During the 1970s, however, his relatively few performances took place mostly in Europe, and so - in this country, at least - the latest developments in his music never received the press coverage awarded comparable shifts in the work of fellow pioneer Minimalist composers Philip Glass and Steve Reich. Like Glass and Reich, Riley lived in New York in those years when Minimalism was fast becoming the trend in avant-garde American music. He quit that scene in 1969, preferring to the Big Apple's pace and pressure the tranquility of a hideaway ranch near Lake Tahoe. By choice, Riley became - and to a certain extent remains - a recluse.

Now his reclusiveness is diminishing, and in a way that suggests that Riley - after all these years - is genuinely attempting to enter contemporary music's mainstream. His visit to St. Louis last weekend, in fact, had all the trappings of a personal appearance by a perfectly conventional famous composer.

The main event was a concert by the San Francisco-based Kronos Quartet that included a new Riley opus titled ''Conquest of the War Demons.''

Although it was premiered last fall, the piece is still being rehearsed. To judge from the performance, it still needs rehearsal; this is difficult music that involves complex rhythms and long, fast passages played in unison, and the Kronos Quartet - as fine an ensemble as it is - has yet to get the score's subtleties under its collective belt.

Ongoing rehearsals of already premiered new works are not unusual. What's unusual in this case is that the rehearsals, like the one held at Washington University's Edison Theatre the afternoon of Feb. 13, are open to the public. According to the official announcement from W.U., Riley is accompanying the Kronos Quartet on its current tour in order to demonstrate ''the process in which musician and composer collaborate to write a piece of music.'' It's more likely he's making the tour simply to be, as they say, a presence. At the well-publicized, well-attended rehearsal he just sat and listened while the quartet did its woodshedding. And at the concert the next evening, he just took his bows.

Taking bows after others have performed his music is a new activity for Riley.

He was not unproductive in the 20 years that separated his trail-blazing 1964 Minimalist classic ''In C'' from the Kronos-commissioned string quartet called ''Cadenza on the Night Plain.'' But most of what he composed in those two decades was in the form of improvisational music in which he was the sole performer.

Riley was born in 1935 in Colfax, Calif., a small town in the foothills of the Sierra Madre mountains. He studied composition first with Robert Erickson at San Francisco State College and later with Seymour Shifrin and William Denny at the University of California at Berkeley. After earning his master's degree from the latter in 1961, he was for a short time a member of both the San Francisco Tape Music Center and the radically experimental Theatre of Eternal Music founded by his UC classmate La Monte Young. Then he moved to New York, and then to Paris, where he spent two years working in the electronic music studios of French National Radio. In 1964 he returned to San Francisco, and it was there that he created the piece that is guaranteed to keep his name in the music history books.

''In C'' is a remarkable composition. It's remarkable, though, mostly for its concept, because the way it sounds depends more on the attitude performers bring to it than on the content of the music itself.

It's a simple concept: Any number of performers, playing any combination of instruments, address a ''score'' that consists of 53 melodic fragments more or less in the key of C Major; the fragments need to be synchronized only with a common that may or may not be audible; the fragments should be dealt with in the order in which they appear on the page, but a player can repeat any one of them ad libitum before moving on to the next; the performance ends when the last player in the group reaches the final fragment.

The concept is simple, yet the textures and rhythms that result from the overlapping of the patently minimalist materials can be extraordinarily rich. Even in a performance that's only moderately good, ''In C'' is a piece that works. It's intriguing to play; it's intriguing to hear; it's intriguing just to contemplate.

A composition based primarily on a concept, however, is a tough act to follow. In 1967 Riley attempted a sequel, an ''In C''-like piece for voices and instruments titled ''Olson III.'' Then he gave up on the idea. It was as an improvising performer, playing jazz piano in San Francisco's Tenderloin district, that he'd launched his professional musical career, and it was as an itinerant improviser on saxophone and keyboards that he had supported himself during his sojourn in Paris. After the labors of notating ''In C'' and ''Olson III,'' he decided that - for him - improvisation was the only way to go.

