Animals as Leaders is not your typical rock band.

For one thing, it doesn’t even have a bass player. And the lineup of guitarists Tosin Abasi and Javier Reyes and drummer Matt Garstka makes progressive, metal-edged instrumental music that is adventurous and involved and worlds away from anything you’d ever hear on commercial radio.

“I think music should impact the listener in a deliberate way,” relates Abasi, on the line from his home in L.A., “and musical complexity is one of the easiest ways to do that.

“We want to be a source of musical impression that you can’t get elsewhere, ’cause everyone else is writing love songs, and everyone else is writing stuff you can tap your toe to. And we want to fill a necessary space, I think.”

Animals as Leaders has been pushing musical boundaries since its self-titled debut of 2009, which was basically an Abasi solo album. Its fourth release, the self-produced The Madness of Many—scheduled for release by Sumerian Records on Friday (November 11)—sees the group continuing to evolve while keeping things tricky.

“We just resigned ourselves to go in directions we haven’t gone in before,” says Abasi. “A lot of the guitar solos I improvised, when I normally compose them.

“And our drummer wrote a song—‘Arithmophobia’, the first track—which was actually a purely rhythmic composition on the drums, and then we inputted guitar into a pre-existing framework of drums, which is something we’ve never done. We call it ‘Arithmophobia’ for a reason. It’s very mathematically driven and kind of rhythmically terrifying.”

The closing track on the new album is the similarly titled “Aepirophobia”—which means the fear of eternity and/or infinite things. So is Animals as Leaders’ apparent obsession with fear and madness directly related to the current sociopolitical atmosphere in Abasi’s native United States?

“Uh, in a way,” he replies. “I mean, I didn’t want to be too literal or anything, but ‘the madness of many’ was inspired when I looked up the term for collective hysteria, like a phenomenon of insanity that seemed to affect many people simultaneously.

“Because between, like, radical Islam, and the Syrian refugee crisis, and just not acknowledging things going on in the environment, as well as the American political situation right now, it seems like all of our intuitions are in strange places or the wrong places. I just can’t relate to the decision-making right now!

“But I also like multiple meanings,” Abasi adds. “You know, this music is challenging music and we’re purposely doing some—I wouldn’t say strange things, but there’s some moments on the album that are not exactly for you to tap your toe to and have a good time.

“So it kind of applies to us in the band as well, like this is our expression of ‘the madness of many’.”

Animals as Leaders plays the Commodore Ballroom on Wednesday (November 16).