"Duke Ellington: Reminiscing in Tempo," a 90-minute documentary to be presented at 8 tonight on Channel 13 as part of the "American Experience" series, tries to get beyond the music to the private man and then make the connections. It's not easy; the very public performer was extremely reticent about his private life. But the producer and director Robert S. Levi, who also wrote the script with Geoffrey C. Ward, the principal writer of "The Civil War," impressively succeeds in marshaling the available facts and avoiding pointless speculation. This biography, something of a musical suite itself, runs until 10 P.M., with pledge-week breaks.

Unlike many other jazz greats of this century, Edward Kennedy Ellington, born in Washington on April 29, 1899, did not grow up impoverished. His father was a coachman and butler who sometimes worked at the White House. His mother, Daisy, considered her son blessed. From the moment he was born, the narrator Julian Bond tells us, Edward was told he could do anything he put his mind to. Standing on his stoop, the story goes, the boy would shout, "I am Edward the noble duke, and people will come running to me!" They certainly would.

By the time he moved to New York in 1923, Ellington was married and already showing some entrepreneurial skill in the music world. The composer Gunther Schuller recalls how the young man basically worked with three notes, "but he had a genius for picking the right three notes."

Ellington and his sextet, called the Washingtonians, were spotted by Irving Mills, who said he remembered thinking, "This is the band I want to build up to the best black band in the country." Mr. Mills would become his manager and publisher, often taking partial credit and 50 percent royalties for songs Ellington had composed alone. They would have an eventual falling out.

But their association led to Ellington's securing a job at the Cotton Club in Harlem, where the mobster owners insisted that the customers, most of whom were white, be entertained each evening with at least one "jungle music" production number. Ellington stayed five years, using a radio show from the club to build his reputation. By 1931, he had a 16-piece orchestra featuring the most sophisticated soloists in the business. He began extending the form of jazz. His "Creole" Rhapsody ran for six minutes, which at the time was considered extremely long. With recordings, tours and movie appearances, he would come to preside over what many critics consider the greatest big band in history.

His public image was impeccably elegant. Here was tall, dark and handsome with a vengeance, complete with a reputation for appreciating good food and beautiful women. And also, evidently, for discretion. His wife, Edna, walked out on him in the 1920's, but he never officially divorced her. Marian Logan, wife of Dr. Arthur Logan, Ellington's closest friend, says on the program: "Edward had lots of lady friends, all of whom made the one fatal mistake of believing they were the one." In fact, the most important woman in his life seemed to have been his mother. When she died in 1935, Ellington did not write anything of significance for the next two or three years, said Mercer Ellington, his son.

Covering all phases of the Ellington career, through the hard times in the 1950's when the band had to play the Aquacade in New York for survival, his subsequent triumph at the Newport Jazz Festival and on to his final "Sacred Concerts," this documentary is crammed with music clips that include such classics as "Take the A Train," "Mood Indigo" and "Sophisticated Lady" (inspired by some Washington schoolteachers). Mentioned, but not explored in depth, are Ellington's intensely close friendships with Dr. Logan, who soothed his hypochondria, and Billy Strayhorn, the arranging genius and longtime collaborator.

In the end, we are left simply with the musician, the man who couldn't walk past a piano without giving in to what he called its flirtations, the band leader who could get his players to give their very best. The musical ideas? "Oh, man," Ellington tells an interviewer, "I got a million dreams. That's all I do is dream, all the time." Fortunately for the rest of us. The American Experience Duke Ellington: Reminiscing in Tempo Produced and directed by Robert S. Levi; written by Geoffrey C. Ward and Mr. Levi; edited by Ken Eluto; narrated by Julian Bond; Margaret Drain, senior producer; Judy Crichton, executive producer. At 8 tonight on Channel 13.

Photo: Duke Ellington, who is profiled on "The American Experience." (Josephine Mangiaracina/Sony Music)