When Jazz at Lincoln Center got going 15 years ago, it was initially perceived as the leading bastion of jazz conservativism, preserving everything that was good about the music’s past. As for the future, the thinking seemed to go, it would take care of itself. In the three years since the opening of Rose Hall, however, there has been more of an effort by JALC to position itself as the organization for all of jazz — classic and contemporary.

Saturday night’s program featured two groups: Masada, the avant-garde jazz ensemble led by alto saxophonist John Zorn and pianist Cecil Taylor’s new Aha 3 trio. The evening represented a major step forward for the idea that JALC can truly be all things to all jazz lovers. Mr. Taylor, a venerated statesman of jazz who has been a controversial headliner for over 50 years, is the archetypical revolutionary. Mr. Zorn has positioned himself as something of an anti-Wynton Marsalis: He runs a performance space (the Stone, on Avenue C, in addition to the record label Tzadik), but whereas Mr. Marsalis champions everything traditional — New Orleans, swing, bebop — Mr. Zorn is the guru of everything downtown, experimental, and just plain flaky.

Masada, which first recorded for a Japanese label in 1994, is both a specific body of compositions and the ensemble, with Dave Douglas, trumpet; Greg Cohen, bass, and Joey Baron, drums. The concept behind this group was to present what Mr. Zorn calls “radical Jewish culture”: ’60s-style free jazz with a decidedly Hebraic outlook — sort of Ornette Coleman meets Mickey Katz in hi-fi. Mr. Zorn’s main tactic here is to start with melodies that sound like they could be played at a Jewish wedding, but the music is rendered with collective melodic improvisation. Mr. Zorn’s saxophone statements — such as shrieks and shouts or disturbances and distortions — are just as much a part of the music as the regular tempered notes. The most conventionally melodic moments are Mr. Cohen’s bass solos, and the quietest passages are Mr. Baron’s drum solos. The group is constantly playing beautiful, minor key melodies, often involving exotic polyrhythms, and then immediately destroying any chance of the audience relaxing into the music with eruptive, explosive dissonances — as if it were a production of “Fiddler on the Roof” staged by the inmates of “Marat/Sade.”

Mr. Zorn, who was recently awarded the MacArthur Foundation’s “genius” grant, also seems to be competing with Keith Jarrett for the role of jazz bad boy. After the first number, Mr. Zorn harangued the Rose Hall technical staff to lower the house lights and refused to proceed until they did, and delivered nearly all of his spoken announcements off-mike, as if he couldn’t be bothered to walk three feet and talk into a microphone. He was dressed like a rapper, in camoflauge pants and hooded sweatshirt, and treated like a rock star, in that the crowd went wild every time he overblew a note. But because his skill as a composer, and his mastery of the horn, as well as the interplay of the quartet, are all remarkable, I was going wild as well.

Cecil Taylor’s major bit of stagecraft was to have his drummer, Pheeroan akLaff, begin the show by tapping on his conga drum, while Mr. Taylor, still backstage, responded by tapping back. (Mr. akLaff sports the largest, most intimidating percussion setup I have ever seen — even more impressive than that of drum star Jack DeJohnette.)

Next Henry Grimes made his entrance, but rather than picking up his familiar olive oil-colored bass, he began scratching random notes on a violin. Mr. Taylor then alighted the stage, but did an odd dance holding what looked like Balinese finger cymbals, gargling what sounded like a death rattle. When he made it to the piano, he plucked a few strings inside the instrument, and read several lines of decidedly nonlinear poetry (seemingly random words) before starting to play.

After a lot of buildup, we were suddenly in the middle of it. Whereas Mr. Zorn’s music employs theme and variations, loud and soft dynamics, fast and slow, Mr. Taylor’s playing is nothing but pure momentum and energy: a morass of rhythmically driven music with nothing that suggests conventional melody or harmony. Never before has JALC emcee Todd Barkan’s standard opening line about jazz being “a journey into the unforeheard” been so accurate. Mr. Taylor’s playing seems at first like pure pounding, an assault on both the piano and the audience, but gradually patterns emerge and a kind of inner logic reveals itself. Mr. Grimes switched between violin and bass, and Mr. akLaff was all over his encyclopedic trap set, but the main force was Mr. Taylor, pushing ever forward. His stamina and technique were remarkable in his 30s, and now, for a 78-year-old man, they are even more impressive. About two thirds of the way through his set, he slowed down, letting our ears relax a bit. The softer and almost tranquil passage that followed seemed beautiful.

Both groups, who played to a near capacity crowd of people younger than the standard JALC audiences, received two of the only standing ovations I’ve seen at the Rose Theater, and both played encores. After tonight, nothing could surprise me, even if Wynton Marsalis were to give a solo, unaccompanied trumpet concert at the Stone.

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Michael Feinstein regularly appears at Zankel Hall with a specific topic and an array of guest stars. Friday night, however, was his first full-length concert in some time on the main stage at Carnegie Hall. Accompanied by his outstanding band (led by pianist John Oddo), he sang from across the scope of the American songbook, beginning with two songs by Burton Lane, “Time for a Love Song” (which could have been the evening’s theme) and “How About You.” He moved on to more contemporary works like Johnny Mandel’s “Where Do You Start?” and “When You Shine,” a new song of his own composition from a show being produced in London. These were all ballad highlights, and the outstanding uptempo was “The Trolley Song.”

When this performer sings in a cabaret setting, as at Feinstein’s at the Regency, he sings in a whispery, intimate style. He did so on Friday night during the audience request segment, but mainly he sang out and open much more frequently, with a big, strong baritone, and a lot of belt endings, à la Judy Garland. His time-honored move is to start with rubato verse, move into tempo for the refrain, and then, slip into a modulation for the last eight bars.

You wouldn’t think that Mr. Feinstein would have much in common with either John Zorn or Cecil Taylor. But Mr. Zorn’s opening composition had a dronelike melody that recalled the bridge to “Lullaby of Broadway,” which Mr. Feinstein sang, and where Mr. Taylor attacks the piano with fingers, fists, elbows, and his open palms, Mr. Feinstein did him one better by jabbing the keyboard with his left buttock during his encore “Great Balls of Fire” — which recalled Jimmy Durante’s famous line, “Funny, I usually play by ear!”