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His music is famous among legions of youngsters even if few of them would recognize his name. The fairy-tale theme from “Shrek” alone has probably earned him a permanent place in the mind of every child in the Western world.

In fact, Harry Gregson-Williams has made a cottage industry out of “Shrek” music: Beyond the initial collaboration with John Powell on the 2001 original (which earned them an Annie, Britain’s Ivor Novello Award and a platinum record), he’s done “Shrek 2,” “Shrek the Third,” Universal’s “Shrek 4D” theme-park ride and the holiday special “Shrek the Halls.”

“That’s it recently,” Gregson-Williams quips. Next year, he will add “Shrek Goes Fourth” to that list.

In fact, a fifth of the composer’s entire filmography consists of animation projects. The first three — “Antz,” “Chicken Run” and “Shrek” — were jointly done by Gregson-Williams and Powell, both of whom worked at Hans Zimmer’s Media Ventures studio at the time and were introduced to DreamWorks animation honcho Jeffrey Katzenberg back when Zimmer was doing “The Prince of Egypt.”

While the “Shrek” franchise tops the list, Gregson-Williams has also bounced around “The Tigger Movie,” swashbuckled through “Sinbad: Legend of the Seven Seas,” sent up high-octane Jerry Bruckheimer movie scores with “Team America: World Police” and navigated the sewers of London in “Flushed Away.”

Gregson-Williams is often called early for animation projects. “Quite often, there’ll be something required of me a year, or a year and a half, in advance,” he says. “On the last ‘Shrek,’ it was Captain Hook playing the piano. It was necessary to have the music before they could animate.”

It would be natural to assume there’s one Gregson-Williams style for animation and a different one for live-action films. Not so, he says. “Nine times out of 10, it’s finding a trace of an emotional arc of some sort — even if it’s ants or chickens or ogres. The music we created for ‘Chicken Run’ wasn’t created because it was stop-motion animation. It would have been the same if it had been live action.”

Case in point: the “Shrek” films. “We have Shrek, Fiona and Donkey, these throughline characters, but there’s always an emotional tug going on in a ‘Shrek’ movie. I never really feel like it’s doing anything different (than a live-action film).”