Rich , The 912 series has a stellar rep. so lets check all the easy things first. I'll assume you checked all exhaust fittings for the rattle or new rubbing marks anywhere on the inside of your cowlings.
Lets take a look at the baffle inside the muffler next. When everything is quiet tap the muffler with a rubber hammer carefully and see if it rattles. I had mine come loose on my 912 years back and it made a weird noise but not at all rpms. If it has come loose you may need a new muffler or like me you may be able to remove the baffle one small piece at a time by breaking it up with a long needle nose pliers through the exhaust pipe inlets but of course you'd have to remove the muffler to do it. Not a great fix and very tedious but it got me flying again and seemed not to affect performance at all. Just a slightly different exhaust note.

allbee already mentioned checking the prop.

I would think if it was a gearbox problem you'd hear something different sounding when you turn the prop by hand or feel extra gear "slop" while hand propping. Do you have a slipper clutch in your gearbox?

Good luck and keep us posted.