Office of the Interior: The Bad Plus is brainy but capable of rocking out.

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Rock-fondling jazz trio the Bad Plus was designed for people who, like me, have sweated blood trying to make a clean break with pop music and all its inanities—metal’s evocations of screaming orcs, Lou Reed performing alongside his tai chi master, Tin Machine. But every time I’ve tried to get into “America’s classical music,” it seems like I end up listening to some masterly take on a show tune. If approaching 40 means choosing between alt-country, dad rock, or pretending that it’s worthwhile to hear some dead junkie deconstruct “The Surrey With the Fringe on Top,” well, Steve Miller Band deep cuts, here I come.

So the New York piano trio, which frequently covers tunes by the Pixies, Abba, Vangelis, and Black Sabbath, would seem like a perfect way for us novices to approach the church of jazz. An exploding cigar for race-and-swing-obsessed critics like Stanley Crouch, the Bad Plus’ desire to rough up two-­­drink-minimum piano-jazz civility with the brute force of a rock power trio almost feels, on paper anyway, like punk rock.

It’s not, and not just because the trio’s choices in source material often lack indie cred. Take Tears for Fears’ “Everybody Wants to Rule the World,” which opens Prog, the trio’s fifth studio album. Pianist Ethan Iverson lets his left hand play the song’s chords straight, while in his right hand, the melodies are either played modally or just kind of melt. I’m not sure what’s the bigger mystery: the deep sympathy that he, bassist Reid Anderson, and drummer David King immediately demonstrate for one another’s playing, or the cresting and ebbing waves of sound they discover in a song that, as a rule, only by people watching VH1 Classic at 3 a.m. listen to on purpose.

Pop musicians sample; jazz musicians quote; the Bad Plus falls somewhere in between. On Iverson’s “Mint,” he cribs from Charles Mingus; “Giant” has some striking similarities to Kool and the Gang’s “Cherish.” But on the group’s originals, it’s easier to note internal than external dynamics—Iverson’s sustain-pedal-heavy, almost tiki-style keyboard runs, Anderson and King’s studiously funky timekeeping.

But here’s where we run into trouble again. The spirit of rock, especially after punk, is that what you have to say is at least as important as how you say it. By dint of their chops, the Bad Plus always hew dangerously close to novelty, like those easy-listening versions of grunge hits that came out in the ’90s. Or think of indie bands that embraced cocktail music in the same period—are the Bad Plus merely Combustible Edison for jazzbos?

A better point of reference for anyone trying to understand the Bad Plus is math rock, another uneasy nexus of genres that began when less-than-virtuosic punk musicians began screwing around with heavy metal and found they could tap into hard rock’s power even if they couldn’t, by any reasonable definition, shred. The Bad Plus never feels as powerful as it does on Anderson’s “Physical Cities,” which toggles between a “Theme From Shaft” groove and a series of refined one-note thuds, like the Hulk typing a letter to the editor. The first time it comes around, King lays a 4/4 beat under the thunking’s odd meter, and it feels less like Iron Maiden than Breadwinner. At song’s end, when the trio lets the pounding go on for more than two minutes, it’s unbearable and transcendent in equal measures.

Prog is named after prog-rock, perhaps rock’s highest expression of musicianship over content. Anderson and King grew up listening to Yes and King Crimson, so it’s not too surprising that the Bad Plus treats Rush’s “Tom Sawyer” as less a jumping-off point for sonic explorations than a frictionless spot for two different schools of insufferable noodling to come together. The Bad Plus ramps up the menace of the bass line and hands Anderson his only real lead part of the album (which, by the way, sounds awesome), but aside from a couple of frenzied atonal passages that take the place of the original’s excruciatingly goofy Moog solos, it mostly leaves the Canadian prog-metal trio’s structure in place, which you gotta figure is less a function of irony than professional courtesy.

The album closes with “1980 World Champion,” which follows previous albums’ “1972 Bronze Medalist” and “1979 Semi-Finalist,” and I’d gladly trade the band’s pretty, if sort of pointless, cover of “This Guy’s in Love With You” or its exploration of the majesty of David Bowie’s “Life on Mars” for nine more tracks like it. It clip-clops between swing and barrelhouse, between the Peanuts theme and second-line stomp, Iverson pulling from Professor Longhair and Martin Denny, King skittering across his kit like a caterpillar on roller skates. It’s wacky and tacky, at once grand and human-scale, and there’s not a whiff of Broadway about it. If more jazz hit me like this, I would totally consider selling my LP of Fly Like an Eagle.

The Bad Plus performs Sunday, May 6, at the University of Maryland’s Clarice Smith Performing Arts Center, University Boulevard & Stadium Drive, College Park. For more information, call (301) 405-2787.