Sylvia Fine Kaye was nervous. She had every right to be. The pedigree of figures from the musical theater world surrounding her was awesome.

Richard Rodgers, Alan Jay Lerner, Agnes DeMille, Abe Burrows, Burton Lane, Steven Sondheim - the names went on and on, spanning over half a century of glittering triumph on Broadway. The list might have been complete had Guy Bolton, now 96, been able to make it. Bolton, who created the modern musical shortly before 1920 at the Princess Theater in New York with P.G. Wodehouse and Jerome Kern, missed the occasion only because of his age, his daughter said.

Still, most of the great names in American musical comedy and a fair number of New York celebrities came to the Tavern on the Green in Central Park Tuesday night to honor one of their own.

They came out of curiosity, too. Sylvia Kaye had written and produced a 90-minute special for public television on the history of musical comedy in this country.

The final result of her efforts, to be aired on public television in October, is a look at four representative musicals - "Good News" from the '20s, "Anything Goes" from the '30s, "Oklahoma" from the '40s and "Company" from the '70s.

"This is a triumph for you," DeMille told her.

"Absolutely first class," added Lerner. "This is a pioneering job. No one has ever done this before, and it's important to see the musical in this perspective."

"I hope it works," added Burton Lane, author of "Fiddler on the Roof." "The people who love musical theater the most are often the ones who can least afford it."

Henry and Nancy Kissinger, Lee Radziwill, Pat Kennedy Lawford and the John Lindsays were among the celebrities who came for the show. Kissinger, who claims to have known Kaye for over 10 years, received the ceremonial seat of honor, flanked by Kaye and Radziwill.

"I don't suppose any of this is nostalgic to you," Kaye whispered to Kissinger during the special. "No," he replied, "but I like it anyway.

Kaye is no stranger to such projects. As the wife of Danny Kaye for 39 years, she has written some of his most brilliant musical and comedy material and earned two Academy Award music nominations in the process. She has taught courses on the subject at the University of Southern California and at Yale and, for the past three years, has been determined to enlighten a wider slice of the American public to its joys.

"I'm very, very devoted to the musical theater," she told the audience of 250 Tuesday night. "This is an indigenous art form to this country, and it's important that its history be recorded for the enormous percentage of people who have never seen a Broadway show. The choreographers of tomorrow should see the musical in its glory days.

"The easiest part was the cast," she said. "They floored me. I called Carol Burnett and she said, 'What time do you want me? Everyone loved the idea and they all got a flat $1,000 for doing it."

Led by the indomitable Ethel Merman, the cast includes Burnett, Bernadette Peters, Bobby Van, Sandy Duncan, John Davidson, Rock Hudson, Richard Chamberlain and Agnes DeMille. Who would have guessed that Hudson and Merman would be singing a duet from "Anything Goes" on public television?

Kaye provides the history and the humor in between the fully choreographed numbers selected from the four shows.

Funding for the venture was her biggest obstacle. Eventually, though, the Prudential Insurance Co. agreed to underwrite most of it, and the National Endowment for the Arts and the Corporation for Public Broadcasting contributed as well.

Then Kaye had to obtain the rights to the numbers she planned to use in the show, which was no great problem except that a number of the parties involved are dead. "I had to work through four estates, and lawyers take their time," she explained.

Tuesday's warm reception is no guarantee that the show will sell in Peoria, but the consensus was that if anyone can sell musical comedy to the public on a wide scale, it's Sylvia Kaye.

"Sylvia was one of the few brilliant women who dared to be brilliant when it was difficult for a woman to be brilliant," said Celeste Holmes. "She called the shots for Danny. She gave him the material he needed. How many wives give their husbands exactly what they need?"

The two met back stage in New York in 1939 when both were unknown products of Brooklyn. They married a year later and she provided showcases tailored to his talents which brought him international success over the years.

Her music in "Five Pennies," in which Kaye plays jazz musician Red Nichols won her an Academy Award nomination, as did "The Moon Is Blue." "He couldn't afford me, so he married me," she quipped.

After some hesitation, she decided to tape the show before an audience of 900 people at a theater in California. "We had a choice of live or perfect, and we decided to go live," she explained. "If this is no good, for the first time I'll have no one to blame but me."

The Tavern on the Green assumed the appearance of a television showroom after dinner Tuesday, as some 15 sets mounted around the dining room all flashed on. The 25 tables of guests were spread out like starfish gazing in every direction. Pockets of applause would rise and fall from different parts of the room during numbers that were particular favorites to the different groups.

Everyone applauded loudly for Miss Merman, still clarion-voiced at 72, when she sang "I Get a Kick Out of You" from Cole Porter's "Anything Goes." Agnes DeMille all but stole the show with her candor and wit as she was interviewed by Kaye about her legendary choreography in "Oklahoma." And Kaye herself got a standing ovation when it was all over.

"People in the theater are a tight group," Lerner said. "They don't see each other all that much, but when they do, it's like we saw each other yesterday. We have a language of our own."

"Yeah, so do auto dealers," Abe Burrows added. CAPTION: Picture 1, Lee Radziwill, left, her son Anthony and Sylvia Kaye; by Donal F. Holway; Picture 2, Kitty Carlisle, left, with Nancy and Henry Kissinger; by Donal F. Holway