Henry Threadgill, who on Monday was awarded this year’s Pulitzer Prize for music, is a composer and bandleader of intense, unyielding originality, nobody’s idea of a compromise. An alto saxophonist and flutist with a distinguished career in the post-1960s American avant-garde, he has amassed a body of work with its own functional metabolism, perpetually humming in a state of flux. He has certain affinities with, but no particular allegiance to, the jazz tradition.

“In for a Penny, in for a Pound,” Mr. Threadgill’s award-winning album, is a suite-like composition released on two discs by Pi Recordings last year. It’s an intricate and thoroughly enigmatic piece of music, but above all it stands as a showcase for his longtime flagship, Zooid. (The group takes its name from a biological term for a cell that is capable of movement independent of its parent organism.) From the first moments of the title track, which opens the album, you experience a distinctively slanted feeling, the byproduct of an unstable but carefully coordinated form of counterpoint. The music has formal rigor and forward pull, but it doesn’t provide an orienting framework, or any clear distinctions between composition and improvisation.

When Mr. Threadgill got the call on Monday that he had been awarded a Pulitzer, he was beyond surprised.

“I was speechless,” Mr. Threadgill, 72, said in a telephone interview. “I said, ‘What for?’”

Asked how he categorized his music, or where it falls on the jazz-avant-garde continuum, he demurred.