A 20-something friend who accompanied me to the opening set of the Bad Plus at the Village Vanguard on Tuesday night asked me if the group was controversial in the jazz world. Not exactly, I replied – there are plenty of jazz fans who love the group and plenty who don’t, but I have yet to meet anybody who resents the success this piano trio has enjoyed. On the other hand, I don’t see why the mostly college-age fans of this very atypical ensemble couldn’t also enjoy more traditional jazz trios like those of Barry Harris or Kenny Barron.

The Bad Plus, in a nutshell, is a jazz trio with a rock ‘n’ roll sensibility – other than that, it’s easier to say what pianist Ethan Iverson, bassist Reid Anderson, and drummer David King are not. They are not, for instance, a 1970s-style “fusion” band like Weather Report, nor are they what has come to be known as a “jam” band, like Medeski, Martin & Wood. As far as I can tell, the Bad Plus is a tradition and a genre unto itself.

The three players follow the familiar piano trio format of Bill Evans or Bud Powell, but they eschew as many jazz traditions as they embrace: Their music is not based on the ideal of theme and variations, nor upon the contrast between pre-written ensemble playing and improvised solos. And though they leave carefully chosen spaces for improvisation and depend heavily on inter-reaction and interplay – trademarks of the best jazz tradition – their pieces are composed works from beginning to end, in the rock or classical tradition. They almost never play lyrical jazz ballads, and their use of extreme dynamics again suggests a link between rock and classical.

Their opening piece at the Vanguard, for instance, was Mr. Iverson’s “Let Our Garden Grow,” which is off the group’s new album “Suspicious Activity” (Columbia 94740). It began with one of the most distinctively jazzy – and conventionally “pretty” – moments of the evening, a bass solo by Mr. Anderson that vaguely suggested the jazz standard “My One and Only Love.”

After this long intro, Mr. King entered in a rather dramatic fashion, scraping his cymbals with the bottom of his sticks. Rather than keeping time, the function normally expected of a drummer in a jazz piano trio, he then took up an intricate part that verged on soloing; as he played, he seemed to be continually taking apart and reconstructing his entire trap kit. (In fact, all three instrumentalists kept wiggling and carrying on like a band full of Keith Jarretts throughout the set.) Mr. Iverson played a steady classical-style line throughout, but, remarkably, the piano melody seemed to be accompanying the bass, drums, and other shenanigans rather than the other way around. This was jazz upsidedown: The song slowly built up to the head rather than starting there.

At times the Bad Plus seems intent on proving Duke Ellington wrong: Swing isn’t everything. Indeed, many of their rhythms have more rock-ish “drive” than the syncopation and “swing” of big bands and bebop – though some rhythms are so syncopated and catchy they make your head spin! Other influences seem to be from beyond music: A piece called “Physical Cities” switched moods so often it had the feeling of radical jump-cuts from some kind of experimental cinematic collage. At one point, Mr. Iverson was playing boogiewoogie patterns with his left hand while pounding out random tonal clusters with his right elbow, offering two very different moods from the same instrument at the same time.

Early on, the Bad Plus attracted notoriety for their jazzy adaptations of rock anthems – among others, Kurt Cobain’s “Smells Like Teen Spirit” on their 2003 album “These Are the Vistas” and Black Sabbath’s “Iron Man” from 2004’s “Give.” In some cases, these seemed to be done merely to shock and therefore interest listeners on both halves of the equation. But some of their more recent “covers” (a term from the rock lexicon that is anathema to jazz listeners) re-interpret genuinely worthy material. Their jazzed-up version of Bjork’s “Human Behavior,” in fact, sounded more like traditional jazz than most of the original compositions the band played Tuesday night.

The new album has only one such “cover,” the 1980s soundtrack-classical-pop-crossover hit “Chariots of Fire,” which in characteristic Bad Plus fashion is both a joke and serious at the same time. Above all else, their musical ability allows them to put forth a jazzy sense – I couldn’t help but think that Thelonious Monk would find their music and their antics rather droll indeed.

At the climax of “Human Behavior,” Mr. King switched from his drums to play a solo of sorts in which he held up two vintage 1980s E.T. dolls and squeaked them back and forth at each other, as if in extraterrestrial conversation. “That’s got to be a first for the Vanguard,” my friend said. I wanted to answer, “No, Bill Evans did that in 1961,” but I kept my big mouth shut.

Until September 25 (178 Seventh Avenue, between West 11th and Perry Streets, 212-255-4037).