The band Twenty One Pilots took its name from the Arthur Miller play “All My Sons,” in which a manufacturer knowingly ships faulty plane parts to the military to save money, leading to the deaths of 21 pilots. As such, the band has tried to remain true to itself since its 2009 start in Columbus, Ohio, with music that blends electronica, emo, hip-hop and balladry with a strikingly visual stage show that often includes kabuki makeup and crowd surfing.

Things ratcheted up for the duo – singer/keyboardist Tyler Joseph and drummer Josh Dun – when two singles off their 2015 album, “Blurryface,” topped the alternative charts and invaded the pop charts. “Blurryface” is still in the top 15 on the Billboard charts and won a Billboard Music Award for top rock album last month.

We spoke recently to Dun when the duo was at John F. Kennedy International Airport, waiting for a flight to London before starting their biggest summer tour yet, which closes with shows at Madison Square Garden.

Dun spoke of adjustments to the band’s growing popularity and efforts to maintain its integrity. In a sign of their popularity: We had only 13 minutes to talk.

Q: It looks like everything on your tour is just about sold out.

A: As far as I know, I think most of the tickets are sold. It’s something we’ve been looking forward to for a long time, this summer tour. We’ve been working on it since January or something like that. I’m just excited that we get to continue to travel and play music and people still care.

Q: Are you making it a bigger show, accordingly?

A: It’s a weird thing. I feel like we’ve played these songs so many times now. And it’s a weird thing, as we travel and interact with artists more, I realize that it’s not an uncommon thing, when you play the same songs all the time, you start to feel like everybody feels the way you do, that you’ve heard these songs so many times.

I hope people aren’t getting bored of these, or completely over it. I think maybe now I realize sometimes we want to make it a little bit fresher and a little bit different just for us. So we can continue to be really excited about it. Which we are, always. But, yeah, we try and change it as much as we can. There’s only so many songs that we have, and so many ways that we can transition from one to the next. But within that, still trying to do things to make it exciting.

Q: Have things changed since you went to No. 1? Have you sensed anything different?

A: Every once in a while I can kind of see that there’s a little bit of a difference, and I think some of that includes just being put on a broader platform, whether it’s different TV things, or radio, or whatever it is. And it becomes an interesting thing when you’re put in front of somebody who doesn’t care or who never asked for us to be put in front of them. A lot of times that’s when you see more of the negativity or negative comments about what it is that we’re doing.

But I think there’s still such a core group of people who have invested in this thing, whether it’s from the beginning or if it’s from yesterday, that are still attached and so committed, that it’s hard to latch onto a lot of the negative comments when there are these incredible people who have been supporting what we do for so long.

Q: How has all this popularity altered your life, as far as what you can or cannot do?

A: Depending on location, it can a little difficult, but I think the biggest thing that we see is that we’re able to play in bigger venues now, in front of larger audiences. That’s what we had in mind for this thing since the beginning – not with the intention of being famous or known or looking really cool – but we really believe in the music and the songs. So being able to present that in a larger stage and play to bigger audiences has been the coolest thing for me.

Q: You’re a band that has had no sponsorships and based your name on an Arthur Miller play, and for a long time you were even your own roadies. Are you still able to maintain that direct control?

A: I definitely remember the days when we would throw on a hoodie or something and set up our instruments onstage and pretend we’re different guys, and then sound-check them, go backstage, take off the hoodies and come out as different people – we’re performance men now!

I think one of the craziest transitions is having people on a crew with us that set up our instruments. It’s a crazy thing for us, because we did it for so long. We’d carry Tyler’s piano down two flights of steps, or up flights of steps in the wintertime and have these big drum boxes, and carry those things everywhere, figure out how to pack a trailer. … With more people added to this tour and crew, it could be easy for us to take our hands off certain aspects, but I like to say we’re still involved, at least to some degree, in every aspect of what you see or hear that has Twenty One Pilots’ name on it. But nonetheless, it’s been nice having a little bit of help setting up my drums.

Q: Do you worry about keeping the equilibrium of the band and the kind of integrity you built it on as things get bigger?

A: I think as more and more people start to feel like they’ve got ownership or feel like they can speak for Tyler or myself, it starts to scare me a little bit more. It’s hard to know if every single person is on the same exact page.

Something that Tyler and I started using that I think is very important is called vision casting. Initially, when we were hanging out years ago and realized that we were on same page about certain things and had these visions and ideas, then it’s about sharing those things with everybody who’s involved.

This whole idea of vision casting is not just a one-time thing, where we sit everybody down and say, “This is the branding” or “This is the kind of thing we’re going to pass on, and say, ‘Absolutely not, we’re going to do that.’ ” … It’s part of a constant thing, where we’ll all come together and have these conversations, and make sure everybody is on the same page. And those times are important.

But I think the group of people we have surrounding us are people who agree with and believe in what it is we’ve started from the beginning. And the integrity, as you said, of what we started in the beginning, and that’s the last thing we want to loosen our grip on, because we do believe in it.

Q: Why do you think your music has become so popular? Have you had time to analyze it?

A: Music is such a crazy thing. There are some things that I’ll never understand. Why is this popular? Why is that cool? And sometimes there’s not a really definitive answer.

With this, I think it’s just being vulnerable. We try to be as honest as we can, even at the risk of not appearing to be super cool.

I think people want honesty. I know that when I look at a band that I enjoy or look up to, I want to see the real versions of them onstage, and I want to see the real versions of them in interviews, and I don’t want to see a fake version, a version that is created out of them trying to be cooler than they are. … I think that we try to be honest as we can, within our songwriting and the way that we portray things. I get the sense people have been able to spend time with the songs and resonate with them in a way that is almost therapeutic. Music is that way for a lot of people. That’s my only guess.