These are often difficult to pinpoint, but the heat shield or exhaust mounting brackets are the most likely.  You get the noise when two effects both come into play.  The first is resonance - every component has a tendency to vibrate at a particular frequency, and metal components are particularly fond of resonating.  Apply that frequency to the component and it'll vibrate vigorously.  The engine will be supplying the right frequency at a range of engine speeds and the most vulnerable components are the thin metal sheet of the exhaust, its mountings and clamps and the heat shields.  The second effect is the tension the component's under.  Even though something wants to vibrate due to resonance, if it's tightly stretched or compressed, it can't.  With the engine under full load or no load, the exhaust mountings are either compressed or stretched, but as you change gear the engine mountings let the engine go from the full load position to the no load position (ie - the movement you can get simply by rocking the engine on the mountings).  This allows the resonating component to be under no tension for a few moments, letting it vibrate and creating the irritating sound - or touch another part that then resonates.  The cure might be tightening a clamp, or packing a joint out or it might be re-positioning the exhaust or heat shield slightly, but the exhaust and heat shield are certainly the most likely culprits.  If you can, get underneath the car on a ramp in a garage and get someone to increase the engine speed really slowly (in neutral, obviously).  You may well hear some slight resonance under the no load condition which will tell you where it's comiong from - then it's a bit or trial and error, tightening and repositioning to see what works.

Good Luck!

Tim