The official title for the ritualistic, immersive, often breathtaking solo piano concert at the Harlem Stage Gatehouse on Thursday was “An Intimate Evening With Cecil Taylor.” Hmm, intimate — I’m not so sure about that. True, there was a striking proximity to the audience in the performance, which had Mr. Taylor, the stouthearted patriarch of free-improvisation, seated at a Bosendorfer piano within seven or eight feet of the nearest listener. And yes, the sound in the room was vivid and pristine, with only the subtlest hint of amplification.


But the nature of Mr. Taylor’s art is formal and unaccommodating; you might sooner extract intimacy from a Gerhard Richter painting. The intensity of his contact with the piano, and the fullness of his commitment to the moment, imposes a distance between him and his audience. I’ve heard him in clubs, in concert and outdoors, and that part of the experience always holds true. He works inside a force field, imperturbable and sovereign. Whatever connection you make with his music, you make within yourself.


Thursday’s audience was well stocked with those who have made that connection deeply. The concert was part of a series built around Mr. Taylor’s formidable legacy, presented by Harlem Stage and Issue Project Room in Brooklyn, where another “Intimate Evening” has been scheduled for Saturday.


The room was at capacity, with a high concentration of musicians, including the pianists Vijay Iyer and Craig Taborn, who had performed in the series this week. An invocation was provided by a collage of testimonials recorded and edited by the Center for Jazz Studies at Columbia University. Its most emphatic voice belonged to Mr. Iyer, who exalted Mr. Taylor as his lodestar and as a defining voice of the 20th century.


Mr. Taylor is 83, and his small frame has gotten a bit smaller. He moved stiffly to and from the piano, wearing a lavender dress shirt that hung loosely on him, and glittery purple pants.


He began his performance offstage, reading a poem called “Argobba,” with connotations of ancestry and brain chemistry, punctuated here and there by guttural growls suggestive of throat singing.


Over the next hour or so Mr. Taylor created cycles of reflection and disruption, occasionally returning to a spiky motif, with triplets set against a four-beat cadence. Elsewhere he made full use of his expansive set of strategies for manipulating sound.


His hands moved with a fluttery grace, or with pugilistic vigor; his fingers were arched, or flat, or clenched. He could seem mantislike in his attack, or like a burrowing gopher. What never changed was a prevailing sense of discipline, both mental and physical.


Some of the most spellbinding moments made you forget about the piano as a mechanism, when Mr. Taylor’s touch was so liquid or supple as to suggest direct manual contact with the strings. He played a few magical glissandi along these lines, faintly evoking Asian scales.


Later he created a lacework percussive pattern that fleetingly called to mind an African thumb piano. And for a while he favored a particular pitch range, perhaps responding to the ringing overtones it produced in the room.


Periodically he stopped playing to riffle through the pages propped on his music stand. (It was sheet music, though he has his own system of notation, and he wasn’t strictly executing a score.) During some of these pauses he read his poetry, which gave the performance both an extramusical framework and another layer of high obscurity.


His language was full of scientific wordplay, scavenging terms from plant biology, human genetics and spatial geometry. At one point he repeated the figure 57.2958, a mathematical constant. (“Radius! Radius! Radius!” he then shouted, causing a ripple of knowing laughter, which tells you something about his audience.)


“A closure,” he said, adopting an unusually soothing tone, in a poem called “Leaves Are Growing.” He added, “A closure amidst feeling and hue.”


Then, almost in his next breath, he rattled off phrases that could have been cribbed from the skeptics he has outlasted: “the esoteric seizure,” “effluvium and effluvium.” Whether or not that was meant as an inside joke, it was a palpably human moment, and Mr. Taylor owned it.