NEW YORK >> When Joan Osborne first met Bob Dylan, the two singers got very, very close. There wasn’t much of a choice — they had to share the same recording studio microphone.

“I’m like literally inches away from his face,” Osborne recalled. “I had to focus so particularly on his mouth and his lips just to get the phrasing right — because I was doing harmony to him and I had to match him — that the whole room became this tunnel.”

On that day in 1998, the two did three quick versions of his iconic song “Chimes of Freedom,” which would play over the end credits of the NBC show “The 60’s.” Each take was completely different.

“You’ve got to be focused on him or you’re going to be left behind. I felt like that was an interesting challenge but also, for me, it was a testament just to the way his mind works so quickly,” she said. “He has an idea. He does it. He’s bored with it, he moves on to something else.”

Osborne, 55, clearly wasn’t bored with Dylan or his songs. The Grammy-nominated singer of the hit “One of Us” has put together a new album of her unique takes on 13 of his classic tunes. “Songs of Bob Dylan,” released today, is equal parts tribute album, musical experiment and fan letter. On the album cover, she stands arms folded as she leans on a car as a subtle homage to an old image of the rock great.

“There’s political songs — like ‘Masters of War’ — and then there’s very tender, romantic love songs like ‘Buckets of Rain’ and kind of everything in between,” said Osborne. “He’s got this incredible range of what he can do as a writer so I wanted to dig into all those different territories of what he’s capable of doing.”

She also shows what she’s capable of doing, especially on “Highway 61 Revisited,” which leans on Middle Eastern rhythms. Osborne was inspired by Dylan’s use of biblical imagery in the song and decided to weave in sounds from the area. “Certainly, Dylan’s version is amazing and incredible and we were not trying to out-do him. What we were trying was to bring a different flavor and a different perspective.”

John Ingrassia, who worked with Dylan when he was an executive at Columbia Records, said he was enthusiastic to hear what Osborne could do. Now Osborne’s manager, he called her “one of our great treasures and underappreciated singers.”

“I was actually excited that she would be interpreting Bob because the songs are rock-solid and I knew she had enough respect not to do any harm. In fact, I think some of her interpretations have opened them up and given them a fresh perspective,” he said.

Osborne has long been haunted by Dylan. She got her start playing acoustic sets at the same downtown Manhattan clubs the future Nobel Prize winner had played years earlier. “His ghost is sort of everywhere,” she said. Osborne covered Dylan’s “Man in the Long Black Coat” on her debut album, “Relish,” and the two met a second time in 2003 when she was singing with The Grateful Dead and shared the stage to sing his “Tears of Rage.”

“During the course of the song, he just started busting out in this big grin. I thought, ‘Oh, this is great. I’ve made Bob Dylan smile,’” she said. “I got a big smile out of him so I felt pretty good about that.”

The idea of doing an album of Dylan songs was inspired by Ella Fitzgerald’s exploration of the Great American Songbook, covering songwriter by songwriter. Osborne wanted to try an updated version, picked Dylan for her initial attempt and honed her skills at two residencies at the intimate Cafe Carlyle in New York City.

“I really tried to look for the songs that I felt some kind of personal connection with, and the songs that really moved me, and also the ones where I felt like the song and my voice could kind of connect in a real sweet spot,” she said. Osborne considers Dylan on par with such artists as Pablo Picasso or William Shakespeare.

But she’s not expecting Dylan to offer any feedback. “No, I don’t anticipate that Bob himself is going to weigh in on it. That would be great if he did. Even if he didn’t like it, just to tell me — that would be cool.”

Osborne is already sifting through other artists’ catalogues for her next album of covers. How does she follow Dylan? Maybe with Lou Reed, Nick Cave or Lucinda Williams.

“Ask me on a different day and I’ll have a whole different list,” she said, laughing.