I have only heard one berg whine like you are describing, it was my 2000 501.
I had a cracked right side case, at the swing arm pivot. My dealer welded it up which caused the case to warp, so he had it surfaced. This removed enough material to cause the transmission main shaft bearings to be preloaded axially, something the tech did not detect upon reassembly.
Eighteen hours later, the bike started to make the whining noise, which by the time I got back to my Van, was really BAD.
The ribbon ball retainer on the Transmission main shaft bearing (clutch side) had failed. The noise was the mismatch in the clutch basket gear/crankshaft gear allowed by the bearing failing.
VERY EXPENSIVE for me to repair! Pieces of the bearing ball retainer were ground up and went through the motor because a large chunk wedged under the reed valve and allowed the trash to get into the bottom end etc. etc. Fortunately, the cylinder cleaned up.
piston kit
connecting rod kit
all engine and transmission bearings
gasket set
valve guides and valves
oil pump
reed valve
cam chain
cam sprocket
I had to relieve the spline on the main shaft to allow the 2nd Gearwheel to fit further onto the main shaft to make up for the material they had removed from my right side transmission case.
In your case, it could be a similar situation, but I doubt it. It is probably gear noise in the secondary shaft gear/balancergear interface, that will gradually wear in. I would drop the oil each ride and check for magnetic particles in the oil. Do a sweep on the floor of the transmission with a piece of a magnet on a rod for chips. If I had done this I might have saved myself a lot $ in parts.
I now do ALL of my own work except for things I cannot do myself, and then I rely upon Dale Lineaweaver's expertise.
Regards,
Joe