Great guesses on the source of the FJR whine. Here's my take:
#1 The gearset on the 2015 and earlier tranny's were straight cut gears and created a bit more "mechanical" noise but that's at a lower frequency and not the source of the whine. Besides, the whine is present on all years of FJR1300s and the 2016+ machines all have helically cut gears in the tranny.
#2 As noted above, the whine seems less related to gear, load, road speed and more related to engine speed.
#3 The primary drive to the clutch housing is a straight cut gear. That could make a bit of noise and it would dutifully follow crankshaft speed but, I think that would produce the same lower frequency noise as the other straight-cut gears present. So, what else spins at the same speed as the crankshaft or some harmonically-related speed? Well, there's the camshafts spinning happily at 1/2 crankshaft speed. They're chain-driven and don't drive any other gears that could produce such a noise. Besides, they're spinning at 1/2 crankshaft speed so, I'm going to eliminate those as a source. So, what's left?
The balancers! There's two of them and they're gear driven and spin at the 2x the speed of the crankshaft! That would certainly produce a higher frequency sound than the cams, tranny, intermediate drive, etc. I'm fairly comfortable with my theory. The straight-cut gear-driven engine balancers are the most likely source of the characteristic FJR1300 whine. They're also a significant part of the reason the FJR's engine is such a masterpiece of smoothness. (images attached)
So, instead of complaining about the "whine", I choose to enjoy that turbine-like sound that just reinforces the power and engineering prowess wrapped in all that beautiful Tupperware® that Yamaha has produced. We who own and have come to appreciate these machines are the smartest of the motorcycling world. Who's on board?