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PHILADELPHIA — Grace Potter may have managed to confine her statue-esque frame into a small leather chair here in her frills-free dressing room at Lincoln Financial Field, where she will soon take the stage to warm up a crowd of 53,000 country music fans at a stop on the Kenny Chesney-Tim McGraw “Brothers of the Sun” tour. But as is typically the case with the fearless and verbose singer-songwriter, her body may not show it, but her mind is running wild.

The free-spirited frontwoman for Grace Potter & the Nocturnals is rhapsodizing about playing these stadium shows, on what is already the highest-grossing tour of the summer. (“You can see the goosebumps up and down my legs. I’m feeling it so much.”) She is gleefully discussing the lineup for the second edition of the band’s Grand Point North Music Festival this weekend in Burlington, in their beloved home state of Vermont, which includes the Avett Brothers, Galactic, and Dr. Dog. (“You should have seen the ticket sales when we rolled out the announcement!”) And the 28-year-old has a waterfall of words at the ready to describe the circuitous circumstances (including the hallucinogens) that went into making the rock quartet’s latest album, “The Lion The Beast The Beat” — which also happens to be their best.

“The truth of the matter is, I just rushed in to make the record and I didn’t have the songs,” says Potter of the early going in the recording of “The Lion.” But she did have songs, 35 of them.

The band — Potter herself on vocals, keyboards, and guitar, drummer Matt Burr, guitarist-bassist-keyboardist Scott Tournet, and guitarist-bassist Benny Yurco — was playing well. Potter and coproducer Jim Scott were vibing. She and collaborator Dan Auerbach of the Black Keys had crafted a few great tunes. But she wasn’t happy.

“I felt that what made the songs sound successful in the early recordings were things that I wouldn’t want to re-create over and over again, little hooks and vibes that just felt too clean and practiced and choreographed,” she says. “I needed more freedom.”

So after two months, Potter put the brakes on the project. She left for a battery-recharging road trip and foray into the woods of California and Vermont, and in her own words, “I took a lot of mushrooms.” She came back from her sojourn energized, full of new ideas and songs.

While she wouldn’t advise that anyone else to employ this method of unlocking the muse, it worked for her. “The Lion” roars. It is a cross section of big beats — including the title track — and small moments. Potter uses her estimable lung power to espouse great ecstasy and deep despair — sometimes in the same song, like the soaring ballad “Stars.” And psychedelic rock and slinky radio pop (including the offbeat Loverboy-meets-Talking-Heads first single “Never Go Back”) make for friendly neighbors. It sounds as if Potter and her bandmates have finally caught up to the version of themselves they had always hoped to be.

“I’m more comfortable in my own skin now,” she says. “So much of the early days of the Nocturnals was proving that I knew how to write songs and proving that I was a musician first and foremost. And then it was owning my sexuality and the fact that I’m a woman, which was something I avoided at the beginning. Now it’s like, ‘Can we sweep all that [expletive] under the rug? You know I know how to write songs. You know I have a pair of legs and am a blonde. Get the [expletive] over it and let’s make some real music.’ ”

Bruce DeBoer

Among the guests at the festival are the Carolina Chocolate Drops.

“I think it shows how diverse Grace Potter is,” says Chesney of “The Lion,” the deluxe version of which includes two tracks he produced for his “You and Tequila” duet partner.

“I think that Grace is such a true artist and great songwriter. I think that the fact that she’s out here on the road with us and the fact that she can pull it off says a lot about how eclectic her audience is and has the potential to be. The thing that I love about her is that she commands it. Her and her band, they go up there onstage and by the time they’re done people are just blown away. I could talk about them all day.”

Chesney was a surprise guest at last year’s festival, but isn’t sure if he’s going to make the trek this year, saying with a chuckle, “She hasn’t invited me!”

Considering the lineup consists of many of the band’s friends, Chesney’s invite is no doubt forthcoming. Potter is particularly excited to see the Avett Brothers, longtime buddies.

Crackerfarm

Among the guests at the festival are the Avett Brothers.

“We feel very close to them,” says Bob Crawford, bassist for the Avetts. “I don’t know how alike Grace’s music and our music is, but I can say on a personal level that we very much love them as friends and are happy for all their success.”

And Grand Point North — which is close to sold out — is the “crowning jewel” in that success, say Potter, who will return to Boston with the Nocturnals on Nov. 30 and Dec. 1 at the House of Blues.

Whether that success continues to grow beyond the current level, commercially speaking, Potter is happy with the creative point at which the band has arrived. “I’m so glad people are enjoying the record. But, honestly, if everybody was tweeting and Facebook-ing ‘What the [expletive] have they done?’ I’d still be so proud of this record.”