In early November, Brad Shultz was nearing the end of a long, quiet period between finishing Cage the Elephant’s new album, Tell Me I’m Pretty, and going on tour to promote it. He was at home in East Nashville, his toddler was asleep upstairs and his wife was running errands.

“We went to the zoo probably 50 times this summer,” he says, sitting on the sectional in the den. “Our daughter is obsessed with animals. She likes the flamingos and the monkeys.”

That home routine is changing drastically now, with the new album debuting last week and several U.S. shows and festivals in December and January. On February 6, the band will open for Metallica at CBS Radio’s The Night Before — as in the night before Super Bowl 50 — at AT&T Park in San Francisco. A week later, they head out for a European tour.

In Shultz’s den, there are three guitars hanging on the wall. One is vintage, small and triangular — like an old cuckoo clock or birdhouse — with a long neck. “That’s something I found,” he says. “It’s called a hootnik. It’s really cool, but my daughter broke it.” Shultz laughs. It’s a single-string instrument and missing its string.

Shultz started Cage the Elephant with his brother Matt and two other high school friends in Bowling Green, KY, where they all grew up. They have told various stories over the years about the name of the band, including that it was a game on the back of a cereal box and that it came to one of them in a dream. “They’re all lies,” Shultz says. I ask if he doesn’t remember how they came up with the name or just doesn’t want to talk about it.

“Honestly, we were young and figuring out a lot of the realities of life,” he says. “Matt and I had been playing together forever.” Music runs through several generations of the family; their great-grandfather played the organ for silent movies, and their father is a songwriter. I’m not sure if Shultz forgot the question or steered past it.

In 2007, Cage the Elephant played a show at South by Southwest that got a fair amount of industry attention. They signed their first record deal with a U.K. label and moved to London. “We really had to build up a following through the live shows,” Shultz says, “and I think that’s where we became a good live band.” The album did so-so in the U.K. but was a bigger hit in the United States, scoring three No. 1 songs — “In One Ear,” “Shake Me Down” and “Back Against the Wall” — on the Billboard alternative chart.

The band’s sound has evolved over four albums and a decade of touring. Cage the Elephant (2008) was high-energy, punk-tinged indie rock on par with the Hives or the Strokes. Thank You, Happy Birthday (2011), which debuted at No. 2 on the Billboard 200, had a bigger sonic range — more rock, more alternative, more production — and a bigger hit single, with “Shake Me Down” going to No. 1 on both the alternative and rock charts.

Melophobia (2013), Cage the Elephant’s third album with producer Jay Joyce, generated a quick No. 1 alternative hit with “Come a Little Closer,” and had a lot of experimentation with backing vocals, poppy keyboards, jazz horns and more ballads like “Cigarette Daydreams,” which was also a hit.

“On Melophobia, we really got into dissecting the track, recording, then living with it, and then pulling it apart and putting it back together,” Shultz says. The album had solid reviews but didn’t quite fit with the more club-show vibe of the earlier albums.

For Tell Me I’m Pretty, the band changed producers and approaches. Dan Auerbach, the guitarist for the Black Keys who produced Ray LaMontagne’s Supernova and Lana Del Rey’s Ultraviolence, brought a live, in-the-moment sensibility.

“Switching producers for this album really pulled us out of our comfort zone, which is what we really wanted to do,” Shultz says. Auerbach had not heard any of the new songs before he started working with the band on Tell Me I’m Pretty, and several tracks on the album were recorded in one take. “Dan would say, ‘OK, that’s good.’ And Matt [Shultz] would say, ‘Well, I kind of messed up on a part right here in the vocals. Can we go back and hear that?’ And Dan would say, ‘No, it’s cool.’”

Tell Me I’m Pretty is grounded in 1960s and ’70s classic rock, with lots of fuzzy guitar and vocal reverb. The first single, “Mess Around,” is a driving, psychedelic rocker that would be right at home on The Rolling Stones’ Sticky Fingers album or a Tarantino trailer. The new single, “Too Late to Say Goodbye,” is bluesy and earnest like the Doors and pre-glam Aerosmith. As Dan Auerbach has done repeatedly with the Black Keys, he gets a richness and buoyancy from blues guitars on Tell Me I’m Pretty that engineers didn’t have the tools deliver for Led Zeppelin in the ’70s. If the first three Cage the Elephant albums were for the car stereo, this one is for the headphones.

“When we first started writing it, we were really into the idea of a spaghetti western,” Shultz says. “The best way to explain it, and the only way it made sense to me when we were formulating ideas, was that we wanted it to sound like John Wayne tripping acid at an Iggy Pop show.”

Late in our interview, Shultz reaches for his phone and I see a purple bruise on the back of his arm.

“What did you do to there?” I ask.

“My fucking brother,” he says. “We have this thing where we grab the inside of each other’s arm.”

“Jeez. That’s a pinch?”

“I got him on Halloween, and he got me back,” Shultz says. “Bastard.”

This wasn’t Matt, the lead singer of Cage the Elephant. This was a younger brother who also lives in Nashville. There’s a fourth brother, the youngest, who still lives in Bowling Green, Ky. Shultz’s family life is wound through the band’s story. Shultz and his wife Lindsay got married in their early 20s shortly before the band moved to London, and she ran the merchandise tent at their shows.

When the band toured two years ago on the Melophobia album, Shultz said Lindsay stayed home with Etta, who was a newborn at the time. “You live your life with the people you love,” he says. “I want her to have some home stability, but she’ll be able to come out on the road some this time.”

Etta, two, has a full drum kit in her playroom. “It’s a Ludwig kit scaled down to a kid’s size. It’s the real deal,” Shultz says. “Come upstairs and look, but we have to be really quiet.”

Shultz and I walk through the kitchen and tiptoe up the stairs to the playroom, which is just down from where Etta’s taking a nap. The drum set looks so out of place in a toddler’s playroom and is so effing cute that it makes me laugh. The cymbals are not even waist-high.

“Can she play it?” I whisper.

Shultz picks up two drumsticks.

“She’ll go like boom chik boom chik,” he says, mimicking like he’s hitting the snare and one of the cymbals.

On the wall opposite the drum set, there’s an organ that looks like an old upright piano. Hanging on the wall above it is a platinum record — sales of one million or more — for the “Ain’t No Rest for the Wicked” single. I ask if he kept any of the other plaques, and he shrugs and shakes his head no.

After we walk back downstairs and as I get ready to leave, the dog ambles over.

“He’s half boxer and half stray,” Shultz says. “We got him when we started the band, so we named him Cage.”