The first Friedheim Competition in 1978 attracted only 54 applicants, not a throng, but not bad either for a brand new award recognizing orchestral works by American composers.

This afternoon at the Terrace Theater, the Friedheim celebrates its 10th anniversary by dividing $9,000 in prize money among four finalists drawn from a qualifying field of 174. String quartets by Gun ther Schuller and Steven Mackey and chamber pieces for strings, woodwinds and percussion by Tod Machover and Barbara Kolb (her entry features computer tape) will be performed free to the public. The judges are cellist Bonnie Hampton and pianists Michael Boriskin and Dina Koston, codirector of the Kennedy Center Theater Chamber Players.

Competition founder and funder Eric Friedheim can look proudly on an event that, aside from its national standing, has helped bolster Washington's arts image. He established the award to perpetuate the memory of his father, Arthur Friedheim, a renowned pianist, Liszt student and leading Liszt interpreter. Eric Friedheim shares his father's Romantic taste. Yet because he is not a musician, he practices a hands-off brand of philanthropy, leaving all major artistic decisions to the experts.

What Friedheim knows best is publishing and the travel industry. He began as a local reporter here with the International News Service during the Hoover administration. "I covered everything from the Washington Senators baseball team to the senators on Capitol Hill," he recalls.

Friedheim was at Griffith Stadium, pad in hand, when the Redskins arrived in 1937, and at the White House on the day of the Pearl Harbor attack. It took a business opportunity, he says, to lure him away. "I finally achieved the ambition of all reporters -- to own his own publication."

He bought the New York-based trade magazine Travel Agent, serving as editor and publisher for many years before selling to Capital Cities/ABC. Now, in the capacity of chairman, he writes editorials and covers travel conventions for the magazine. He also owns the Palm Beach Social Pictorial, whose domain is society balls, concerts and theater.

Given his background, it's not surprising Friedheim originally intended the prize to honor music journalism. New York Times critic Harold C. Schonberg thought little of the idea, but passed it along to Irving Lowens of The Washington Star, who in turn contacted Martin Feinstein, then executive director of performing arts at the Kennedy Center. Feinstein agreed with Schonberg, and suggested instead a competition for American composers that would alternate annually between orchestral and chamber music. All works surviving the last cut would be played at a free concert, after which the judges would determine the winner.

This year's finalists represent a healthy cross section of styles. Schuller's String Quartet No. 3 made its Washington debut last spring, courtesy of the Emerson String Quartet. This three-movement work evolves from a 12-tone rowthe composer swears is magic, since, as he says, it spans "the whole range from triadic tonal music to the most chromatic."

Skeptics with the false notion that 12-tone automatically means harsh and impersonal need only consult the slow movement -- a lyric aria for first violin -- to hear what he means. Following the lead ofGeorge Perle, Schuller has broadened the technique to achieve, in his words, a "high individuality of language."

This little row has seemed so nearly inexhaustible he has used it for his last 15 pieces. While sketching the Third Quartet's finale, he learned that the row is "Beethoven-friendly." Violinist Louis Krasner, to whom the work is dedicated, lent Schuller a copy of a rare Beethoven manuscript containing a little G minor canon he had sketched for a female visitor. Schuller describes his revelation as if it were a brush with immortality.

"When I actually sat down to think about incorporating it, I realized -- with a flash -- that the first seven notes of Beethoven's theme are identical with the first seven notes of my row. It was like Beethoven reaching out to me, or me reaching out to him, across a 200-year span."

"Nature's Breath" by Tod Machover alludes to the repose and pastoral imagery of French country life. Cellist-composer-computer specialist Machover was a resident at IRCAM (L'Institut de Recherche et Coordination Acoustique/Musique) in Paris between 1978 and 1984. Afterward, while on a sabbatical in Burgundy, he completed this work, commissioned by the Serge Koussevitzky Foundation of the Library of Congress.

The change of scenery from a cloistered, high-tech computer environment to the wide open spaces comes out in his score. Through the course of three uninterrupted movements, a slowly unfurling melodic strand confronts and becomes absorbed by shifting harmonic relationships and timbral combinations. Machover's pacing is calm and assured. Despite a few brief references to traditional chords, the piece remains tonally ambiguous. Yet the fresh textures conjure strong visual images, in a manner not far removed from Copland and Debussy. "Nature's Breath" has already been recorded by Bridge, and the label's president, David Starobin, will conduct it this afternoon.

Barbara Kolb, perhaps inconsistent with her composition's Italian title, devised the computer sounds for "Millefoglie" several years ago during her stay at IRCAM, where she had been invited under the auspices of Pierre Boulez. "Millefoglie" translates literally to "a thousand leaves." (Gourmands may better recognize the French cognate, mille-feuille, a rich layered dessert more commonly known here as a napoleon.) Kolb varies this to read "many layers," referring to how she superimposed harmonies and rhythmic patterns -- vertical and horizontal ingredients -- so they interact to produce bracing, dynamic sonorities.

The computer tones form an important layer both as a separate voice and as a well-integrated complement to the other instruments. Kolb, a clarinetist, assigned some of the toughest passages to the winds, particularly the oboe. The marimba and vibraphone parts also are complex. "Millefoglie," she claims, is not typical of her other, mostly chamber-sized works. This is her first involving the computer, and she insists, "It's without a doubt the most complicated piece I've ever written, and I don't intend to write music this complicated ever again."

Steven Mackey's "Fumeux Fume," premiered last March by the Concord String Quartet in nearby Columbia, occupies a different world. The composer develops musical images much like a skilled photographer adjusts his shutter setting. He selects elusive, soft-focus kinds of sounds; bright, flashing overexposures; strange, bleeding double exposures. For him, Part I is the presentation, Part II the reexamination from a different perspective.

"The first movement was like I was on a tour bus and I drove by really interesting things. But because of the nature of the tour and my obligations, I had to keep moving. After I finished the tour, I put on my backpack, grabbed my bicycle and went back and explored some of the things I had passed along the way."

Mackey, 31, is one of the youngest Friedheim finalists ever. Certainly he is the only one with lute as a primary instrument. "Fumeux Fume," named for a 14th-century rondeau (a poetic and musical form), is loaded with string-generated plosives and diphthongs, hurdy-gurdy sounds and strange resonances, as well as quick flashbacks to medieval polyphony. Contrast and continuity exist simultaneously. "Similarity doesn't give you unity," he maintains. "Interdependency brings unity."

By some quirk of fate, all four composers have some connection, even if only coincidental. Gunther Schuller taught Barbara Kolb at Tanglewood; his music publisher is the same as Mackey's. Kolb and Tod Machover were at IRCAM at the same time; Machover, an IRCAM mainstay well known for his computer works, has submitted one without a computer part, while Kolb advances to the finals with her first computer composition. Schuller must miss the presentation today to be in Pittsburgh to conduct the premiere of a two-act jazz-age ballet named "Gatsby." His assistant, Tibor Pusztai, will be excused so he can conduct Kolb's "Millefoglie." Steven Mackey's "Square Holes, Round Pegs" likewise receives its premiere today, but in Boston by the Boston Pro Arte Chamber Orchestra. He'll be here.