Lesson No. 1 From a Master of Improvisation: Never Repeat Yourself

Lee Konitz played his first line for laughs at the Village Vanguard on Tuesday night. The band had just conferred backstage, he said, sidling up to the microphone, “and we decided we weren’t going to play anything we know.” Of course that wasn’t really the case — the set ended up consisting mainly of familiar standards — but as he lifted his alto saxophone to his lips, the promise buried in the joke felt tangible enough. His unaccompanied prelude gave the impression of an interior monologue full of open-ended questions.

For reasons that no one seems able to explain precisely, Mr. Konitz is headlining at the Vanguard this week for the first time since 1983. (Both he and the club’s owner, Lorraine Gordon, tried to account for the lapse with deflective humor.) Mr. Konitz, 81, is taking the opportunity to present two ensembles, each composed of responsive younger players.

During the first half of the run, through Thursday, his cohort includes the German pianist Florian Weber, the American bassist Jeff Denson and the Israeli drummer Ziv Ravitz. As a trio these musicians perform under the name Minsarah. As a rhythm section they have recent experience with Mr. Konitz, appearing throughout his album “Deep Lee,” which was released last year on Enja.

Mr. Konitz worked contentedly with the group in Tuesday’s first set, often answering to a scrap of suggestion from Mr. Weber. This interaction was most obvious in “Body and Soul,” which began as a saxophone and piano duet. After a languid bass solo Mr. Weber re-entered with an odd chord, venturing out on a harmonic limb. Without missing a beat Mr. Konitz joined him there, expanding on the idea before bringing the song home.

The rhythmic fallback for Minsarah is a fluid eighth-note cadence, more streamlined than conventional swing. This led to some mild tensions in the set, as when Mr. Konitz, who has his own dry variation of swing, tackled “Invitation,” backed by Mr. Denson and Mr. Ravitz. Later, on “Alone Together,” Mr. Ravitz led several bright experiments with boppish propulsion, and the flashes of ebullience were tantalizing.

Mr. Konitz gave Minsarah its own brief showcase: the trio played what sounded like “As the Smoke Clears,” a sparkling post-bop waltz by Mr. Denson. Here all three musicians gave in to effusiveness, with Mr. Weber exerting some classical technique. But their impact was diminished without Mr. Konitz, its outside conscience.

From Friday through Sunday he will work with a different group, featuring the young pianist Dan Tepfer. It seems likely that they will devote part of their engagement to duets, as they did on a new album, due out soon on Sunnyside. And it’s a safe bet Mr. Konitz will continue to be himself: an explorer inclined to test any premise, including his own.