I would have searched this, if I even knew what to search.
Recently I have been hearing this weird noise when accelerating. It almost sound like it's purring to be honest. It's not really a knock or a tick. I know its odd but the best way I can think of is that it reminds me of what is sounds like when you hit your hand against an empty plastic water bottle. Except (obviously) simultaneous to the engine speed.

Only had this MINI for 2k miles and never heard a noise like this on my last cooper S.
Side note: I did Seafoam about 600 miles ago, but haven't heard this noise until the last, say maybe 300 miles.
And it only has 36k miles.
Does anyone think they know what I'm talking about???

 

Motor mount bad causing exhaust rubbing?? If it changes during turning I would suspect CV joint. I guess you have no engine fault codes.

 

Yeah, no engine codes, dummy lights etc. it sounds like it's coming from the top end. It's really audible if you just put your ear close, and even more when driving. I know it's not a CV joint because I just had everything checked out and it doesn't make any other weird noises (or while turning). And it only does it sometimes.

 

Look at the engine mount...the fluid filled upper mount specfically.
It is like a ball filled wilh oil, in a metal can....they are supposed to stablize the motor and minimize vibration...on the 05,+ it is a oil filled one that leaks...then the motor rocks, and thunks.
a quick serch here will get you lots if pics.