The BBC 3 Strikes logo is a logo where three lines move around and eventually form the letters BBC above it. Music similar to that heard at a funeral is heard during it. It was first seen on some of the first few VHS tapes with this logo in tandem with the "COW Globe" and was in tandem with the "Flying Boxes" and is "somehow not scary" there goes your sleep tonight.
On the 1995 VHS release of the Doctor Who episode "The Five Doctors", the logo is snatched up by the Time Scoop (the device that kidnapped the Doctor's incarnations and his companions at the beginning of the story. This variant is present on the 2008 DVD of that episode as a so-called "Easter Egg".
Low to Nightmare, because of the logo's ominous nature, combined with the piano piece, as it may unnerve some viewers, and might as well give viewers bad dreams, especially to young children. The scare factor is none for people used to seeing it, or fans of BBC, and it's a favorite of those not scared of it. If said logo is played in reverse, the scare factor may go higher than Nightmare.
Medium to Nightmare for the Doctor Who variant, as the sudden appearance of the Time Scoop and sudden sounds would get to those who hadn't seen it before.