Apart from being arguably the best trombonist around and a distinguished composer and bandleader, Steve Turre has an underutilized gift for putting together jazz repertory projects. In 1998, he masterminded a marvelous re-creation of the music of Juan Tizol, a key member of Duke Ellington’s musical universe and Mr. Turre’s predecessor as a Latin-American trombonist-composer.

His current repertory project, which is being presented at Dizzy’s Club Coca Cola this week (some of which he recorded on his 2004 album, “The Spirits Up Above,”), is even more personal: It’s the music of his mentor, Rahsaan Roland Kirk, the multi-instrumentalist and all-around wonder of the ages.

Kirk (1935–77) had a direct influence on future generations in three ways that are immediately apparent. He was one of the first modern jazz men to look back to earlier forms of the music, an aspect of his legacy that was reflected by the pianist Hilton Ruiz. Ruiz, who played with Mr. Turre in one of Kirk’s final bands, could switch from bop to stride piano to avant-garde playing in a heartbeat.

Kirk also encouraged players to pick up unusual instruments and make new jazz sounds with them. Mr. Turre himself is a leading exponent of this idea: In addition to the trombone, he has shown it’s possible to play real jazz on a set of sea shells (which he did only briefly at Dizzy’s on Tuesday).

Finally, Kirk possessed an amazing capacity to play two or three saxophones at once. For years it was taken for granted that this was unique to him. But just this year, saxophonist Joe Lovano recorded on the auluchrome, a new French instrument consisting of two sopranos welded together in a fashion directly inspired by Kirk.

The best way to honor Kirk’s accomplishments, however, is simply to play his music. Mr. Turre not only played Kirk’s compositions, but did so in a way that came as close as possible to replicating the way his mentor played them. No one man could capture Kirk’s sound — even on the auluchrome — so Mr. Turre transcribed Kirk’s one-man-horn-section arrangements for his trombone and two saxophones (Billy Harper on tenor and Vincent Herring on alto and soprano). The rhythm section for Mr. Turre’s sextet is Gerald Cannon (bass), Dion Parson (drums),and, on piano, the formidable Mulgrew Miller, who was equally impressive last week leading his own sextet at Jazz Standard.

“Three For the Festival” began Mr. Turre’s set and, in a sense, it also began Kirk’s career.The tune is a fast and furious blues that Kirk played for the first time at the 1962 Newport Jazz Festival, introducing the jazz world to his incredible one-man-horn-section. It was also where Kirk proved all over again the effectiveness of the stop-time break, a device he restored from early jazz and blues, in which the soloist and the rhythm section stop dramatically and resume a few beats later — a surefire way of holding the crowd’s attention.All three horn soloists did this at Dizzy’s, including Mr. Herring on soprano.

Mr. Miller soloed first on the second tune, “One for Kirk,” Mr. Turre’s original dedication to his friend and mentor. He played a passage that made me think of Red Garland, and apparently Mr. Turre felt the same way, because he began his improvisation with a quote from “Billy Boy,” Garland’s much-played feature with Miles Davis.

Mr. Turre then brought out the guest star for the week, flutist Dave Valentine. Mr. Valentine is about the most aggressive flute player imaginable, so intense and often over-the-top that I tend to prefer him in small doses, as a guest star rather than playing a whole set. His shtick, however, is perfectly appropriate for a tribute to Roland Kirk, who would surely have appreciated it. Mr. Valentine led the charge on two Kirk flute features, the jaunty “Serenade to a Cuckoo,” and one of the late giant’s key musical and spiritual mantras, “Bright Moments” (which Kirk recorded live at the Keystone Korner, a club owned by the current Dizzy’s manager Todd Barkan). Like Kirk, Mr. Valentine shouted into and at the flute, crooned into it, blew into it, and produced frighteningly avant-garde multiphonics and split tones. The cacophonic ending of “Bright Moments” even gave Mr. Turre a chance to briefly play two of his conch shells.

“The Inflated Tear” is the polar opposite of “Bright Moments,” a dirge written by Kirk in 1967 to mourn the loss of his eyesight, which occurred when a nurse misdiagnosed him and put the wrong medicine in his eyes when he was 2 years old. It’s probably the saddest piece Kirk ever wrote, as was Mr. Turre’s three-horn arrangement, which employed chilling silences between the main phrases of the melody.

The first show wound up with “E.D.,” Kirk’s dedication to his first wife, a killer fast bebop romp over the chord changes to “Tea for Two.” Mr. Parsons kicked off the tune with a set of pressrolls, and in the time-honored tradition of jazz clubs, the show climaxed with an extended trade of fours between all the horns and the drummer. As on Kirk’s 1962 recording, the display of virtuosity here wasn’t playing three horns at once but negotiating these changes over such a breakneck speed. As Mr. Turre and his Sextet showed, Roland Kirk may have played a lot of flakey stuff, but his true brilliance was in what he did with the fundamentals.

The after-hours set at Dizzy’s continues what Mr. Barkan refers to as the “Rahsaan-athon.” Night owls who can’t get enough of Kirk’s works are encouraged to stay for the very late set by Claire Daly. This fine baritone saxophonist is leading a band she calls “Bright Moments,” and which co-stars pianist Sonelius Smith, who played with Kirk in the early 1970s. By a fortunate coincidence, Ms. Daly’s late gig also serves as a preview for the Diet Coke Women In Jazz Festival, which begins at Dizzy’s next week.