Hello everyone!
Here I am writing my first post because of a problem my Mini had.
My Mini (1.4 95hp Mini One) started making a weird sort of whistle, almost a screeching sound at around 1000 rpms. The noise increases as the rpms go higher and then it almost disappears (probably drowned by the engine's noise, not too sure).
The car runs fine, the chain is not rattly and silent, unless the noise comes from there.
The chain has not yet been replaced, the car has around 107k km (66.500 miles).
My mechanic, gave the car a very quick look and guessed that it might either be the alternator (which I hope) or some component of the chain. He literally listened to the thing for 30 seconds though.
The car is a Mini One, which I don't know if it was made available in the US, with a 1.4 95 hp petrol engine.
I really hope you'll be able to take some guesses. I'm also uploading a short video from where you should be able to hear the noise.

 

I don't hear any screeching sound.

If the noise is present at cold start a test that can sometimes be done is to remove the serpentine belt and start and run the engine only long enough to confirm the noise is still present or is absent. If present the noise is coming from inside the engine.

If absent then the accessory drive is the source. It can be an alternator but my experience -- with other cars -- is the idler roller bearings get noisy. In another car the water pump made a noise. Not a screech but a low rumbling sound.

But a tech will use a stethoscope to probe each accessory idler and tensioner to try to pinpoint where the noise is coming from.