First time Ive heard this in my F56, never in my R56.
Yeah, I hear the real atmosphere vented BOVs on Subies.
But from a stock MINI??
Had in Sport+ mode (AT), went for some spirited driving with my window down.
Im hearing the BOV, sorry, ...... diverter valve, out my exhaust, between shifts!!!

COOL!!!

 

I had a Forge diverter/BOV installed on my R56. It was vacuum activated and bled excess boost to the atmosphere and sounded pretty cool. It smoothed out shifts by reducing excess boost that caused a partial compressor stall when up shifting. They don't make one for the F56.
When I had the CravenSpeed and the AWE intakes installed on the F56 the sound was more apparent, but to me it sounds like the car was having shivering fits. I didn't care for the sound at all. With my ArmaSpeed intake I can sometimes hear it faintly, but it's not loud enough to irritate me.

 

I hear what your saying its not a straight release, rather a open close open close.
But nevertheless, it took me a minute to realize what I was hearing.
Since I waited till 500 miles to _really_ open her up.

 

Is "BOV" the high pitch brief whistle/chirp I hear when I step on it and it shifts into a higher gear? Mine comes from up front I think and I can hear it with the windows up. I thought it came from the turbo. I didn't hear it with my R56 MCS just this JCW.

 

Since the "BOV" in a MINI dumps back into the exhaust, it sounds like an exhaust burbling, as opposed to the pop and burble.
I hear it as it upshifts on my AT.

 

Would you guys believe the F56 doesn't even have a diverter valve? The boost is controlled by waste gate.

extracted from here good write up on the working of your engines

Turbocharger

The exhaust turbocharger of the B46 engine is a twin-scroll exhaust turbocharger. To facilitate a fast and direct response, the exhaust flows from cylinders 1 and 4, and 2 and 3 are merged and routed to the compressor via two separate channels. This principle is referred to as pulse turbocharging. The exhaust manifold and exhaust turbocharger housing have been designed as one common cast part and cannot be replaced individually. The charging pressure in B46 engines is controlled via an electrically adjustable wastegate valve.

Blow-off valve
A blow-off valve is not used in current models. Pressure peaks, caused by sudden load shedding due to the inertia of the turbine of the exhaust turbocharger, can be avoided by careful tuning of the Digital Motor Electronics software. With foresighted charging pressure control, pressure peaks can be predicted and reduced by quick adjustment of the electrically-adjustable wastegate valve. Assisted by a delayed load control of the Valvetronic (in the minimum lift direction) or the throttle valve (in the closed direction), the remaining charge air which is produced can be routed to the exhaust emission system via the engine. This form of control thus prevents the exhaust turbocharger shaft from being exposed to excessive torsional stress due to high pressure peaks.

Wastegate rattle
Apparently BMW is fine with a little wastegate rattle at startup. They state if the wastegate valve is opened when cold, pulsation of the exhaust gas may cause vibrations in the wastegate valve, which are perceived as noise. This is not due to a defective component, and is normal running noise. This noise becomes less audible as the temperature of the component increases.

 

OK, Ill rephrase, I can hear the wastegate through my exhaust between shifts!!