Ah, sorry for missing some important points...
It's a 6 speed. And, I can hear the whine between 1500 and 3000 rpms or so. Maybe a little higher too, but by that point the engine and exhaust start to drown it out.
I tested rolling along in 2nd gear around 2500 rpm. Heard the whine. Took it out of gear, and kept on the gas to hold it around 2500 rpm, and still heard the whine.
It changes pitch as the rpm changes. It sounds like the same kind of whine that some cars make when you're stressing out their power steering by turning when you're at a standstill or cranking it to the stops.
Also, maybe related, when I'm starting from a standstill in 1st, sometimes I hear something spooling up. Sounds a little like a jet engine does when it starts, or maybe like a turbo. Like a few things spooling up in quick succession. I suspect this noise is something else though, like transmission or diff.