Summer is supposed to be a slow season for jazz (and everything else), but this week there are two ensembles, both led by veteran players, that are so outstanding that I want to go back to every good review I have written in recent months and revise them all downward.

On Tuesday, pianist Cedar Walton and his quintet – co-starring trombonist Steve Turre and saxophonist Vincent Herring – opened a two-week run at Dizzy’s Club Coca-Cola. This marvelous band plays with forethought and obvious preparation, and I left the show thinking I would have to wait until the fall to see such good live music again. As it turns out, I only waited until Wednesday, when the alto saxophonist Lee Konitz opened with his New Nonet at the Jazz Standard.

You won’t be hearing a more remarkable group in many a season. Mr. Konitz calls this group his “new” nonet to distinguish it from other nine-piece bands in his past, such as the Miles Davis Birth of the Cool collective of 1949 and his own Yes, Yes, Nonette of 30 years later. The New Nonet is one of several projects Mr. Konitz has collaborated on in recent years with the Israeli tenor saxophonist and composer Ohad Talmor. Mr. Konitz, who lives in Germany when he isn’t touring, writes out original compositions and variations on standards, then faxes the lead sheets to Mr. Talmor, who then orchestrates them for the nonet.

The new group is also different from previous Konitz nonets in that it features a total of 10 musicians, or rather nine plus Mr. Konitz: Mr. Talmor, who plays tenor and conducts, Russ Johnson (trumpet), Jacob Garchik (trombone), Oscar Noriega (clarinet, bass clarinet), Dennis Lee (bass clarinet), Dimos Goudaroulis (cello), Ben Monder (guitar), Bob Bowen (bass), and Matt Wilson (drums). Most of these players are roughly half of Mr. Konitz’s 77 years.

Fifty years ago, Mr. Konitz was classified primarily as the no. 1 “student” of pianist-philosopher Lennie Tristano, but in recent decades he has become a whole school of jazz unto himself. His style and sound have been in constant evolution since the 1950s, and as his current ensemble shows, all sorts of younger players have grown up on Mr. Konitz’s music and learned from his example.

Like Benny Carter’s orchestras, Dizzy Gillespie’s big bands, or Sidney Bechet’s multi-tracked one-man band, Mr. Konitz’s New Nonet was built from the bottom up to showcase its leader and reflect him as accurately as his own improvisations do. Even though Wednesday was the New Nonet’s first night performing as a unit, the group was so together that during the ensemble passages they sounded like an orchestra band of Lee Konitzes – rather like the band of Buster Keatons in “The Playhouse.” During their solos, the players showed more of their individual personalities, but everything they played fit into the larger framework of Konitziana.

For the opening set on Wednesday, the Nonet played two variations on Jerome Kern, “All the Things You Are” and “The Song Is You,” along with an original waltz (apparently by Mr. Konitz) and an especially lovely new balled by Mr. Talmor called “Warmer in Heaven.” In these pieces, inspired by Mr. Konitz’s 60 years as a major soloist, nothing is arbitrary: Even the most abstract-sounding line will turn out to be linked to a chord change or a melody.

The climax of the evening was a very ambitious collage of blues themes that Mr. Konitz has played over the years, combined and orchestrated by Mr. Talmor into something like suite form. The subsections move in and out of different keys and tempos, and Mr. Konitz, who has an insatiable appetite for puns on both of his names, titled the work “Chromatical-Lee.”

Because Mr. Konitz and his fellow Tristano-ites have long trumpeted their love of classical music, we tend to forget what a superb blues player he was – and is. “Chromatical-Lee” encompasses everything from the Tristano-Brubeck style of baroque blues with lots of counterpoint, to out-and-out funk, set in a minor mode and an odd, uncountable meter. With typical wit, the funkiest section highlighted the least funky instrument, the cello.

It’s unlikely that any living jazzman (save possibly Sonny Rollins) could usurp Mr. Konitz’s position as the star attraction. His solos remind me of a man exploring a dark cave with a flashlight, going over every inch of it and finding everything that’s in there, but seeing just a little bit at a time. Amazingly – make that amazing-Lee – every time he visits a song, he finds something neither he nor anyone else has ever seen before, and even a tune he’s played a thousand times before becomes fresh terrain.

Until August 14 (116 E. 27th Street, between Park and Lexington Avenues, 212-576-2232).