I can't remember which I chose for sure. But I think it was relaxed mode because it gave me lots more time than I needed, even though there was a timer ticking down. The ending I got was
It was revealed as a result of your investigation that Francis' now elderly daughter had poisoned Johann and was taken away in handcuffs by the authorities. She'd felt guilty after Francis' luck and health had declined after Johann's death, and had been the one playing the sonatas as a sort of tribute to his memory. Of course she won't be doing that any more now that she's in jail, probably on death row, thanks to you. Talk about your depressing endings...
If you got a different ending with the timed mode, please post back. The timed mode is supposed to be the "normal" ending and the relaxed mode the "alternate" ending.