Students at the University of the District of Columbia are joining the faculty outcry over the firing of 55 UDC professors, a cost-cutting move that the students say will decimate ethnic studies and music programs at the 12,000-student institution.

About 50 students, most of them music majors, assembled in front of the District Building yesterday in a demonstration of support for outgoing faculty as the UDC Jazz Ensemble played to wilting lunchtime passers-by.

Professors teaching jazz and gospel as well as the directors of the school's marching and pep bands have received layoff notices from Acting UDC President Claude A. Ford.

Ten percent of the university's teaching staff is scheduled to be laid off before classes begin Aug. 21, a reduction that university officials have said will save $2 million.

In the history department, the layoffs will affect black and African history programs, reducing the number of faculty members from 12 to 4.

"One of our complaints is that the board never offered the students a forum within which to voice how they feel about the reduction in force," said Katea Sitt, a sophomore voice major. "Faculty members can get another job, but we students are at this university trying to build our careers."

Nonmusic majors also are worried about the impending staff reductions. Thomas Butler, a physics major, said gospel and jazz music are "an integral part of the black community and something started by the black community." About 74 percent of students enrolled at UDC in the 1985-86 school year were black.

UDC spokesman John Britton said yesterday that university officials are continuing to search for alternatives to the layoffs, which have been denounced as unnecessary by the Faculty Association, a union affiliated with the National Education Association.

"The university has the option of declaring that there are certain programs that they can't do without," he said. "They can decide that there are some programs that they must keep."

Even if the trustees do make such exceptions, the union contract still stipulates that such reductions in force be determined by seniority. "Rightly or wrongly, that's what it is," said Britton.

The layoffs planned by Ford will be most keenly felt in the education and liberal arts programs, where enrollments have dropped the most, according to university officials. UDC's enrollment has declined by almost 25 percent in seven years.

Judy Korey, a jazz studies and music theory professor who has been at UDC since 1972, paced the perimeter of yesterday's rally with a layoff notice in her pocketbook and words of enthusiasm for her students on her lips.

Watching as the young musicians swung into a Dizzy Gillespie number, she said: "It's like they're telling a person to lose weight and then they cut out their heart."