Joan Tower's music is a little like her name - i.e., something that seems to be on its way up.

That's true of much of the music itself, whether it be the skyward branching of "Sequoia" (1981), her first major orchestral work, or the vertical thrust of "Silver Ladders" (1986), last heard here in 1990, when the Utah Symphony performed it the same week it won the $150,000 Grawemeyer Award.But it's also true of its reputation, indicated not only by that and other awards but by the growing frequency with which it is being commissioned and performed by American orchestras.

As it happens, the latest of these commissions, her Violin Concerto, will receive its world premiere on next weekend's Utah Symphony concerts, Friday and Saturday, April 24-25, in Symphony Hall. Written for violinist Elmar Oliveira, who will be soloing with the orchestra and music director Joseph Silverstein, it would seem to bear the now-familiar Tower trademarks.

"It's about 18 minutes long," the composer says from her home in Red Hook, N.Y., "in one movement, as usual. I seem to have trouble writing pieces that have multi-movements."

Calling it a "kind of fantasy for violin and orchestra," she says it "tends to explore extremes of feeling," citing "on the one hand a kind of celestial-like tune for violin and strings that just descends, then on the other these very heavy motivic jabbings, or puctuations." Other features include a pair of violin duets within the work - "sort of a tribute to Elmar's brother, also a violinist, who passed away last summer" - and a rhythmic motive in the last section of thepiece that derives from Bartok's "Contrasts."

Commissioned by the Snowbird Institute and the Barlow Foundation at Brigham Young University, the concerto, according to Tower, was turned out in nine months' time between January and December of 1991.

"That's about my usual speed," she says, "about two minutes a month. I'm very slow. That's just one of my problems."

Another, she says, is finding performers willing to take a chance on new pieces, not to mention audiences.

`I think if you look at soloists that come through on most orchestras' subscription series, it's very rarely that you get to hear them play a new piece. Lately that's started to change, thanks to people like Yo-Yo Ma, Manny Ax and Elmar - he's been doing it pretty consistently. But either way the message is a very strong one. If a soloist comes in with a new piece and says, `I want you to hear this,' it sends a very different signal to the audience than if he doesn't. Then he is saying there is something wrong with contemporary music, which reinforces most audiences."

Actually, I inform her, audiences here seemed to like "Silver Ladders," which turned out to be part of one of the best-attended, and most vigorously applauded, programs of the season.

Clearly she's pleased. But she nonetheless recalls a pre-concert lecture she gave some time ago to a group of people about to hear "Sequoia" for the first time.

"I asked, `How many of you are prepared to dislike this piece?' and 98 percent of the hands went up. So my next question was, `How many of you think that's unfair?' and the same hands went up. So it's really not a fair pre-disposition. In fact the biggest compliment I usually get from an audience member is, `I actually liked your piece,' meaning they were surprised. And I had to climb Mt. Everest to get that opinion."

In this instance, however, Tower's Mt. Everest would appear to have had its roots in South America.

Born in 1938, in New Rochelle, N.Y., she spent her growing-up years between 9 and 18 in Bolivia, Chile and Peru, where her father worked as a mining engineer. "It changed my life," she says of the experience. "It took me out of the comfort zone of Westchester County and threw me into the wilds of a new culture, with a new language and everything."

Piano lessons continued, as they had in New York. At the same time, however, her contact with the native population opened up a new world of music as well.

"We went to a lot of festivals," she recalls, "where there was always a lot of music and dancing. I was always playing percussion as a child, so a love of dancing, rhythm and percussion became important to me."

That influence can be heard in a good many of her compositions, including "Amazon" (1977) and "Island Rhythms" (1985). And significantly both "Sequoia" and "Silver Ladders" begin with percussion strokes.

However, the formal die appears to have been cast as early as 1960, when, as an undergraduate at Bennington College, Tower was assigned to write a piece for an orchestra of 13 instruments.

"That was a big piece for me," she confesses, "and I had no idea what I was doing. So I decided to write in the style of `Bolero,' adding one instrument, then two, then three and four. Henry Brant was the conductor, and when he read it through it was mind-boggling to hear. I guess it worked, but I don't really remember it. I don't even have it anymore."

Nevertheless she retained the organic, from-the-root style of composition. "I know some composers can jump from section to section, even start in the middle," she says. "But to me the whole outgrowth and identity of the music moves from left to right, from a beginning to an unfolding, with the music's character unfolding as it goes."

Along those lines, "Sequoia" likewise became something of a turning point for Tower. Having helped found the Da Capo Chamber Players in 1969, she had been composing primarily for that group, as well as playing piano, when the executive director of the American Composers Orchestra approached her with the idea of writing a piece for them.

"I remember saying to him, `I don't think I can do this. I don't think I'm ready,' " she recalls. "And he said, `Oh yes, you are.' " The whole experience, she confesses, "was extremely torturous," in terms of both the writing and the premiere. But the result brought her unprecedented recognition, and ultimately an appointment as composer-in-residence (from 1985 to 1988) with the St. Louis Symphony. The rest, at this point, is what might be called history in the making.

Beyond this week's premiere, she is currently at work on a "Fourth Fanfare for the Uncommon Woman" for Kansas City, a score for Katheryn Posin and the Milwaukee Ballet, and a new piece for the Muir Quartet, to be performed during its Snowbird Chamber Music Festival residency in 1994.

"If you had asked me 10 years ago if this would be happening, I would have told you you needed your head examined," Tower says, adding that she is "very happy with the number of performances I am getting. I think if I had any more I wouldn't have the energy to go back and compose. I just hope it continues."

And that despite the torture she says she still goes through not only in the writing but in the hearing.

"It's like you're bringing something to life for the first time and you're not sure what you have. I'm about to go through this with the Violin Concerto. When you first hear it in rehearsal, it's very painful because the orchestra doesn't know it and the balances and dynamics are all off. So you kind of have to turn that off, and just answer their questions, and be very mechanical about it."

In that context she recalls the premiere of her Concerto for Orchestra in St. Louis last May, at 28 minutes her longest piece to date.

"I remember at the first rehearsal I was by myself listening to it and I almost died," Tower says. "Then at the second rehearsal there were maybe five other people and I died a little less. Then for the third and fourth they had an invited audience and I died even less. Finally by the concert things had gotten better and better, and so had my perception of the piece. It's like the audience was a giant set of ears, improving my perspective."

In short, making it go up, too.

Also on next weekend's program: the Chausson "Poeme" (again with Oliveira as soloist), Haydn's Symphony No. 92 (the "Oxford") and the Sibelius Fifth Symphony.

Starting time is 8 p.m., with Silverstein delivering a pre-concert lecture each evening at 7:15. Tickets are priced from $10 to $30, with student tickets available for $5.

For information call 533-NOTE.