By PHILLIP LUTZ

Four months from his 90th birthday, Dave Brubeck will bring his quartet to Litchfield on Aug. 6. Mr. Brubeck, who in December received the Kennedy Center Honors only months after a serious illness, said he was now in fine fettle, restricted from flying long distances but fully able to lead his group through tunes like “Take Five,” the hit in 5/4 time that helped bring odd meters into the jazz mainstream in the 1950s.

Since those early days, Mr. Brubeck has branched out, producing ambitious works for orchestra and chorus that have been performed throughout the world. He gets special satisfaction, he said, from a symphonic piece inspired by Ansel Adams’s photographs of the Yosemite Valley, not far from where he grew up in California. Written with his son, Chris Brubeck, the piece had its premiere last year.

But while Mr. Brubeck is working on several writing projects, including a torch song and a film score, it is the material from his landmark 1959 album “Time Out” to which he inevitably returns with his quartet — featuring the saxophonist Bobby Militello, the bassist Michael Moore and the drummer Randy Jones — and which he thinks will elicit the most response at Litchfield.

“They all want to hear ‘Blue Rondo à la Turk,’ ‘Take Five,’ ” he said. “Some nights we play ‘Three to Get Ready.’ That’s what the audience loves.”

Like Mr. Brubeck, Chick Corea, 69, was at the forefront of an experimental movement, collaborating with Miles Davis and later leading his own band, Return to Forever, as they turned toward electronics to fuse jazz and rock. Starting in the 1970s, Mr. Corea enjoyed great success with the band, ultimately seeing his innovations, like Mr. Brubeck’s 20 years earlier, become part of the jazz lexicon.

But Mr. Corea, who early on played with musicians like the saxophonist Stan Getz and the flutist Herbie Mann, has often returned to acoustic music. That is what he will be making when he leads his aptly named Freedom Band — the saxophonist Kenny Garrett, the bassist Christian McBride and the drummer Roy Haynes — in his small-group debut at Caramoor on Aug. 8.

Mr. Corea, who won raves for a solo turn at Caramoor last October, said that the band members would allow themselves maximum latitude. While drawing on jazz standards — he cited Thelonius Monk’s “Blue Hawk” and “Monk’s Dream” as group favorites — their improvisations might at any point refer only obliquely to a song’s chord changes, meter or overall form.

“The band is comfortable floating in and out of structure,” he said, noting that the musicians had developed an unspoken agreement on their approach to standards, starting a decade ago when all four first worked together. “If you know what’s coming, it gets to be boring. So you try to create situations where there are unknowns. You’re kind of skating out there.”

Mr. Corea is among the musicians cited as influences by Mulgrew Miller, 54, who will be the lone act on opening night at Caramoor. Mr. Corea, in turn, praised Mr. Miller for the fluency of his playing — honed as a sideman with the singer Betty Carter, the trumpeter Woody Shaw and the drummers Art Blakey and Tony Williams — and as an influential leader in own right.

Mr. Miller, who led a sextet at Caramoor two years ago, will be playing with a trio this year. He said that the group, with Ivan Taylor on bass and Rodney Green on drums, will mix his originals — among them “When I Get There,” an angular blues, and “Carousel,” a lush waltz — with popular standards like Harold Arlen’s “A Sleepin’ Bee.”

Compared with the Freedom Band, Mr. Miller’s trio might adhere more strongly to structure in the treatment of standards. Mr. Miller, who deepened his appreciation of classic form playing with the Duke Ellington band in his early 20s, said he would most likely state the theme and take improvised choruses before returning to the theme.

“I believe in giving due respect to the melody, playing it as true as possible,” he said. “As far as I’m concerned, a solo is a creative process that improves the melody. That’s why they call it improvising.”

The festivals are representing the Cuban tradition with three pianists who boast a bucketful of awards among them. Arturo O’Farrill Jr. and Chuchito Valdés, scions of musical dynasties, will lead big bands at Litchfield and Caramoor, respectively; Elio Villafranca will lead a quintet at Caramoor. Mr. O’Farrill, whose father was from Cuba, just turned 50; Mr. Valdés and Mr. Villafranca, both natives of Cuba, are in their 40s.

But the youngest pianist to lead a group at either festival will be Gerald Clayton, 26, who will bring a trio to Litchfield on Aug. 7. Mr. Clayton said he admired Mr. Miller’s sense of flow, and that could be reflected in the architecture of his sets, intimate efforts — the pianist and his band mates, the bassist Joe Sanders and the drummer Justin Brown, live in the same Harlem building — that often yield an uninterrupted stream of ideas with little pause between tunes.

Mr. Clayton already claims an impressive résumé, having played Caramoor last summer and led groups in the best clubs. He enjoys acceptance in the small circle of top-rank pianists — he once played in a four-piano extravaganza with Mr. Miller, Kenny Barron and Benny Green — and the kind of approval from historians that sometimes heralds a major career.

“Clayton is terrific of the young players coming up,” Mr. Morgenstern said. “He’s really gifted.”