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Listen a lot to Katy Perry’s “Roar” (yes, I have two daughters) and you will notice the outline of another song within the 2013 mega-hit. It’s there in the jabbing piano chords at the beginning and the jaunty beat that tells us that, although poor Katy has been dealt a harsh hand by love, the plucky gal is going to be just fine.

The song being echoed is that great anthem of American resilience “It’s the Hard Knock Life”, from the 1977 Broadway musical Annie. It is sung by the inmates of the girls’ orphanage where the eponymous heroine is incarcerated, a grim brick pile in Depression-era New York. There, we encounter an unmitigated picture of hardship, a “full of sorrow life” without kisses or treats, a place where, as “It’s the Hard Knock Life” dolefully informs us, Santa Claus never treads.

It’s a scenario straight from the blues. “Once a day don’t you wanna throw the towel in?” the girls chorus. Yet they deliver their lament in indomitably chirpy all-American voices, bulwarked by that jaunty beat that later turns up in “Roar”. Meanwhile (in the wonderful 1982 film) the drudgery of cleaning the orphanage is transformed into cheery dance routines with mops and brushes. At the end of the song, rather than throw in the towel, Annie attempts a bold escape in a trolley of dirty laundry. She ain’t a quitter.

“It’s the Hard Knock Life” was ingeniously revived by Jay-Z on his 1998 track “Hard Knock Life (Ghetto Anthem)”, adopting the girls’ perky chorus as an accompaniment to his rags-to-riches tales of Brooklyn hustling, the song’s beat recast as hip-hop. It was a worldwide hit, the song, like Annie’s laundry basket, that smuggled him into the mainstream.

Jay-Z’s ‘Hard Knock Life’ and ‘Roar’ by Katy Perry both take inspiration from the 1977 Broadway number

Jay-Z gained permission to use the “Hard Knock Life” sample by writing a letter to the musical’s composer Charles Strouse and lyricist Martin Charnin expounding on his childhood love of the show, having won a ticket to see it on Broadway as a prize in an essay-writing competition at his hard-knock Bedford-Stuyvesant school. The letter was, he later admitted, an “exaggeration”. In fact the rapper came across the hip-hop version, by producer Mark “the 45 King” James, at a rap show and bought it for a rumoured $10,000.

His association with Annie continues with the recent film remake. Co-produced by the rapper, it updates the story to present-day New York and gives the soundtrack a hip-hop makeover. The result was roasted by the critics. Yet “It’s the Hard Knock Life” has all the bustling energy of old, neatly prefaced by one of the foster girls (orphanages are so 1930s) asking what a “hard knock life” means. “It means our life sucks!” spits a colleague.

Katy Perry pops up in the new Annie, tweeting about her love for the heroine. In “Roar”, “It’s the Hard Knock Life” leads a medley of empowerment references. Helen Reddy’s feminist anthem “I Am Woman” (1972) is alluded to in the title (“I am woman, hear me roar”). Survivor’s Rocky theme tune “Eye of the Tiger” is quoted in the lyrics.

The context is Perry’s divorce from comedian Russell Brand. Co-written with her friend, singer-songwriter Bonnie McKee, “Roar” gives a Californian spin to Annie’s tale of hard-won social mobility. Perry celebrates going “from zero to my own hero”, a dazzling act of personal validation. It’s like orphan Annie graduating from the school of hard knocks, moving to LA and swapping Sandy the dog for a personal trainer. You go, girl.

Listen to a podcast with clips from the songs

Photograph: Getty Images

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