I had the same sound in my E36 M3. I could also feel a faint vibration in neutral at about 1500 rpms. I took the car to two different dealers. I even left it at the second dealer because they had a German tech coming (I guess they "tour" dealerships for hard to solve cases) so he could look at it. They ripped apart everything and could find nothing wrong. They said it is a "normal operating condition"....I knew better....
I then was told of a local shop that was good. I took it in there and within literally 1 minute, he identified the problem as the flywheel. Apparently the E36 had a dual mass flywheel. When the "spring" (I dunno wtf it is) between the two pieces of metal wears out, it makes that sound, and can cause a vibration.
Needless to say, he swapped the flywheel out and no more noise.
I am not sure if the E90/2/3 M3 has a dual mass flywheel or not, but the noise you are describing, and when it happens, sounds identical. It's worth checking out I guess.
Does anybody know if the M has a dual mass flywheel?
Tim <--- apparently likes "3" cars
2014 MB E63S
2008 E90 M3 -- Selling
2004 GT3 -- Sold
1997 M3/4 -- Sold
1995 M3 -- Sold