Long before there was Beyoncé’s Beyhive, or One Direction’s Directioners, there were Deadheads, a group of fans so loyal and (it’s fair to say) obsessed with the Grateful Dead that they followed the psychedelic rock band across the country on tour, town after town, concert after concert.

Now keyboardist Jeff Chimenti has joined a creative team hoping to wrangle that passion and draw fans to the Minetta Lane Theatre, where an Off-Broadway production of a new Grateful Dead musical, “Red Roses, Green Gold,” opens on Oct. 29. The musical — a comedy about a family of swindlers in the 1920s — features songs written by Dead band members Jerry Garcia (before his death in 1995) and Robert Hunter, with additional music by the Dead’s Phil Lesh, Mickey Hart, Bob Weir and drummer Greg Anton. The book is by Michael Norman Mann.

Chimenti, a San Francisco native who serves as musical supervisor and arranger, has performed with former Dead members since 1997 in the bands RatDog, The Dead, Further and Dead & Company.

Grateful . . . Dead . . . musical. One of those words seems out of place. So how did producers first pitch this idea to get you interested?

They said they were looking for someone to give guidance and keep the Grateful Dead music authentic. This isn’t trying to be a Grateful Dead cover band. There’s a story here. It’s my job to make sure the music is represented as properly as possible.

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So the songs won’t be performed the way they are in concert — the performers sing in character.

Exactly. Some songs are shortened, to go along with the story. The bulk of the material comes from the studio records “Workingman’s Dead” and “American Beauty,” albums that came early in the Grateful Dead’s career.

Fans have a reason to see this — but what about folks who aren’t familiar with the Dead songbook?

That’s the hope — to get both worlds. Fans will come to hear their favorite songs. They just have to understand it’s not going to be like a Grateful Dead concert. As for those who aren’t fans . . . well, it’s beautiful and diverse music. These are cool songs and I think newcomers will appreciate that.

Why IS the Grateful Dead fan base so strong? There are any number of bands from that era, like The Beatles and the Doors, with mighty followings, but there’s something . . . I’m not quite sure what the right word is . . . there’s something different about Dead fans.

I know exactly what you’re saying, and it is hard to describe. The way the band members paved their career was incredible. They did everything opposite of the industry standard. And there’s something in their material — they tapped into Americana, and they’ve connected with people of all walks of life.

Do fans still follow you on tour?

Oh, we’ve got people who’ll do the whole tour with ya. You’ll see them every show. People come from all over the world — Europe, Japan, Australia. They’re coming long distances to see these shows. It’s pretty magical. I’ve never seen anything like it — ever.

Were you a Deadhead growing up?

I’ve been involved with the guys for 20 years, starting with Bob Weir’s RatDog. But . . . myself . . . I didn’t know Grateful Dead songs — not one — coming into it.

You didn’t?

I was more in the jazz world. I had no idea. But once jumping into it, I was like . . . “Wow, how did I miss this?” There are so many songs, and they’re so diverse. And to be onstage and share it with the actual guys — that’s been a blessing for me. But, no, I didn’t come from that world. It’s definitely been a learning curve. I’m still learning.

Once the show opens, what’s next for you?

I’m home for like a week, then coming rrrrright back to New York. [He chuckles.] I’m jumping on tour with Dead & Company. [The band, which includes former Dead members Hart, Weir and Bill Kreutzmann, plus guitarist and Grammy-winning pop vocalist John Mayer, opens its fall tour at Madison Square Garden Nov. 12 and 14.]

One last thing — how’s it been straddling the music and theater worlds?

I’m blown away by the talent it takes in theater. The performers have to learn the music and dialogue — then the story gets changed the next day and they have to relearn it all. I guess the way they sometimes improvise . . . it’s like how musicians riff. But the big difference is how organized the theater world is. Like with the schedule — if they say, “Here’s the start time,” or “This is when we’ll take a break,” then that’s the start time, that’s the break. In music . . . well . . . . [He laughs.] There’s a potential start time, but who knows when the concert’s gonna start.