It's what they refer to in the trade as a marketing nightmare.

Take a new recording titled Rip Tear Crunch by an industrious Chicago indie jazz brigade called the Rempis Percussion Quartet. Granted, the heavily improvisational outfit doesn't make the sort of music that will readily appeal to the masses, even the jazz masses. But that turns out to be the smallest obstacle. In fact, the album's title nicely defines at least a portion of the band's huge sound.

No, the trouble at first comes with the band's name. How do you explain the fundamentals of a so-called percussion group when its leader, Dave Rempis, is a reed player equally at home on alto, tenor and baritone saxophones? A percussion quartet led by a sax man? What's up with that?

Then there's the matter of the music. Every titled tune on the band's albums, every work it unveils onstage, is an improvisation. The resulting music is an on-the-spot creation.

So how does the Rempis band -- a percussion quartet fronted by a saxophonist, remember -- promote on the road a new album of music it can't possibly re-create onstage, and wouldn't want to even if it could?

Luckily, Rempis doesn't concern himself with the rules of music business commerce, any more than he does the conventional methodology of a jazz band.

"These are really good questions, though," Rempis said, laughing. "That's because so much other music is about reproducing what happened on a record.

"We deal with a live art form. A record is an anomaly. It's what happened at one point in time, an exact record of a particular time and place. So for us, records exist as documents of that time and place as opposed to some sort of finished product we try to reference back to at all our performances.

"In performance, we get up onstage and go. We don't start with any preconceived ideas. It's all freely improvised. With the record, particularly with the shorter pieces, there may have been a general idea of a style or dynamic level. Outside of that, everything was improvised."

If anything on Rip Tear Crunch approximates the Rempis Percussion Quartet's drive onstage, it's the 28-minute title track. But the association is mostly one of length. Rempis said his band usually turns sets into single 40-minute explorations. On record, Rip Tear Crunch's title work begins with raspy baritone figures that scour the surface of a boppish groove before deconstructing and reassembling into lighter, less openly melodic soundscapes where alto sax colors the contours.

Such adventure leads us back to the second of our main questions. Though the band fronts two exemplary drummers (Frank Rosaly and frequent Lexington visitor Tim Daisy), how is it that a saxophonist is in the driver's seat?

"You see, a lot of the things I'm doing as a saxophone player are coming directly out of the rhythmic ideas suggested by the group," Rempis replied. "They're tapped into rhythm as opposed to melodic lines."

Having a group of like-minded players behind him helps. Rempis works with Daisy in a number of other free-jazz projects, including Triage, the Vandermark 5 and a long-running duo collaboration. Quartet bassist Anton Hatwich also plays in Daisy's Festival Quartet.

And if you want to see just how communal the indie scene becomes in Chicago, there's the case of bassist Jason Ajemian, who completes the Triage trio with Rempis and Daisy. He regularly collaborates with folk-rock stylist Josephine Foster, who shares Thursday's Mecca bill with the Rempis Percussion Quartet.

Oh, yes: Did we mention Rempis and Foster went to college together? The links seem endless.

"It all gets a little schizophrenic at times," Rempis conceded. "Yesterday, I ran from work (his day job involves helping organize this summer's Pitchfork Music Festival in Chicago) to a rehearsal with one group to a gig with another group.

"You always kind of bat yourself from one thing to another up here. But it's exciting and fun. The adrenaline rush alone keeps you going."