Grace Potter’s childhood playground in Vermont didn’t have slides and swings in the conventional sense.

Her parents ran a media company, setting photos to music, so Potter grew up amid the slides and swings in their eclectic music collection filled with the likes of Manhattan Transfer, Dylan and Bonnie Raitt.

However, it was their fascination with Irish traditional and U.K. folk music, sparked by the British Invasion, that ignited their daughter’s interest in songwriting.

“My songwriting influences didn’t necessarily come so much from country music, but they did end up there a lot, with folk and gospel and Americana music that really had found its way over from across the Pond,” Potter, 33, said by phone from a summer stop in Aspen, Colo.

“Jethro Tull was a massive influence. That band ... was the crossroads. Ian Anderson definitely had a pied piper/man of the woods feeling to him. I always think of him as Tom Bombadil from ‘The Lord of the Rings’ — this kind of wily character. But really, the entire movement welcomed any and all experimentation in that world.”

Citing the documentary “The Rolling Stones Rock and Roll Circus,” she said the biggest names in the British Invasion were “giving out that energy that we’re all playing in the same sandbox, but everybody’s got different sand.”

Fast-forward a couple of decades, and Potter has created a sound that blurs lines between genres and genders. She’ll be bringing her molten rock amalgam and a seven-piece band to the Paramount Theatre in Cedar Rapids on Sept. 29.

“Music has changed forever because of that era,” she said. “I owe a huge deal of my influence and the gravity of what I’ve been able to do, on the people who came before. Heart is a big influence on me. It’s not female- or male-driven. It’s about the evolution of rock ’n’ roll and what it did to the human spirit at the time. And it wasn’t just in America — it was everywhere.”

Through the sheer power of her vocals and lyrics, she’s evoked comparisons to Stevie Nicks, but laced with definite streaks of a Joan Jett rebel yell that mirrors her life.

“I was kicked out of band,” she said with a laugh. “I was pretending to read music, but I didn’t actually know how to read music.”

Her teacher suspected she was playing by ear, since she played every note correctly, but failed every sight-reading test. She wasn’t playing according to his rules. She got the last laugh, however, now playing piano, guitar and Hammond B3 organ. Even though she doesn’t consider guitar to be her main instrument, she’s proud that she and Joan Jett are the only two female guitarists to have a signature Gibson guitar made for them.

Her band experience, however, “has echoed through my life since then,” she said, “because I don’t do things right. I’m musical, I’m not a musician. I’m not a student of music, I’m musical. I have a dear friend who always says, ‘Grace doesn’t find the notes, the notes find her.’”

Fans have found her, too. A veteran of the biggest music festivals on the circuit — including Coachella, Lollapalooza and Bonnaroo — in 2011 she founded Grand Point North festival in Burlington, Vt. In Iowa, she wowed the crowd in her Hinterland concert Aug. 6 in St. Charles, south of Des Moines.

A musical chameleon, she has collaborated with country star Kenny Chesney and alt-rockers The Flaming Lips, finding songwriting influences in the things that make her happy and sound original.

“I’ve always been drawn to vocalists who defy gender and transcend genre,” she said. “That’s people like Robert Plant and David Bowie and Mick Jagger. Whether it be physically or vocally, there’s just this inherent confusion that goes with it, like ‘Where is this coming from?’

“There’s this real energy in masculine-feminine that indoctrinates the true rock stars in the world. If you look at all the really magnetic, seminal artists of our time, they always bring in elements of both male and female. So that feels important to recognize,” she said.

“Joan Jett is the queen of that. Her masculine and feminine balance, and the way that she’s carried herself through her career is extraordinary. Annie Lennox does the same thing. Stevie Nicks and Bonnie Raitt (also do) the same thing, coming from different generations.

“We do find ourselves, time and time again, attracted to multidimensional voices, multidimensional characters and multidimensional songwriters who bring out and ask more important questions, deeper questions — sometimes simply by being, by listening. They encapsulate something that we don’t actually understand ourselves,” she said.

“If I understood what I was trying to chase down, as far as my influences go or if I understood what my demographic was, I would probably implode. I’m certainly not chasing anything — it just comes out of me.”

GET OUT!

WHAT: Grace Potter; opening act Muddy Magnolias

WHERE: Paramount Theatre, 123 Third Ave. SE, Cedar Rapids

WHEN: 8 p.m. Sept. 29

TICKETS: $29.50 to $65, Paramount Ticket Office, (319) 366-8203 or Paramounttheatrecr.com

ARTIST’S WEBSITE: Gracepotter.com