Derbyshire, working in the BBC Radiophonics Workshop, created the original theme to "Doctor Who" back in 1963.
Sir Paul said of their encounter: "I even found out where Miss Derbyshire lived, and went round to visit her. We even went into the hut in the bottom of her garden.
"It was full of tape machines and funny instruments. My plan in meeting her was to do an electronic backing for my song, Yesterday.
"We'd already recorded it with a string quartet, but I wanted to give the arrangement electronic backing."