WHAT IS A FAMILY?" asks Burton Bernstein.

"Why is it so damn important to every one of us? Is it a curse or a blessing or both?" Rhetorical questions maybe, but interesting ones; questions which form the backbone of world literature and the core of social science. They are painful questions to confront, extremely difficult to answer well. While they provide the writer with wonderful material with which every reader can identify, they can also be an invitation to journey through an endless hall of mirrors. How does one objectify one's family? Can one write what one honestly feels, particularly if family members are living? What are the writer's obligations to what he perceives as truth? To the form he has chosen? To the privacy of the people he is writing about?

Fiction has always been replete with barely-disguised portraits of mothers, fathers, husbands and wives; and many readers often spend more time examining the autobiographical sources of a work than the work itself. But recently--spurred perhaps by a fascination with psychology, genealogy and that peculiarly American belief in "sharing" experiences of all kinds--American writers have not been bothering to fictionalize. Each year there is more nonfiction probing the intricacies of family history--a kind of public, artistic counterpart to our conversations with friends or sessions in a psychotherapist's office. Cruelty to children, incest, mental and physical illness, biculturalism or corruption are the ostensible themes of these family memoirs but underlying them are the more urgent personal questions: who were my parents? How did they get the way they were? And how do I stand in relation to them?

Family Matters, originally published in The New Yorker, is about a family of more than casual interest. Samuel and Jennie Bernstein were two of the well over 1 million Russian Jews who emigrated to the United States between 1880 and 1910, and their three children --Leonard, Shirley and Burton--each became involved with major institutions of American culture.

Samuel was born in 1892 and raised in the tradition of the rabbi/scholar in the shtetl of Beresdiv. He rebelled against his family, ran off to America where he built up the Samuel Bernstein Hair Company of Boston, and was honored on the occasion of his 70th birthday by such officials as the attorney general of Massachusetts. Charna Resnick, who like I. B. Singer's Yentl, was so bright and curious that she studied Torah with the boys, was renamed Jennie by a clerk at Ellis Island. She quit school to become a factory hand at 14, was married four years later, and became the proverbial Jewish mother.

Sam and Jennie expected their three children to grow up in a conventional manner, marry well, and continue the family business. Instead, their eldest son Leonard-- arguably the most famous American musician in the world--refused any part of the beauty business, married a Chilean actress who was raised a Catholic and became a jet-setting conductor/composer/pianist. Their daughter Shirley rebelled against the notion of repeating her mother's experience, refused both the beauty business and a married life, and became a producer (of, among other things, the quiz show The $64,000 Question which was found to be rigged nearly 25 years ago). Their son Burton, who reveals very little of himself, did not want the beauty business either and became a staff writer at The New Yorker.

Wonderful material: great characters; deep-seated conflicts playd out against the backdrop of the New York Philharmonic, the fledgling television networks, the country's most discreet and discriminating magazine; the clash between the closed, religion-bound world of the parents and the secular, seemingly boundless world of the children. The trouble is that the extraordinary personalities in this family never come alive and any sense of their interaction remains largely dependent on the reader's imagination rather than on the writer's skill.

Rather than trying to select significant events and dramatize them, Bernstein has chosen to string together anecdotes and interviews. "I identified with Mama to the point where I vowed that I wouldn't live her life over again," he quotes his sister. "I know Daddy really loved me but he showed affection with great difficulty." So much for Shirley and her parents. He treats the relationship between his father and older brother with kid gloves and a gentle nostalgia when in fact (as Leonard Bernstein has described often and at length) their struggle over the future conductor's musical ambitions was violent, embittered and long-lasting. Perhaps because Burton is the youngest child (born when Lenny was already 13) his version of the family romance is suspiciously rosy and polished, as though what he sees is really what he has been told in story form by the grown- ups. His reportage on Russian-Jewish life is solid. His prose is fluent, circumspect and graceful but how accurate? How alive? There are probably dozens of very good books that could be written about the Bernstein family. Sketches for some of them are scattered through the pages of Family Matters. But Burton Bernstein, it seems to me, has chosen not to disappoint his family and, in so doing, has let his reader down.