The tricky thing about Butch Morris is remembering to watch. Normally when I listen to music, I bury my head in my notebook or close my eyes in rapture (except, of course, when Karin Allyson or Cassandra Wilson is on the bill). With Mr. Morris, however, visual cues are the most important part of the musical process. Mr. Morris creates the composition spontaneously as he conducts, and there is no written music to fall back on.

This month Mr. Morris is performing with a dozen or more different ensembles in about that many different venues spread across the city. In all, he will perform more than 50 sets as part of a festival titled “Black February” – a celebration of the 20th Anniversary of what he calls “Conduction.” On Tuesday, Mr. Morris played two sets at the Knitting Factory, using an orchestra of five brass, five reeds, two trumpets, two trombones (tenor and bass), as well as tuba, drums, and string bass.

Through the conduction process, much of the music is created right in performance. Mr. Morris utilizes a preset vocabulary of gestures to which they have been trained to respond. Still, hard as I try to concentrate, it’s impossible to make out the meaning of his motions without a guide map.

There is no traditional sectional playing in Mr. Morris’s music: You will never hear, for instance, four saxophones harmonizing together. Yet his music relies heavily on the jazz tradition of call-and-response. Sometimes a soloist makes a statement that is answered by the rest of the horns. Sometimes an ensemble plays behind a soloist, several horns improvising spontaneously, or all 12 musicians will play variations on the same figure in rough counterpoint.

As a conductor, Mr. Morris is one of the few jazz composers to make heavy use of orchestral dynamics, and he takes advantage of the classical tradition of indicating to the ensemble whether to play pianissimo or mezzoforte. The result can sometimes be very dissonant and loud. The first piece played at the Knitting Factory on opening night, for instance, was ear-splitting and cacophonic. Yet there’s organization in this chaos.

On Tuesday night, the tenor player started soloing, first under the other horns, then gradually emerging in the spotlight. His improvisation was essentially a collaboration with the conductor. At times everyone in the group played on top of him, at times he strode (as they say) with bass and drums. For brief moments he even played completely unaccompanied. He continued to play for most of the 30-minute piece, and most of what the rest of the orchestra played was in response to him.

As avant-garde as such a piece sounds, Mr. Morris’s music is clearly a product of both American and European traditions of orchestral music. The solo breaks are essentially cadenzas, and the piece on the whole could be characterized as a suite: a series of distinct melodies. The difference is that, in Mr. Morris’s music, the individual movements run in and out of each other organically. There’s never a point where one melody simply stops, the orchestra pauses, and the next part begins.

The second piece of the first set was clearly in concerto form, in which a single instrument (in this case, a trumpet) starts the piece by himself and is accompanied by the orchestra for most of the rest of the work. This work was softer and more consonant than the opener, even though it employed some very angular harmonies. Indeed, it was somewhat similar in tone and texture to the Miles Davis-Gil Evans “Sketches Of Spain” or Stan Kenton at his brassiest.

Then, after two fast-moving hours of mostly high volume, entirely high intensity music, Mr. Morris ended his two sets with a brief, catchy tune that pivoted on a two-bar lick. Who says an avant-gardist can’t have a sense of showmanship?

Mr. Morris will perform at various locations every night this month. For details of his performance schedule go to www.conduction.us.