Updated my last reply with picture of the most common 'ring' source and additional source of 'ring' notes.
I should also note entire system will be rather metallic sounding when new because you got a ton of bare metal in there. Over the first 1000 miles carbon slowly coats all those surfaces and damps that out of it's character, it mellows a ton. So, if something is really vibrating it will actually stand out more with some miles and be easier to locate. Otherwise, put the car on a lift, have somebody rev the gas while it is on the lift so you are making exhaust noise in same RPM range where you hear the ring, that makes it MUCH easier to chase down. We do that all the time here and we have found all sorts of things that can ring.
On my Racing ND this was the source of a ring, a damper that is hanging from the rear of transmission with loose rivets. NEVER seen this item as a source, would not likely have found it without running the car on the lift with several of us under the car in the hunt for the ring we could hear when driving. Look close and you can actually see the rivet nearest the camera is loose, not flush. Talked with friends at Long Road Racing (they build the Cup Cars) and found out they remove these to save weight, it is a solid couple of pounds and designed to reduce NVH. Thus, the irony here is item designed to reduce NVH was adding it instead. Having never seen this as a source of ring, I ended up giving this item back to Dave Coleman (Mazda Engineer) so they could send it back to Japan to look at how to prevent these rivets from failing in the future.