At Sunday night’s memorial service for the jazz saxophonist Dewey Redman, a lot of fellow musicians and friends came forward with suppositions about what made Mr. Redman special.

There was a consensus that it had something to do with his hometown, Fort Worth, and the generous, countryish sound of saxophonists from that part of the country. But he might have been a great jazz saxophonist had he grown up in a dozen other places too. Mr. Redman had no fixations on a Southern style; he just played as if he came from somewhere in particular and was of something.

Few jazz musicians these days have so much X factor in them, some quality that lies outside of technical discipline, harmonic scholarliness, high concept or compositional skill. Mr. Redman was never a master of improvising through chord changes in the traditional sense. But first in the late 1960s as Ornette Coleman’s tenor player, later in groups with Keith Jarrett and Charlie Haden and finally as a bandleader himself, he made it clear that he had a natural, communicative power to engage and provoke.

“People play their best when they play with me,” he once said to Matt Wilson, one of his drummers and the evening’s M.C. At least part of the time, that was actually true.

One of his friends, the saxophonist Joe Lovano — who is 54 now — spoke of how his father, the bop-era Cleveland saxophonist Tony Lovano, adored the fairly far-out Ornette Coleman record “New York Is Now!” for the way Mr. Redman’s solos seemed to be “speaking every line to him”; this was a common reaction.

Mr. Redman died of liver failure in September, at 75. The quality of the praise directed toward him gave the sense that Sunday’s memorial concert, at St. Peter’s Lutheran Church in Midtown, might be the first of many.

Things got deep quickly. The show began with a group including the pianist Geri Allen, the bassist John Menegon, the drummer Jack DeJohnette and the singer Teri Roiger, playing Mr. Redman’s “Dewey’s Tune.” Then the guitarist Pat Metheny, with Mr. Haden, the bassist, and Mr. DeJohnette, played “The Bat,” a ballad of Mr. Metheny’s that, on the Metheny album “80/81,” contains one of Mr. Redman’s most delicate solos. There was beautiful, long-line melodic improvising in it, over the barest drumming and cymbal-tapping.

Most of the musicians from Mr. Redman’s own bands of the last 25 years played something, including the pianists Charles Eubanks and Frank Kimbrough and the bassists Cameron Brown and Mark Helias. A few singers — Ms. Roiger, Sheila Jordan, Judi Silvano — honored both the vocal quality of Mr. Redman’s playing and his tendency to perform durable old ballad standards.

The pianist Ethan Iverson and the bassist Reid Anderson, both of the trio the Bad Plus, with Mr. Wilson on drums, got off a version of Mr. Coleman’s “Broken Shadows” that demonstrated the slippery harmonic mobility Mr. Redman played so easily. And Joshua Redman, Dewey Redman’s son, played a startling piece on tenor saxophone, unaccompanied, and very unlike the rest of his music: it was slow and minor and wary, using the horn’s full range, putting space between short phrases.

Inevitably, it all came down to the blues, which Mr. Redman could play as well as anyone. The show ended with Mr. Coleman’s blues “Turnaround,” with a group for the record books: Joshua Redman, Mr. Metheny, Mr. Haden and the drummer Roy Haynes. The solos were built of rangy lines with direct impact, and Mr. Metheny played with slangy country phrasing. The rhythm section put the tune aslant, giving it attitude and resonance and swing.