EUNICE BROWN didn't write her first piece of music until 1975, but she managed to take it pretty far: "The Bicentennial Waltz" was first performed by the Peter Duchin Orchestra at the National Symphony Ball as President Ford twirled around the dance floor, with many other notables.

The waltz also was featured at society balls and entered into the Congressional Record (which, unfortunately, can't be played). Eventually, a recording did find its way into a four-foot steel time capsule at the Kennedy Center. The capsule -- which also contains theatrical playbills, clippings, musical scores, tapes and a weather forecast for January 2076 -- is in the center's basement, marked by a bronze plaque admonishing Washingtonians not to open it until a century has passed.

"I'm not a great musician, please understand that," Brown insists. "This is a fun thing to do at this stage in my life. The ideas come and I put them down. I've just been lucky."

Brown, who now lives in Palm Beach, Fla., after spending eight years in Washington where she had been active in supporting the National Symphony, had wanted to contribute something to the upcoming bicentennial celebration. One night, she had trouble sleeping and went to her piano. In the morning, she had the beginnings of "The Bicentennial Waltz."

"I felt that you should dance at a birthday party and that we'd had enough marching," she says. "I couldn't write a gavotte so I had to write a waltz. It was just a thought, an idea." But it was one that she sketched out and had a friend put on tape. Brown then took the tape to a couple of symphony players and "asked if it sounded familiar, if they had ever heard the music before or if it was new. They said they'd never heard it and that I ought to do some copyrighting right away. And I did." She sent the tape off to Duchin, who inserted an orchestrated version into his concert program. Brown says that "when I looked around and saw all those people dancing to it, I couldn't believe it."

One thing led to another -- television interviews, performances elsewhere, a recording by the National Symphony String Quartet accompanying Myra Merrick, now with the Metropolitan Opera. There was also a meeting with Queen Elizabeth during her visit to America; the monarch had specifically requested a performance after hearing a tape sent to Buckinhgham Palace.

In 1977, Brown moved to Florida with her husband, Russell, a lawyer. She has continued to write, mostly waltzes, with at least one other composition also receiving attention. In 1979, she created "Song of Peace" inspired by the Camp David accords between Israel and Egypt; Brown had written out a rough lead sheet the very night the agreement was signed. "My feeling was, my goodness, if people can't speak it [peace], they might as well sing it."

The next day, Brown, who sells real estate in Palm Beach, was showing an apartment in her own building to Dr. Benjamin Suchoff. "I thought he was a medical doctor. He asked me if a baby grand piano could fit in the apartment, so I invited him upstairs to see how ours fit in. When he sat down to play, I thought, my goodness, how does a doctor get off playing that way?"

It turned out that Suchoff was a musicologist and director of the Bela Bartok Foundation. "He saw the lead sheet, played it and loved it, said, 'I'd love to do a choral arrangement and try and get it published for you.' I said, 'If you do that, you own half of it.' And he did. We worked on it together because we had to change it a little to make it more of a folk-type song." The four-part chorale has been performed several times, notably at a disarmament conference: Copies were sent to Eqyptian Prime Minister Anwar Sadat and Israeli Prime Minister Begin, who both returned notes of appreciation.

Brown is now working on a piece that will celebrate the 350th anniversary of Maryland, which comes up in 1984; the song will emphasize Maryland's being the first state in America to establish religious freedom (the transplanted Rhode Islander points out that way back then, her own home state was tolerant mostly of Puritans). Sample lyrics: "Peace and comfort you'll command/When you live in Maryland/Who burst the chains of all oppressed/to worship free with liberty."

Brown is also retitling and writing new lyrics for "The Bicentennial Waltz," which shows her practical side. The new name, "The Great American Waltz," is guaranteed to get it played more than once every 200 years.