By Ben Silverman and Craig Holland.

The Bad Plus might be considered a piano trio, maybe a progressive band or possibly a jazz fusion group. What they are, however, is a totally acoustic power trio, consisting of drums, piano and upright bass, playing everything along the jazz spectrum from furious avant-garde stylings to jazz standards, to slow-tempo, soft ballads to tweaked, sometimes absurd renditions of Flaming Lips, Yes and Nirvana songs.

The members of The Bad Plus met as teenagers and formed the band in 2000, releasing their self-titled debut album the next year. Five albums and nine years later, the band will return to the Iron Horse Music Hall in Northampton this Thursday.

The Bad Plus compositions show a wide range of dynamics and often change the tempo and timing – with an extra measure, flat, short or an almost indiscernibly syncopated drum solo inserted where one would expect the melody.

Some compositions might make you cringe. Others might make you frustratingly tap your toes and fingers to try and figure out a time signature. Others still will command your attention and make you work up a sweat trying to get a grip on what is happening musically, and then tease you when you can’t.

If John Bonham or Keith Moon had Tony Williams or Billy Cobham as a drum teacher and learned how to focus their drumming energy into a tiny, 4-piece drum set, they might sound like Dave King, who plays as bombastically and furiously as he does controlled, syncopated or disciplined. His fills are full of polyrhythms, and last as long as he wants them to, and his grooves may playfully, even distractingly, dance around the rest of the band’s music. But in the end, nothing else would mesh so perfectly with the rest of the group.

Bassist Reid Anderson is more subtle. He lays down the low-end while adding melodic fills and chords, and provides a solid foundation for the drums and piano to build on. He also writes many of the group’s more impressive compositions.

Pianist Ethan Iverson has a unique, powerful piano technique, often playing two completely independent and difficult musical figures simultaneously. His textured, rhythmic and often “out” playing is the melodic face of the band.

For listeners new to the band, check out “1979 Semi-Finalist” and “And Here We Test Our Powers of Observation” from the band’s 2004 album, “Give,” and the cover of Rush’s “Tom Sawyer” from its 2007 album, “Prog.”

The Bad Plus is a musicians’ band, catering to a crowd who would also appreciate music by Frank Zappa, Miles Davis and Igor Stravinsky. The most devoted fans appreciate the artistry of the compositions and interpretive covers while being wowed by the technical expertise involved in playing the music. The Bad Plus is dynamic, moving like a piece of romantic classical music, and bringing the rock when it’s time.

The composition of its original pieces stands out even more than the impressive skill required to play them. There are many jazz tunes that do very interesting things harmonically and rhythmically, but leave the untrained audience behind. People like to feel something when listening to music, and The Bad Plus brings this emotionality out in its compositions.

The Bad Plus will be playing the Iron Horse Music Hall in Northampton on Thursday, Oct. 29 at 7:00 p.m.

Ben Silverman can be reached at [email protected]. Craig Holland can be reached at [email protected].