You could almost hear the wink that came with the pun John Magnie offered when asked to describe new Subdudes music:

“Yeah, I would just say it’s pretty Subdude,” he said from New Orleans, “which I think has always been about songs that’ve got good harmonies to sing and really good grooves. And this one has a lot of good, soulful grooves on it. I’m trying to think what would be the right direction for it. Just Subdude music, I guess.”

Longtime fans know that the music made by this swamp-rocking New Orleans quartet, which plays the Tower Theatre on Thursday, is anything but subdued.

Despite the band’s stripped-down nature — percussionist Steve Amedée’s tambourine playing in place of a full drum kit has long been a hallmark of its sound — The Subdudes hit on a rollicking mix of jazz, Cajun Zydeco, blues, R&B, funk, soul and gospel early in its career.

“When we came to our first gig, the idea was you had to bring the most minimal (equipment) you could,” Magnie said. “So instead of a piano, I just had an accordion. Tommy and Johnny were playing electric guitar and bass, but they just brought acoustic guitars. And Steve, instead of bringing drums, he just brought a tambourine.

“… It’s kind of a primitive sound, and we had sort of a folk approach maybe to songwriting,” he continued. “And it was really based on where the other three in the band grew up, which was a little sugar cane town up river of New Orleans called Edgard, Louisiana. Of course, New Orleans got such a rich musical tradition, but the Edgard thing pulled it a little more into country, so I think that’s The Subdudes sound.”

That sound has proved influential across 10 studio albums and two reunions (the current iteration, featuring Magnie, Amedée, co-founding guitarist/vocalist Tommy Malone and bassist Tim Cook, has toured since 2014). The band’s distinctive vocal harmonies have featured alongside Roseanne Cash, Joni Mitchell and Shawn Colvin, to name a few, and in-studio collaborators include Keb’ Mo’ and Glyn Johns.

Shortly after forming, The Subdudes relocated to Fort Collins, Colorado. Magnie, who grew up in Denver, said the move helped the band’s New Orleans-influenced sound stand out amidst Fort Collins’ burgeoning creative scene.

“We had the idea that we needed to go somewhere with it, and it was just — I knew that if we came back up here to Colorado that we would be different,” he said. “The idea was to be able to work playing our original stuff, and so I kind of dragged everybody up here. Especially Fort Collins, which is a little bit like Bend, I think in that it’s a fun little town with a lot of creativity in it. But for the Subdudes, going from New Orleans to there was like going to the wild frontier.”

The Subdudes split for the first time in 1996 and reunited in the early 2000s as a five-piece featuring original members Malone, Magnie and Amedée, with Cook replacing original bassist Johnny Ray Allen and guitarist/bassist Jimmy Messa also joining.

The band split again after releasing the 2009 album “Flower Petals,” and wouldn’t have reunited again if it wasn’t for Allen, Magnie said.

“We had broken up again and got together for the funeral of a friend of ours in New Orleans,” he said, “and Johnny just had this mission. He just was like, ‘We have to get back together.’ So we did, and it kind of healed some of the rifts that we had before and stuff. But then four months into it, Johnny died. … It was like Johnny Allen getting us back together but then checking out, and we’re going on from there. But it all seems to be right for some reason.”

Cook returned to the fold, and The Subdudes released 2016’s “4 on the Floor.” That album aimed to re-create the group’s acoustic encores, in which the band members sing from the front of the stage with just Malone’s unplugged guitar for accompaniment.

This all led up to the new album Magnie teased that was just completed in New Orleans. The yet-to-be-titled album — due out sometime in the next couple of months, Magnie said — will be the group’s first set of new, original material since “Flower Petals.”

“We weren’t knowing if we were going to do anymore writing together or just play the gigs and play the old songs and have fun,” Magnie said. “All of a sudden last year just came around: ‘Man, we gotta do a new record; we gotta just jump in and write a record’s worth of material.’ And once we kind of turned that key and got it started — it got going about last May, and we did a bunch of writing sessions over the summer — we got a new record of songs that we really like. It’s a whole new blood for us.”