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The human voice is like fruit. It ripens,” says Madeleine Peyroux, gazing out of her London hotel room window. “My voice has definitely become stronger, filled with more emotion.” Her intelligent eyes flash. “Which makes sense, since the voice is part of the body. All your life experience goes in there, whether you like it or not.”

We’re talking about the American singer-guitarist’s latest album, Secular Hymns, a clutch of tunes by composers from Leonard Cohen and Tom Waits to British dub poet Linton Kwesi Johnson and late American gospel singer Sister Rosetta Tharpe, which Peyroux recorded in a 12th-century church in rural Oxfordshire. The venue’s natural acoustics highlight the wonderfully unhurried nature of a repertoire she unveiled 20 years ago with her acclaimed debut, Dreamland. While it’s a vibe she’s continued over several albums of impeccably chosen material — including a smattering of sweet-sad originals — on Secular Hymns the new maturity in Peyroux’s sultry voice is striking.

“That small space pushed me to have more clarity vocally,” says Peyroux, 42, who discovered the church when singing at an event there. When her engineer remarked that it was the perfect place to make a record, she returned with her bassist Barak Mori and electric guitarist Jon Herington (formerly of Steely Dan) to put on a free live show for a 200-capacity local audience.

“There was a wooden ceiling with the sort of sacred reverb you expect from a church — the idea that there is so much room above your head, you are literally connected to the heavens.” A smile. “But it was a small enough space for me to still keep my feet on the ground.”

Tall, dark-haired and ever so slightly prickly, Peyroux might, on a dating site, describe herself as “spiritual but not religious” (she’s quipped that she gave up pets, plants and children for her art). When she disappeared for eight years after the release of Dreamland — an album whose stripped-down blend of jazz, blues and pop marked her out, pre-Norah Jones, as the great white hope of commercial jazz — the story that came with her exemplary 2004 follow-up Careless Love was that she’d lost her voice and been hanging out in a Christian commune.

Mostly, however, Peyroux had been criss-crossing the US, running from the pressures of fame and busking here and there before returning to New York to play low-key clubs with her then boyfriend, a singer and harmonica player named William Galison. Two years after they split Galison released a seven-track album of their songs (2005’s Got You On My Mind) that Peyroux’s lawyers unsuccessfully tried to stop.

“I did actually explore religion in my twenties but it wasn’t for me,” says Peyroux. “I want to see the world through an atheist lens. I think what is humanist — a piece of music, a sunset — can be just as spiritually amazing.”

‘I had my guitar and some talent; I hung out with smart people. I could talk my way out of tricky situations’

Her parents were committed atheists, radicals who met in Canada during the Vietnam War. Her late father, a New Orleans-born academic and “prize alcoholic”, would hang signs outside their home in Athens, Georgia, with statements such as “We are Marxists” written across them. “My dad wanted to piss people off — and it worked,” she says with a shrug. “He eventually lost his job at the university.”

Peyroux’s mother, a banker and Francophile (“She named me Madeleine after the famous passage in Proust”), insisted they move to New York, where the young Madeleine took up guitar and wrote songs whose lyrics reflected a family life marked by turmoil. Her parents divorced in 1987, the same year she relocated with her mother to Paris.

Always curious, there she was wowed by old-school jazz and the street buskers of the Latin Quarter. Increasingly she would bunk off school to watch them. “I’d been a really good student until we moved to France,” says Peyroux, who went from passing the hat for the Riverboat Shufflers, a group of Paris-based American musicians, to becoming their lead singer. “The teachers in Paris were going to fail me so my mom sent me to a boarding school in England [in Littlehampton, West Sussex] so that I’d knuckle down and do this A-level thing, which looked insane to me.”

The self-confessed “hormonal teen” picked up her guitar and ran away. “I hopped on a train to Dover, paid for the ferry — you can’t jump a ferry — landed in Calais in the rain and hitch-hiked to Paris. The British police were looking for me for three days,” she says with a good-natured grimace. “I wasn’t in school much after that. I just kept hanging out.”

Peyroux went on to tour the world with another itinerant American collective, the Lost Wandering Blues & Jazz Band, singing songs by blues greats including Ma Rainey and Fats Waller. She continues to be amazed that, having survived many a close call, she never got into serious trouble. “I had my guitar and some talent; I hung out with smart people. I could talk my way out of tricky situations.”

While life on the streets lent authenticity to her blues covers, its cold harshness quickly got to her. By the age of 20 she was done. Back in New York she was discovered and signed by Atlantic Records and thrust, blinking and unprepared, into an international spotlight. “I was just a kid who was given a chance to record some songs,” she has said of Careless Love. “Nothing prepares you for what happens after that.”

For all her ups and downs, and despite her ambivalent attitude to her success, Peyroux’s belief in the power of song has never wavered. “Hearing the human voice can be so soothing and healing,” she says. “You know, when we did this concert in Oxfordshire the vicar came up to me and said, ‘Thank you, Madeleine. You filled the room with secular humanism’. It was the best compliment I have ever had. I really think of the songs I sing as hymns.” She pauses, smiles. “Music. Song. The voice. This is my spiritual life.”

Madeleine Peyroux plays the Royal Festival Hall on November 20 as part of the EFG London Jazz Festival.

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