Keith Jarrett ambles out on the stage, sits down (slouches, really) at the piano, pauses a while to meditate, and then a simple melody begins to spin itself, allegro moderato. It sounds like a folk tune; no chromatics and only the barest of harmonies. Jarrett flips it over, examines it from various angles, speeds it up, turns it inside out, examines its smallest details as though with a microscope.

By now, he is bent over the keyboard so close that his forehead nearly touches it. Is he looking for new light on this theme in the cracks between the keys? Can it be that 10 fingers (the most phenomenal fingers now employed in what we have to call jazz) are not enough? Perhaps he wants to have his nose ready for an additional note, his forehead in position to bang out a tone-cluster?

A few minutes into a Jarrett improvisation, you have to listen closely to hear the music's connection with its unadorned beginning - but if you have been listening carefully all the way, the connection has been seamless.

Jarrett may have played with this tune before, but the standing-room audience Saturday night at the Warner Theater was hearing music new-born, with fantastically elaborated details emerging spontaneously in a way that had never been heard before. You go to other musicians' concerts because you have heard and liked the way they do "Take the A Train" or "Stardust"; or because they have composed and recorded something that you want to see done in person exactly the way it sounds on the record. You go to Jarrett concert partly because you never know what will happen - and neither does he.

But you know it will be good; you know that if you could write down every note and analyze it at leisure, as the Japanese "Swing Journal" did once, taking up an entire issue, and it would all hang together like a classical theme and variations.

There is plenty of fan-magazine fodder in Jarrett's private life - the isolated New Jersey farm where he sits brooding over his piano, the public trances he goes into at the keyboard, the taut nerves that make him insist on no flashbulbs during a concert, the scorn for critics and interviewers - largely justified, because what he does is almost impossible to write about. There is a fantastic life story - he began playing the piano when he was 3, gave a public recital of classical music when he was 7, came into jazz right at the top, with Art Blakey, Roland Kirk and finally the Charles Lloyd Quartet before he was 21.

But there is practically no cult of personality in a Jarrett audience - a heterogeneous group that most resembles the kind of audience you encounter when Arnold Schoenberg or George Crumb is on the program. The chief difference is that there are so many of them. You can't quite call Jarrett's music jazz and it isn't exactly classical, but look at the way tickets are gobbled up and you have to conclude that it is popular.

Rightly so. I know of no pianist, jazz or classical, whose fingers are so nimble and precise - no composer who can improvise such large structures with such constant interest and sequential logic. The last performer who did this king Jarrett with the level of acclaim Jarrett has been receiving was Franz Liszt.

Playing with Jarrett Saturday night was the latest edition of this quarter: Jan Garbarek on tenor and soprano saxophone, bassist. Talle Danielson and drummer Jon Christensen. This is a complete change of personnel since the last time I saw Jarrett, two years ago at the Kennedy Center; there is considerable loss in the departure of Charlie Haden, an extraordinary artist on the double bass, but it is more then compensated by the acquisition of Garbarek, a saxophonist who is in a class with Jarrett and able to engage in dialogue with him on a basis of equality.

With the change of personnel, there has come a change of style. Two years ago, the classical composer Jarrett most resembled was Scriabin. Now, he calls to mind Bach and Haydn - hard edges, tight ensemble and a keen intelligence at work in the music. I think it is a sign of growth.