We're used to over-inflated rock superstars referring to themselves in the third person, but for Alice Cooper "Alice Cooper" really is a man apart.

The person behind the make-up is a 64-year-old golf fanatic and committed Christian who has been with his wife for 36 years and is the father to "great kids who have never been in trouble for anything". His name is Vincent Furnier.

Alice Cooper, meanwhile, is the shock rock pioneer who has spent 40 years of his life on stage decapitating babies, spraying blood and gore across the footlights and doing unspeakable things with snakes. Furnier basks blissfully in the 100-degree heat of Phoenix, Arizona; Cooper is forever entombed in some dank Hammer Horror lair. The pair seem to get on pretty well.

"The fact that every bit of stress is out of my real life gives me the freedom to play Alice so easily," says Cooper. "I love putting on the make-up, getting in the costume, hitting that stage and really just destroying them with Alice. It's therapy for me. I get off stage and think, 'OK, I'm good for another 24 hours.'"

Cooper is a breezy showbiz pro these days, witty, endlessly affable and accommodating. It's easy to forget that back in the embryonic days of heavy rock his band were contemporaries of Led Zeppelin, The Stooges and Pink Floyd. Later they had a pivotal influence on glam rock and rapidly advanced the evolution of live music's theatrical side, melding garage rock to grand guignol and old school horror imagery. "We were influenced somehow by vaudeville," says Cooper. "I saw an old movie called Hellzapoppin' when I was very young which was just insanity. I thought, if you put that with rock it would really be something."

Beneath the pantomime villain there has always lurked a serious musician. Although eager to underscore his credentials – 14 top 40 US singles; feted at one point by Bob Dylan and John Lennon – these days he concedes that in the public view "the edge goes to the performer and the show. It took School's Out, Elected, 18 and all those big hits before critics and radio appreciated we were actually pretty good. For a long time we felt a little inferior because people tried to convince us the show was more important than the music, and we always knew it was the other way round."

Even today, he says, "if we have a 10-hour rehearsal, nine hours are on the music. The theatrics come pretty easily to us, but the music is what you really go for".

That said, he wishes more of today's pretenders would put in a little more effort in the name of entertainment. "I look at young bands now and I wonder, do they need a shot of testosterone? Why are they so afraid of being rock stars, these kids who look like they go to the mall together to buy their corduroy pants? They don't look any different from anybody else. It's so boring. I want to see more bands who understand that rock and roll is played from the crotch and not the brain."

Cooper is bringing his tongue-in-cheek gothic circus to Scotland on Hallowe'en, "the one night when the audience should be weirder than the band; we might come dressed as insurance salesman". His Hallowe'en Night of Fear show divides into three parts: after giving the audience both "the very glitzy, glammy, showbizzy Alice" and "the nightmare Alice", the final section is a homage to the departed members of the Hollywood Vampires, Cooper's 1970s LA drinking club whose members included John Lennon, Keith Moon, Jim Morrison, Jimi Hendrix, Mickey Dolenz and Harry Nillson.

A recovering alcoholic, Cooper stopped drinking in the mid-80s, but not before it almost killed him.

He recalls: "It was last man standing, every night at the Rainbow in West Hollywood. So I decided the third part of this show would be set in a graveyard, and it would be a tribute to four of the fallen vampires. We'll do two John Lennon songs, two The Who songs, two Hendrix songs and two Doors songs.

"It's a total tip of the hat from me: OK, these guys are gone but their songs aren't. If anyone can do a tribute it's someone who used to get drunk with them, right?"

He's delighted to be in the capital on Hallowe'en. Not only because "Edinburgh really is the creepiest place you can be that night", but also because "Scotland has always been huge for Alice. I'm from Detroit and the first time we ever played here the audience were dressed in black leather and long hair, they were all drunk and fighting and they loved rock and roll. And I thought, I'm back home".

Alice Cooper's Hallowe'en Night of Fear is at the Usher Hall, Edinburgh, tomorrow.