Grace Potter and The Nocturnals play Fillmore Miami Beach on Saturday

Grace Potter and The Nocturnals is one of the most under-the-radar bands around, capable of rocking a huge arena crowd, yet not well-known enough to sell quite that many tickets. Lucky you! Catch the group at the relatively intimate Fillmore Miami Beach on Saturday night before the secret’s completely out. GPN performs in support of its fifth studio album, “The Lion the Beast the Beat,” parts of which might remind you of powerful female-led acts such as Heart and Florence +The Machine. But don’t think you can pigeonhole the band – you’ll also hear many other influences including country and blues, all powered by Potter’s incredible voice, which has been described as a less raspy Janis Joplin.

Potter talked to about the show, the myriad influences that helped her realize her rock-star potential, and the creative freedom of not aspiring to “sing pretty.”

Are you excited about coming to Miami?
I cannot wait – it’s one of the big hits on our list, because we’ve been in the cold, cold northern parts of the country. So I’m so excited to get to Florida – you have no idea.

So what can we expect from your show?
A little bit of everything, honestly. It’s hard to tell, because every show’s different. One thing that’s interesting about this tour is that the audience is our guide for what they’re gonna get, because I take requests. I decided that the Nocturnals’ tour was gonna be all requests, so depending on the night and depending on the city, we get a throng of different people suggesting different songs for us to play. So they kind of choose their own destiny, which I joke about, like, “If you don’t like the show, it’s your fault!”

Are you enjoying it?
Absolutely. It’s good for us, and it keeps us on our toes, and keeps the tour fresh, because every single venue matters, every place you play. It’s easy for musicians to forget where they are and what city they’re in, so it’s a great way to come back down to earth and remember that whatever night you are in whatever city, there are people who have been looking forward to it for months. So you’ve gotta give them whatever they ask – sometimes the fans know better than we do what’s going to sound great, so we always like to give it a try.

Your style of rock ‘n’ roll has this old-school swagger that’s pretty rare these days. Who did you grow up listening to?
I mean, everyone! My parents had a great record collection, and it started with The Band, Neil Young, Crosby Stills & Nash, Bob Dylan and The Beatles. But then I dug deeper into their collection and I discovered The Ventures and The Animals and The Kinks, and even deeper with the blues with Muddy Waters and John Lee Hooker and side projects that [Little Feat frontman] Lowell George would do with Robert Palmer. And obviously The Who and Led Zeppelin were massive influences on me, and Iggy and the Stooges and James Brown. The list goes on and on.

What about country? I hear a lot of that in some of your songs.
That’s the funny thing, because I didn’t have a lot of country influence as a young kid, because I came from Vermont, where instead of country music, there was “traditional” music, like stuff from the U.K. and Joni Mitchell, which has a twang to it. And if you listen closely to Crosby Stills & Nash and Neil Young, there is that country element to it. And J.J. Cale and Eric Clapton – country music has always been present in their sound, even though they don’t have that pedal-steel twang or that just-so fiddle.

I think in my voice, especially early on, I was more hearkening to every influence that I had, and somehow it blended together into this twangier sound than we were expecting. And I listen to that earlier stuff, and it’s crazy, because I wasn’t listening to country music, but it was somehow transcending whether I knew it or not, kind of like how The Eagles accidentally landed in this crossover world.

Many critics who see you perform live say they can’t believe you’re not selling out stadiums. How do you feel about that?
I kind of agree [laughs]. I mean, we’ve worked really hard to get where we are, so I’m grateful for everything we’ve had – listen, sold-out shows in large clubs and theaters with a couple thousand people a night isn’t so bad. It’s actually the happiest I’ve ever been – this tour has been one of the most rewarding and thrilling experiences of my life, because we’re finally reaping the benefits of many years of hard work. We have those audiences where we used to open for bands and go, “Wow, wouldn’t it be cool if that was our crowd someday?” And now we’ve got that.
Do you feel like the band is at its creative peak now?
Yeah, we can’t even help ourselves – we’re starting to write accidentally. Every day we get up for the sound check and there’s some new idea lyrically and melodically, and we have to fight the urge to write, because you just can’t on the road. I used to do it a lot, but I found that it created a bit of a tension for me as a writer, because I tend to like to isolate myself when I write. So now what I’m doing is recording all of our sound checks, and I’m going to take them back home and go through them and hear the inspiration that’s coming out of us right now, because there’s really some exciting things happening. And I don’t want to lose these ideas.

Do you think it surprises people when they see you sing for the first time – with the power that emanates from you?
I don’t know! I’m legally blind, so I don’t see people see me. So sometimes when I start singing, it’s more like, what do I have to say that no one has said before. And where’s the perspective in my voice, where they’re not going to immediately compare me to five other f—ing female singers, you know? And that’s my goal – not so much how people are reacting to me, but what it’s gonna mean later for me as a singer. Because I’ve really worked hard to understand what it means to be a female singer and kind of not oversell that point. And the power comes from recognizing that just because I’m a woman doesn’t mean I have to sing really pretty. And if I had been born a man, it’d probably be Gary Potter and The Nocturnals, and we’d probably be doing exactly the same thing, and I’d probably be like Jim Morrison with my d— out half the time. [Laughs] That’s not true.