"There will never be a definitive biography of Duke, who was the least definitive of geniuses," writes Derek Jewell in his recently published "Duke: A Portrait of Duke Ellington."

Jewell, who interviewed Ellington - on and off the record - over the course of 11 years, continues: "I don't think anybody will explain the enigma of Ellington - why he worked so hard, why he pushed his private life away so much as he did, why he sacrificed in a way because there was nothing else in his life except music."

That may be true, but Jewell's book, the initial posthumous biography of Ellington, lifts for the first time the private life - his equivocal relationship with his son, Mercer, and the ambiguous relationship with Elvie Ellis Ellington, the woman whose life he shared for 35 years but never married.

Jewell also examines Ellington's close ties to his sister, Ruth, and the sporadic association he had with Fernanda de Castro Monte, a cabaret singer, who traveled as his companion for almost 15 years.

The book also comprehensively chronicles Ellington's musical development from his youth in Washington to his death in New York in 1974 at age 75. Yesterday marked the 78th anniversary of his birth.

Tributes throughout the week have marked the Ellington birthday. Yesterday, radio station WPFW-FM, the local Pacifica outlet, played Ellington music and ran interviews with former Ellington associates and admirers for 24 hours, as part of its listner subscription campaign.

Earlier this week in New York, a group of musicians rode - and performed - on the "A" train, from 125th Street in Harlem to 59th Street in Midtown Manhattan, to publicize a week-long appearance by an Ellington alumni band. The maestro's theme song was "Take the 'A' Train."

In his review of the book, jazz critic Leonard Feather wrote, "For several of us who were close to Ellington the temptation to write a biography was hard to resist." He resisted because he knew that if he recounted certain personal incidents concerning Ellington, the maestro would add his name (Feather's) to the Ellington mental list of nonpersons.

Jewell, who writes popular music criticism for The London Sunday Times "for therapy" and otherwise is a publishing director for several divisions of the newspaper company, says that true to the legend "he (Ellington) had plenty of girl friends. Women were very attractive to him and he was very attractive to women. He was 6 feet 1 and about 185 pounds, give or take a few, and enormously charming."

Ellington's youthful marriage broke up after a few years, but he never divorced his wife. In 1939, he started his long relationship with Beatrice Ellis, who was known as Evie Ellington. Though they never married, she made a home for him in a Harlem apartment and was always at his beck and call.

However, Jewell paints a picture of a lonely, embittered woman, who rarely appeared with Ellington in public. When Richard Nixon gave the birthday salute to the maestro in 1969, Ruth Ellington stood by her brother's side. Evie sat alone in her Harlem apartment.

Ellington's companion in the '60s and '70s was Fernanda de Castro Monte, described by Jewell as "a tall, arrogantly striking blond of great sophistication whom he (Ellington) always introduced as 'Countess.' She was imperious - a handsome woman rather than beautiful. She acted like a countess."

She spoke five languages, was conversant with art and had gourmet tastes.

Ellington's private life both inside and outside his family was closely guarded, says Jewell. But many people knew of the way he lavished gifts on his sister, Ruth, or had an uneasy relationship with his son, Mercer.

In examining the uncertain relationship between Duke and dedicated to maintaining a youthful image and didn't know how to handle having a handsome but older-looking son.

Mercer also was a member of the Ellington orchestra and served as band manager for 10 years. He played trumpet but never took a solo, always functioning as an ensemble - a team - player. Some say that Duke never introduced Mercer on the bandstand.

Jewell says Duke could never decide whether Mercer should be in the music business and he compared with his father or build an independent career in electrical engineering.

Even after writing the book, Jewell concedes that he still finds Ellington the side of Ellington "that would have told me why he did all these things."

Jewell, 49, who first heard Ellington's music as a student at Oxford in 1945, says, "I don't think it's definitive, but it says more than any other book on Ellington - because they've been no attempts to write a true biography. There are many things that are missing.

"You can't totally explain why he was so obsessed with work. I think there are one or two clues. He was a very religious man. I think he thought he was genuinely put on this earth to create."