Like the title of one of his most enduring songs, George Gershwin (1898-1937) had rhythm. Also fame, money, women and a genius for melody. But according to Joan Peyser's controversial new biography, The Memory of All That, Gershwin, a perennial bachelor, also had parents (and music critics) he struggled in vain to please—and an illegitimate son he supported but never acknowledged. That ostensible son, a shy, impecunious 67-year-old who calls himself Alan Gershwin (and who says he has written 1,250 songs, of which 12 have been published), lives in mid-town Manhattan in a studio apartment and is reported to be preparing a legal claim against the family-controlled Gershwin estate, valued at no less than $50 million. He refused to be interviewed for this article, though he has talked to Peyser, 61, former editor of "The Musical Quarterly and author of a best-selling 1987 biography of Leonard Bernstein. She discussed her new book with writer Joanne Kaufman.

What attracted you to George Gershwin as a subject?

You can't be a musician in the U.S. without having Gershwin's music in your blood. He had an absolute genius for melody—writing a song came as naturally to him as breathing. And he wrote some of his most lovely songs, including "They Can't take That Away from Me" and "Love Is Here to Stay," at the end of his brief life, when he was in constant pain. But he did not have a commensurate command of the English language to express himself—he did not, for instance, keep a journal or write revealing letters—and so he was a mysterious figure too.

What kind of relationship did George hare with his son?

George would occasionally send a limousine to Brooklyn to pick up Alan, and then he'd take him to shows and parties. "Alan Gershwin" is a name he adopted in his teens. He was raised as Albert Schneider by Fanny and Ben Schneider, the sister and brother-in-law of his mother, Mollie Charleston, a showgirl Gershwin saw on and off for a number of years. On their visits in the '30s, George and Alan would compose 16-bar pieces together. But all the time Alan was with his father—and Alan was 11 when George died—George never said, "Listen, you're my son." In fact, when they went out. George identified him as "the child of a friend." Meanwhile, Alan told me he always knew he was George's son because Fanny and Ben kept reminding him of the fact. And Alan says he was terrified as a child because the drivers who picked him up used to threaten him never to tell anyone about his visits to George or "you won't live a healthy life."

Michael Sukin, an attorney for the Gershwin family, says. "No research has ever turned up anything to support what Schneider says." How can yon be so sure about the relationship when there's no documentation?

In the first place, the people challenging my book are all intimately connected with the Gershwin family's interests and are not impartial. Secondly, I spent 15 months researching the matter before I was fully convinced. The first positive confirmation came from Gershwin's longtime valet, Paul Mueller. I took Alan to see Mueller at his home in Manassas, Va., and he told me he remembered Alan as a child coming to visit with his mother. Eventually, I also found Fanny and Ben Schneider's son, Murray, who grew up in the household along with Alan. Murray recalled limos coming to pick Alan up to take him to see George. Then, Alan himself told me that after George died, Oscar Levant took him to see George's mother, Rose, in an apartment on West 72nd Street in Manhattan. No book or article has ever mentioned Rose living at that address, but when I checked various documents in Surrogate Court, I found out that indeed she had lived there at the time Alan specified. All those things together convinced me Alan was telling the truth.

How might your book change people's concept of Gershwin the man?

The conventional picture of George's life and career is that they were nothing but successful. He did have a string of successful shows in the '20s and was hailed for Rhapsody in Blue in 1924. But in the '30s classical music critics carped about his lack of compositional technique; they saw him as a Tin Pan Alley Jew trying to push his way into their rarefied world. Because of all the belittling he'd endured as a child, Gershwin's confidence was thin. To friends who criticized his music, he would often say, "Maybe you're right."

What did Gershwin's parents do to undermine his confidence?

As a child, George fought and played hooky. So his father, Morris, who ran Turkish baths and restaurants in New York City, used to tell him he would be nothing but a bum. Meanwhile his older brother, Ira, who later became his permanent lyricist, was the good boy who did well in school, didn't run after girls and went on to college. Not that Rose was much warmer to Ira than she was to George. She was a cold and distant woman for whom nothing was good enough. Even at the height of George's success, Rose wanted to know why he couldn't write hits like those of the songwriting team of DeSylva, Brown and Henderson ["The Best Things in Life Are Free"].

George and Ira did make beautiful music together, but you suggest their relationship was not harmonious.

When George was at the height of his career, he was arrogant and demanding. At the end of his life—when he was living with Ira and his wife, Leonore, and was so sick—Ira moved him into a friend's vacant house with a male nurse and kept George's valet, Mueller, behind. The very day after George died, Ira filed papers in Surrogate Court in Los Angeles to gain control of his brother's money. But four days later, George's mother filed in New York City opposing Ira and gained control herself.

When George started developing strange symptoms as a result of the tumor that eventually killed him, why didn't anyone insist he go to a neurosurgeon?

There were friends who suggested he see a neurosurgeon, but the Gershwin family accepted the diagnosis of George's psychoanalyst that all his complaints—smelling burning garbage when there was none, intense headaches, dizziness—were signs of neurotic depression. After George went into a coma on July 9, 1937, and was rushed into surgery, doctors found that one side of his brain was so enlarged by a tumor that it had crushed the other side. He died on the operating table on July 11. He was 38. The diagnosis reported to the public was that the tumor had been fast-growing and inoperable. But I obtained photos of slides of the tumor, which I showed to two neurosurgeons. Their conclusion: If it had been excised even one month earlier, it would probably never have recurred, and George could well have lived a normal life span.