If the bassist Ron Carter was recruited by NASA to be rocketed to Mars and became the first jazzman to perform on another planet, he would still be most famous for one thing: having played with Miles Davis’s “second great quintet” of the 1960s. That group has exerted such a profound and unimpeachable impact on virtually all jazz in the last 40 years that nothing any of its members did afterward — including Davis’s featured soloists and composers Herbie Hancock and Wayne Shorter, and even the trumpeter-leader himself — was ever able to surpass it.

Following Davis’s example, none of the three surviving members of the quintet have been inclined to look back — perhaps in observance of Satchel Paige’s dictum that something might be gaining on them. However, this year Mr Carter is the first veteran of the ’60s quartet to do a tribute album to his legendary employer, the newly released “Dear Miles” (Blue Note).

On Wednesday night, Carnegie Hall and the JVC Festival made Mr Carter the star of a program called “Ron Carter: The Master @ 70,” the predicted highlight of which was the reunion of Mr. Carter with Messrs. Hancock and Shorter.

This was still not entirely a case of looking back, because unlike the all-star tribute shows we have come to expect at JVC and elsewhere (like the Oscar Peterson fête two weeks ago), this was a concert by Ron Carter as opposed to for Ron Carter. He was on stage the whole time, and rather than attempting a retrospective of all the different kinds of music he’s made in his 50 years, the emphasis here was on three contemporary ensembles that he leads today, in addition to the ’60s Summit Reunion.

The music Mr. Carter made with Miles Davis was, for the most part, hard-driving bebop, at once complex and simple, opened up by a modal approach with extended solos and tempos that were either blisteringly fast or agonizingly slow. In his own groups, Mr. Carter has preferred a kind of chamber music structure, with frequent references to two of the most celebrated jazz chamber groups: the King Cole Trio and the Modern Jazz Quartet. This was especially apparent on Wednesday in Mr. Carter’s opening trio with the pianist Mulgrew Miller and the guitarist Russell Malone. The piano-guitar-bass format replicated that of the King Cole Trio, and the set concluded with a snappy rendition of the Modern Jazz Quartet’s famous blues, “The Golden Striker.”

The second ensemble was a duet consisting of Mr. Carter and the guitarist Jim Hall; even for these two virtuosos, Carnegie is a big space for so intimate an enterprise as a jazz bass-and-guitar duo. Their three-song mini-set was aces, but it hardly had the impact that the same twosome had at the Blue Note a few months ago. I wish Mr. Carter had also taken this opportunity to showcase his more extroverted duo with the expert saxophonist Houston Person, with whom he recorded two outstanding albums of bass and tenor in 1989–90.

After an intermission (Mr. Carter announced he was going to seek out three ATMs for cash to pay the band), Mr. Carter convened a 20-minute meditation on Miles with Mr. Shorter and Herbie Hancock, and the drummer Billy Cobham, who participated along with the other three in Davis’s early electric experiments.

Can you go home again? Sometimes. Mr. Hancock, who is something of a chameleon (as he acknowledged in one of his most famous compositions), can effortlessly return to the highly angular style he applied to slow standards 40 years ago, as he did in a duet with Mr. Carter on “Stella by Starlight.” Mr. Shorter, on the other hand, works through one style and sound at a time without switching gears, and lately he has become a much more introverted player than any of the famous Davis tenors. Still, Mr. Shorter played “All Blues” comparatively aggressively — by his own current standards — even if he always does seem to stop just at the point when I would love to hear a few more choruses.

The last group, Mr. Carter’s “New Quartet,” was, unexpectedly, not an anticlimax. The bassist has actually been using this format, with the pianist Stephen Scott and two drummers (currently Payton Crossley on American traps and Rolando Morales-Matos on a formidable battery of Pan-Afro-Latin percussion), at least since his 1997 album “The Bass and I.”

This is bass-centric chamber jazz of the first rank, combining elements of both the MJQ style and the Second Great Quintet (or “2GQ”) with a tight ensemble and plenty of interplay, consistently spiced by the variety of percussive devices employed by Mr. Matos, whose mission is less to make the group sound South American than to give it an extra rhythmic kick.

The Quartet offered “Mr. Bow Tie,” Mr. Carter’s original signature of recent years, as well as two Davis perennials — “Flamenco Sketches” and the blues “Joshua” — and two standards, “You and the Night and the Music” and an unaccompanied solo bass tour de force, “Willow Weep for Me.”

Often, these tribute shows — particularly when the subject has reached an advanced age — have the feeling of a last hurrah. For a musician at the top of his game like Mr. Carter, the evening was a hurrah all right, but hardly a last one.

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Other than the big JVC salute to Nancy Wilson tonight, the mustsee jazz events in the city this weekend are Claire Martin at the Algonquin and the 18-year-old alto saxophone prodigy Francesco Cafiso at Birdland.

The latter is a concert-worthy presentation of the famous “Bird With String” arrangements spotlighting Charlie Parker in the early 1950s. It will feature I Solisti di Perugia, the 10-piece string orchestra, along with piano, bass, and drums. To hear these charts played by an ensemble who has taken the time to rehearse them properly (more so than the studio bands that originally recorded them with Bird) is an overwhelming sensation, but so, too, is Mr. Cafiso, who comes close to capturing Parker’s essence on the written parts, but is his own man in the improvised sections. Mr. Cafiso recorded this program in 2005 on “A Tribute to Charlie Parker” (Giotto Music/Umbria Jazz) at the age of 15, but both the soloist and the orchestra play it with even more authority now.

This music, both urgently swinging and irrepressibly romantic, was not only among Parker’s own favorites, but his most popular with the public, and it’s easy to hear why. Were this any time of year other than Festival Week, I would surely be going more than once.

wfriedwald@nysun.com