Last July, three leaders of contemporary American music gathered here to judge the Kennedy Center's eighth annual Friedheim Competition for new music -- once a relatively easy task and now a considerable undertaking. There are four remaining contenders, and three winners will be selected this afternoon at the Terrace Theater.

In its early days, Friedheim judges could polish off the entries in a few days. But by 1982, when Gundaris Pone''s terse, atonal orchestral work, "Avanti!," captured first place, the judges had 80 orchestral works to contend with (the prize alternates yearly between orchestral scores and chamber music).

This year, with the focus again chamber music, the judges faced no fewer than 130 entries. During a three-day period in July, the judges sat with headphones glued to their ears in the Kennedy Center library. Then they took home tapes and scores of the 10 semifinalists, and by late August, after a lengthy conference call, the four were chosen.

Rest assured that going through this much new music is no easy task, as I have learned just from studying the tapes and scores submitted by this year's four finalists -- composers Robert Erickson, Stephen Hartke, Donald Martino and Gunther Schuller. The center has been fortunate in getting judges of particular note in the field: Joel Krosnick, a frequent performer on the Washington music scene as cellist of the Juilliard Quartet at the Library of Congress; Joseph Silverstein, the longtime concertmaster of the Boston Symphony, who recently transferred his primary focus to conducting as music director of the Utah Symphony; and Joel Sachs, codirector of the group Continuum and coordinator of contemporary music performance at the Juilliard School. The judges will rate each work separately and compare the results.

Judges of this caliber do not come easily, especially at such modest fees (the budget is tight), but the increasing prestige of the Friedheims seems to have added an extra lure. More and more, the awards -- named after late pianist, composer and teacher Arthur Friedheim -- have become one of the respected indexes of musical trends. And it is this that attracts the large number of applicants, for the prizes themselves are modest: $5,000 for a first, $2,500 for a second and $1,000 for a third.

Krosnick has not only heard, but played, Donald Martino's dense and intricate String Quartet (1983), which was commissioned by the Elizabeth Sprague Coolidge foundation to celebrate the Juilliard Quartet's 20th anniversary as the Library of Congress' quartet-in-residence.

Since performance at the Friedheim by the Juilliard of Martino's quartet would be deemed a conflict of interest, Krosnick recommended that it and the other work for quartet in the finals, Robert Erickson's "Solstice" (1985), be assigned to the Kronos Quartet from San Francisco. It is no mean feat, to put it mildly, to have mastered these two works in a mere two months.

Schuller's "Duologue" (1984) is familiar in Washington as well, having been commissioned by the McKim Fund of the Library of Congress. It is played on the tape by violinist Rafael Druian and pianist Benjamin Pasternack, who will perform it today.

Hartke's "Sonata-Variations" was first played at the University of Southern California and violinist Ronald Copes and pianist Robert Shannon will play it this afternoon.

There has been a tendency in some years for the finalists in the Friedheims to represent a general trend in music -- last year's toward Neo-Romanticism, for instance. That is not the case with these works. If anything, they reflect the increasing diversity of both harmonic and rhythmic language, as well as emotional effect, that is perhaps the healthiest new sign in music.

However, the least conventionally romantic of the pieces, Martino's "Quartet," certainly is not dry-as-dust in the way that much work in its atonal idiom has been in recent decades. On the contrary, it exerts enormous force -- ferocity almost.

Erickson's "Solstice" is a similar merger of unconventional idioms with intense feelings -- another work of considerable power. The nomenclature with which he explains it is a little far out, but do not be put off. It is all very well, as he explains in the notes, that the organizational device is the "hocket," which is described as a device from medieval polyphony. But one doesn't really have to know what a hocket is in order to enjoy the music. Its mood speaks for itself.

The Hartke is a set of 15 variations so romantic in sound that some of it could almost be mistaken for the 19th century -- maybe even Franck in some of its lovely, tender moments. The Schuller, too, is basically tonal, but far more acerbic.

Silverstein, incidentally, is going to special trouble to participate. He had a concert last night in Salt Lake City, and is scheduled to arrive 52 minutes before today's concert begins. He has told Kennedy Center officials not to worry because there is usually a considerable "tail wind" on that flight, but don't count on the concert's starting on time.