In a perfect world, the ICP Orchestra would be the Monday-night band at your neighborhood jazz joint — so you could check in with them every week as they checked in with the world, week after week, their spontaneous reactions producing a different "piece" each time out. Because no matter how many different compositions the ICP play, every set is in effect a new piece. Unfortunately, the last time this Dutch nonet came to Boston was in 1999 as guests of the Boston Creative Music Alliance. Fortunately, the BCMA is bringing them back this Wednesday, to the Institute of Contemporary Art.

It was pianist and composer Misha Mengelberg, drummer Han Bennink, and saxophonist/composer Willem Breuker who formed the ICP (Instant Composers Pool) in 1967 in Amsterdam. The music has deep roots in American jazz (Mengelberg and Bennink both played on jazz deity Eric Dolphy’s Last Date recording) while also reflecting all the currents of the avant-garde for the last 50 years. Their sets veer from tightly composed chamber-group fugues to free-form brass-band parade music to good ol’ avant-garde squall and Ellingtonian swing. Sometimes sections of the band break off into warring parts — strings against brass (the current line-up includes American violinist Mary Oliver), rhythm against horns. Yet they cling, miraculously, to an overall unity.

"It took me about 30 years to find the people to do that with," Mengelberg tells me over the phone from a tour stop in San Francisco. "I think it’s starting to . . . go. I feel okay about it I think."

Mengelberg says he’s especially proud of the Oh, My Dog! CD on the band’s own label. "For a long time I wanted to make a record with mainly improvisations. No more pieces, in the classical sense. And we did that. I think it has become a very nice record."

At any moment during an ICP concert, any member of the band may cue a prearranged piece, or try to steer the band with a groove that the others can follow or not. "Well, yeah, there are lots of things going on there," says Mengelberg. "There are, of course, the things you mention, like the ignoring of certain impulses from maybe two or three persons or one to invoke in the band a certain process. Then we can follow those impulses, but we can also ignore them. I think to ignore them is more our style than following."

Mengelberg’s preferred method, however, still seems to be to play "free" rather than prearranged pieces. Do such pieces start with even a sketch or an agreed-upon chord or melody? "No, no, no," he says gently. "We start just by looking at each other and starting the music."

Such procedures would seem to encourage traffic jams, clots of noise, but ICP’s textures are surprisingly light, lucid — impressive when you consider the complexities of a nine-piece band versus, say, a trio or duo. "This band now is very able to do it," Mengelberg explains. "It’s a matter of discipline, I would say, of doing not too much all by yourself."

These days, the method of ICP and other "new Dutch swing" players has been adapted by others in Europe and America — Mengelberg has recorded with downtown New Yorker Joey Baron, and he speaks approvingly of Chicago drummer Hamid Drake, who’s played with him as well as with former ICP member Peter Brötzmann. "Yes, it goes much faster with younger musicians. And now, some of my pupils from the conservatory in Amsterdam have made bands that travel in those respects that we mentioned much faster than we ever did. But they have, among other things, us as examples."

The ICP Orchestra play the ICA Theater, 955 Boylston Street, this Wednesday, November 28, at 8 p.m. Tickets — $16 general admission; $12 students and seniors — are available in advance at Twisted Village in Harvard Square and on the day of the show after 5 p.m. at the ICA box office. For more information, contact edhazell@ccicrosby.com or call (617) 266-1512.