Introducing the weird and wonderful Temp Tats, whose music doesn’t fit any one box

The members of the year-old Temp Tats are not used to talking about their band. They sit side by side, the four of them crammed onto 27-year-old bassist Chris Paul’s couch in his Shawnee home, sipping beers and occasionally eyeing the TV. The game has been switched off, but Paul’s eyes dart toward it now and then as he wonders when he can resume watching the Royals beat the Twins. It’s a Tuesday night, the band’s weekly practice and hang time, and though I’m welcome, it’s clear that my presence is a puzzlement to these four young men.

This is in stark contrast to a few moments ago, when I was eavesdropping on run-throughs of “Astroid Rage” and “Piercing Tongues.” In the tiny room, the four Temp Tats delivered a confident, idiosyncratic sonic experience. Guitarist and lead singer Eric Schuman, 25, spun his usual webs of complicated guitar chords. His brother, keyboardist Joel Schuman, 28, echoed his precision with vibrant, jazz-rooted scales. (He also plays with the Waldo Jazz Collective.) Drummer Luke Waye, 26, was constantly in motion, building bridges from one sound to another as the band melded math rock, jazz and R&B.

“I called it spastic R&B at one point, and we liked that,” Joel tells me. “Or, like, prog soul.”

“We never really talked about what kind of stuff we wanted to play at all,” Eric says. “I don’t even think we really heard it until we went to record everything and were able to kind of sit back and listen to it.”

He’s referring to Temp Tats’ debut, Ions, which the band plans to release in November. Jorge Arana — of the similarly experimental prog-jazz group Jorge Arana Trio — handled that recording in his studio.

“They were super-easy to work with, well-rehearsed — it went really fast,” Arana says. “I feel like they’re the closest that we have here to, like, art songs for rock bands. I feel like here’s a bit of a cross-inspiring going on right now between them, us and [prog-rock band] Riala. We’re the closest bands to each other, though we all sound different and have a different vibe. Temp Tats has a really good sense of melodies and rhythms. They have the most pop sensibility, but they do it in a way that’s very unexpected. Eric — I think he’s probably my favorite songwriter in town at the moment.”

Eric explains that, while the guitar parts and lyrics are his, he considers every song a collaborative effort.

“I generally write songs and then just bring my parts to the band,” Eric says. “I don’t really tell anybody what to do or give them much direction. Everybody is completely involved with their own part — they’re not playing a part that someone else wrote for them or something like that, so they can kind of expand it however they want.”

When I suggest that this style of songwriting could lead very easily to a tone-deaf mess, Eric laughs. “We don’t avoid cacophony,” he tells me. “There’s a lot of confusion.”

While his bandmates snicker at his word choice, I consider Eric’s position. The three songs on the demo tape that he has passed to me — a preview, he says, of Ions — indeed suggest four members with varying positions and backgrounds, but the results aren’t really befuddling. There are a few purposely discordant notes — impulses left over from Waye and Eric’s previous band, a prog-punk act called Ambulants — and songs push well past the four-minute mark most of the time (“Slackjaw” stretches past seven), but these elements add up to sophistication. This is a band that could fit as easily in a jazz club as it does in a rock venue.

The secret weapon here is Eric’s voice, a smooth tenor with just enough power to muscle through the layers of other sounds. His moody, introspective lyrics — though not the centerpiece of any song, they aren’t throwaways — are delivered with the assured nonchalance of a singer who has been at this awhile. This is what Arana means, and what elevates Temp Tats above an instrumental outfit with a nominal singer.

“Kansas City has a lot of really great talent, but as far as originality, it’s hard to match those guys,” Arana says. “Especially because they do it in a way that makes their music very approachable. They have really nice melodies and very kind-of-catchy grooves. It’s one thing to make really weird music that pushes people away, but it’s another to make weird music that’s hard not to enjoy.”