PERFORMING ARTS : Have Baton, Will Travel : Far, that is. The very up and coming, very peripatetic Robert Spano has a repertoire that covers the world’s music--and a style that’s all-American.

Robert Spano is on the phone from Stockhausen country. That is, the young conductor is talking from his hotel room in Amsterdam, where two weeks before traveling to Los Angeles to conduct Rimsky and Rachmaninoff at the Hollywood Bowl, he is about to appear in one of the most acrobatic three-ring circus acts in music.

Spano and conductors Oliver Knussen and Reinbert de Leeuw are at work on Karlheinz Stockhausen’s “Gruppen.” Each of them is responsible for one of three orchestras that will be positioned on different sides of the Concertgebouw, Amsterdam’s premier concert hall. The music is ferociously complex and intricate, and the orchestras must be coordinated with a mathematical accuracy that would strain even an updated Pentium chip.

How, then, to move, without missing a step, from one of the most gorgeous-sounding concert halls and a unique surround-sound symphonic experience to the generalized, amplified expanse of the Bowl? How to go from Stockhausen’s Space Age modernism to the lush Orientalism of “Scheherazade” on Tuesday night, and the ripe sentiments of Rachmaninoff’s Second Symphony on Thursday?

“I guess at some level I feel that all this music has more in common than it might seem on the surface,” Spano says, almost as if trying to reassure himself. “And I try to be in touch with the specific nature of each piece. But, yes, I do have to adjust my values. Each kind of music requires something else of me.”

As an up-and-coming conductor, Spano does this kind of thing all the time. For most of the last couple of years, he has been on the road, juggling vastly different types of engagements. He might be found one week conducting Francesca Zambello’s postmodern production of Britten’s “Billy Budd” at Covent Garden and the next leading Brahms in the Midwest. On his way from Stockhausen in Amsterdam to Rimsky in Los Angeles, he will detour to Cardiff, Wales, for a meeting about a new production of “Carmen” he is to conduct with the Welsh National Opera in the coming season.

“It’s a taxing life,” Spano acknowledges, “and it can be very tiring. But I love how stimulating it also can be.”

I ndeed, Spano’s peripatetic life has been full of stimulation. As his globetrotting attests, he is much in demand for both symphonic and operatic work. And, at 33, he has also won the Big Prize for young conductors: an orchestra of his own. Next year, Spano will take over the venturesome Brooklyn Philharmonic at the Brooklyn Academy of Music.

Spano made a name for himself as a fast-rising conductor right from the start. His professional conducting debut was four years ago, as a 29-year-old assistant conductor at the Boston Symphony. And in his review, Boston Globe music critic Richard Dyer noted that the orchestra seemed as enthusiastic about Spano as the audience and that the audience gave him a standing ovation. Though he didn’t want to jump to conclusions, Dyer nevertheless wrote: “It isn’t rash to point out the truth, which is that Spano’s concert could hold its own with any in the season, and it was demonstrably superior to the efforts of a half a dozen guest conductors over the last couple of years.”

For all his globe-trotting ways, Spano is essentially an all-American boy. For one thing, amid his eclectic repertory, he has become known as something of a champion of U.S. composers--Carter, Barber, Copland, Gershwin, Rorem, Thomson, Druckman, Schwantner, McPhee, Schuller, Torke and Fine all dot his programs next season.

And then there’s his style. He has an American’s fearlessness (nearly half the works he conducts each season are firsts for him) and an all-American sunny disposition.

Both of these qualities are evident to anyone who has seen him work. For instance, two summers ago, while rehearsing the Stockhausen feat in Tanglewood in Massachusetts, again with Knussen and De Leeuw, Spano seemed untroubled by either the appallingly sticky weather in the outdoor concert hall or an impossible counting task.

Keeping one eye on Knussen’s coordinating beat, a second on his orchestra of worried students and still watching the score (no one memorizes Stockhausen), he would, when the music got overwhelming, simply display a marvelous grin. When things fell apart, as they inevitably did, he broke the tension with an uproarious laugh, and carried the musicians right along with him.