In 1965 Riley moved to New York; in 1967 he became a ''creative associate'' at the Center for Creative and Performing Arts at the State University of New York at Buffalo, and at around the same time CBS Masterworks offered to commit to vinyl ''In C'' and anything else he had to offer. But only one other recording followed in the wake of ''In C''; it was a pairing of pieces from 1967 and '68 called ''Poppy Nogood and the Phantom Band'' and ''A Rainbow in Curved Air,'' both of them lengthy improvisations in which Riley solos freely over swirling accompaniments produced by electronic keyboard instruments played through tape-loop systems.

Riley left New York in 1969 and returned - once and for all - to northern California. The next year he was paid a visit by La Monte Young, who brought with him the Indian vocalist Pran Nath. Riley had long been interested in North Indian music; the affinity is evidenced in the modal harmonies and florid melodic patterns that dominate the ''Poppy Nogood''/''Rainbow'' album. But his knowledge of Indian music was limited to what he could understand simply by listening to it. When Pran Nath offered to teach him what Indian music was really all about, Riley jumped at the chance.

Pran Nath's visit to California happened in May of 1970. In September of that year Riley made a pilgrimage to India, where he spent six months living and studying with Nath; he's been back to India a half-dozen times since then, and he still works closely with Nath for extended periods of time whenever Nath is in this country.

During the 1970s Riley severely curtailed his performances in order to practice singing in the Indian style. His intense involvement with Indian music had a profound influence on his compositions.

Two of his recorded works from the '70s (''Descending Moonshine Dervishes,'' on the German Kuckuck label, and ''Shri Camel,'' on CBS) are solo improvisations for electric organs and pianos re-tuned to various North Indian scales. A group of solo pieces from 1980 (released by Kuckuck in 1983 on an album titled ''Songs for the 10 Voices of the Two Prophets'') combines synthesizer improvisations with singing faithful to the Hindustani tradition. His latest solo recording, a two-disc set on the Celestial Harmonies label, is titled ''The Harp of New Albion''; the 11 improvisations on acoustic piano are not specifically Indian in flavor, but their sound is nonetheless exotic, for all of them feature an instrument adjusted to an Oriental variant of the tuning system called ''just intonation.''

In 1971, after his first trip to India, Riley became an associate professor of music at northern California's Mills College. He remained on the faculty until 1980, the year in which he was asked by the members of the Kronos Quartet to write - actually write - something for them.

His response to the Kronos' request was the recycling of music he'd originally conceived for his own solo electric keyboard performances, and the results - ''G-Song'' and ''Sunrise of the Planetary Dream Collector,'' arranged for quartet, synthesizer and voice - were well received when they were premiered in 1981. Over the next several years Riley produced a few works that involved him, the Kronos Quartet and the Indian sitar player Krishna Bhatt. It was not until 1984, however, that he composed - for the Kronos ensemble - a fully notated piece that did not require his participation.

In his 1974 book ''Experimental Music: Cage and Beyond,'' Michael Nyman describes Riley as ''a performer and improviser who composes, rather than a composer who performs.'' Riley is still that, essentially, but today he is also a composer who simply composes.

And it could be that - at least in some of his recent work - this legendary lion of the avant garde is now out of his element.

Some of the sonorities Riley elicits from the string quartet are sumptuous, indeed. And some of his rhythmic ideas - to a certain extent in the works on the Kronos Quartet's Gramavision album that includes ''Cadenza on the Night Plain,'' to a large extent in the new ''Conquest of the War Demons'' - generate the same propulsive power that drives the recorded version of ''In C.'' But none of Riley's thoroughly composed pieces hang together as well as do his improvisations. None of them exploit their instruments in ways that are really interesting. None of them contain so effective an interplay of tension and release; none of them, for this listener, are as exciting.

In the Nyman book, Riley observes:

''Music has to have danger. You have to be right on the precipice . . . not gliding along playing something you know. If you never get on the brink you're never going to learn what excitement you can rise to. You can only rise to great heights by danger, and no great man has ever been safe.''

After last weekend's open rehearsal, Riley said:

''As you get older you tend to want to express natural things in harmonious ways. Hiking in the Sierras, I see natural movement all the time: in the clouds, in the water, in the trees. This play of energy is dynamic, but it's also peaceful. The Indian word for it is 'tantra,' and it's what I'm striving to communicate in all my written-down music.''

Terry Riley looked serene when he said that, just as he looked serene during all the moments he was in the public eye last weekend.