advancing and a retreating blade, the advancing blade is going fast, so fast that the tip generates too much lift, so the blade is actually pitched so that the tip produces very little lift. Given the twist of the blade, most of the lift is being generated about a third of the way out the blade.
For the retreating blade, the part near the hub is actually flying backward, at a certain point down the blade its actually stopped and it is the tip that is producing the lift while the rest of the blade is along for the ride.
As the blade rotates in forward flight, the center of force moves back and forth along the blade setting the blade up an oscillation that works out to three per rev.
He said that there's a magic relationship for 5 blades. Somehow with 5 blades, if you do it right, a lot of these forces and factors cancel out. So theoretically, if a five bladed rotor system is done right, you should require minimal vibration treatment.
.... There's my five cents worth.
I'm sure if the Sultan reads this, I'm sure he can do a much better job of explaining the particulars of vibration, since he's so adept at tuning them out. (Which is why he's the Sultan (of smooth)) .... By the way Sultan...it was JH that gave me the 3-per-rev explanation.