Spano comes by his all-American-ness honestly. Of Italian heritage, he was born in Conneaut, Ohio, and grew up in Elkhart, Ind., in the heart of band country.His father is a clarinetist in the Elkhart Symphony, which was the first orchestra Spano ever conducted, at age 14.

At the time, he was a budding composer who had won a composition prize and was invited to conduct his score himself. “My high school violin teacher taught me the beat pattern,” Spano recalls, “and I read through it [with the orchestra] without stopping.”

Not only did he not stop, but he was so thrilled with the experience that he thought there would be no need for further rehearsal. “It was a kind of drug, I think,” he acknowledges. “The podium is a great place to listen to an orchestra.” Spano was, in fact, hooked.

He indulged the addiction almost immediately. By the time he was 16, he had formed his own string orchestra of friends, on whom he experimented, learning the basics of conducting. Later he continued his studies at Oberlin and the Curtis Institute, eventually dropping composing altogether to concentrate on the baton. His first job after school was teaching, at Bowling Green University in Ohio, but it wasn’t long before he made the move to Boston, to be Seiji Ozawa’s assistant at the BSO.

In the two years since leaving the Boston Symphony post, Spano hasn’t always had a home address. He has led the Cleveland Orchestra, the Sydney Symphony in Australia, the New Japan Philharmonic and, debuting in 1993, the Los Angeles Philharmonic. He summers in Tanglewood, where he teaches student conductors, leads the impressive student orchestra and guests with the Boston Symphony. At Oberlin, he heads the opera program, and his operatic invitations--such as the one Covent Garden extended for “Billy Budd”--have become increasingly prestigious.

Some of this furious activity may subside next year, when Spano takes over at the Brooklyn Philharmonic. But although the job probably means he will settle down a bit more geographically, Spano has no plans to settled down musically.

And that would seem to make him a good fit in Brooklyn. The high-profile symphony participates in BAM’s annual avant-garde extravaganza, the Next Wave Festival, and it’s known for thematic programs that often include a full weekend of concerts, lectures, demonstrations and panels on one composer or a musical theme.

This season, for example, Spano will give Brooklyn a preview of his style when he leads the orchestra’s weekend devoted to Orientalism. The plan, he says, is to investigate just how Rimsky’s magical Baghdad of “Scheherazade” might fit in with Ravel and the Balinese-inspired American composer Colin McPhee.

For Spano, such connections are the point.

“The definition of American musical culture is the mix,” he explains from Amsterdam, where, he says, that city’s ethnic diversity makes him feel right at home. “It is our history, and it is how music developed in our society. Once, don’t forget, our orchestras were primarily German or French or Russian. Our country was the beginning of a global culture.”

In the same way, Spano has no intention of choosing between his work in the opera pit and on the concert stage.

“I think it’s a trap these days to do only one or the other,” he contends. “I’ve gotten so much from each. I love being in the pit and working with singers. I love much of the repertoire. I love the theater. I love collaborating with directors. And I don’t want my work to be without opera. I’ve found that the understanding of the music and, particularly, an awareness of its theatrical sense is highly appropriate to the concert music I conduct.”

And his concertizing will also remain as eclectic as ever.

“I don’t feel like a specialist,” Spano says. “And while I try very hard to get American works played, I also conduct a lot of Sibelius and Tchaikovsky and Mozart. I guess I’m running the gamut, and I intend to be. . . . I’m attracted to a lot of music, and I’m loathe at this stage to repeat myself too much.”

ROBERT SPANO, conductor, with the Los Angeles Philharmonic, Hollywood Bowl, 2301 N. Highland Ave. Dates: Tuesday, 8:30 p.m., with Jean-Yves Thibaudet, piano; Thursday, 8:30 p.m., with Ronald Leonard, cello. Prices: $1-$72 Phone: (213) 480-3232.