“I think my new album is the first attempt I’ve made to be modern,” says Madeleine Peyroux, reached on her cellphone in Brooklyn. Of course, modernity is a relative thing, especially when one of the newer-sounding numbers on Standing on the Rooftop, released this month, was written by fellows named Lennon and McCartney.

“I spent much of my career until now studying the music of the first half of the 20th century—in terms of blues, jazz, and folk,” Peyroux explains. “So I’m only just getting around to that second half.”

What about the 21st? The 37-year-old chanteuse, who spent the early part of her career in the shadow of Billie Holiday, left the contemporary touches to producer Craig Street, known for his tasteful handling of singers such as Norah Jones and k.d. lang. And it didn’t hurt that her band included pianist Allen Toussaint, bassist Meshell Ndegeocello, and guitarist Marc Ribot.

Some tracks have an almost cavernous feel, such as “Lay Your Sleeping Head, My Love”, the W. H. Auden poem Peyroux set to original music Ribot brought to the table. Bob Dylan gets the rootsy acoustic treatment on “I Threw It All Away”, the Beatles go banjo on “Martha, My Dear”, and there’s a spooky, dreamy aura to Robert Johnson’s “Love in Vain”. That blues classic in no way resembles the Rolling Stones version, but that didn’t keep Peyroux from writing “The Kind You Can’t Afford” with bass legend Bill Wyman.

“We met at a festival in France,” the singer explains, “and I ended up going to London and sifting through things he had written over the years. We hit on that one, which I think reflects his rough-and-tumble origins.”

The album’s covers are fun, but the originals are its most memorable offerings. “The Things I’ve Seen Today” is one of two atmospheric, guitar-driven charmers Peyroux wrote with violinist Jenny Scheinman. The title song’s chugging strings give it a stark momentum, and “Meet Me in Rio” has a ’70s soul vibe. “Don’t Pick a Fight With a Poet”, with its loping Latin rhythms, was inspired by “that writer sitting quietly in the corner of your local bar”, she says.

Peyroux might be that writer, but her stage is much bigger than any pub.

“We’re all looking for what’s new and exciting in art, but more than that, we are looking for our identities,” she says. “And this is my exploration of what it means to be a woman of my age today.”

Madeleine Peyroux plays the Centre in Vancouver for Performing Arts on Saturday (June 25).