The book ends, really, at the story's beginning; after 315 pages (which are followed by another 30 pages of excellent notes), Sergei Prokofiev, 17, has received his diploma as a "Free Artist" from the St. Petersburg Conservatory (with a B in composition) and is trying to get his music performed.

Still in the future are the "Classical Symphony," "Alexander Nevsky," the great concertos, sonatas and quartets, the magnificent ballet music-in short, the only reasons anyone would want to read his autobiography.

Also in the future are the Russian revolution, the years of exile, the painful return and the trials of being an artist under Stalin.

The English edition of these memoirs would have been more accurate if it had retained Prokofiev's Russian title: "Notes From Childhood."

Not that a publication of Prokofiev's "Notes From Childhood" is a bad idea; Prokofiev was a child prodigy (he entered the conservatory at 13 bringing with him the manuscripts of four operas, several piano works and a symphony) and like that other prodigy, Mozart, his early years are unusually well documented.

Curiously, Prokofiev developed his taste for Mozart rather late in his precocious life. "My antipaty was so well defined," he remarks, "that when someone began to praise him I would exclaim, 'How can you like Mozart!'"

Letters from both Prokofiev and Mozart illuminate their early years away from home. Mozart went off on barnstorming musical tours of Europe with his father and wrote childishly exuberant messages (full of incongruously shrewd musical judgments) to his mother and his beloved sister Nannearl. Prokofiev's letters to his father (his mother went to live with him in the city that is now Leningrad) are more sober (his father was a more serious, dignified person than Mozart's sister) but minutely informative, including even a diagram of the room where he took his entrance examination for the conservatory.

Prokofiev's father, a college-trained agronomist pioneering scientific farming pricniples on a large Ukrainian estate, was affluent enough an expert tutor (the composer Giliere) for the summer months after it became apparent that little Sergei's talent was out of the ordinary. Some of the brightest, most charming pages in the memoir are devoted to his encounter of a brash, talented 11-year-old with a seasoned, professional musician-the boyhs impetuous eagerness to forge ahead and write a whole symphony as soon as he has learned how the orchestral instruments are used, and the tutor's bemused, short-lived resistance to the child whose reputation would ultimately eclipse his own.

Like most prodigies, Prokofiev was somewhat unbalanced in his development. He was composing adult music before he was allowed to read adult books (which he graded, as he did the music he heard, giving Turgenev and Tolstoy and A, but some of Beethoven's music only a C), and his sexual awareness, by his own account, arrived unusually late.

Despite the 135 years that separate their births, Prokofiev, like Mozart, grew up in an essentially feudal society. But Prokofiev's society was heading rapidly for violent change, though he shows very little awareness of the processes at work until they begin to disrupt his life.

For devotees of Prokofiev's music (who will be, naturally, the book's primary readership), possibly the most fascinating part of this memoir will be the musical notation (in the composer's own handwriting) of themes from his early works, beginning with "a tune that took on a completely acceptable form," composed when he was only 5. Most of the music presented is otherwise lost or, if not lost, quite forgotten, but sometimes it shows a scintilla of his later genius and his comments on it give a fascinating glimpse of a young genius learning to become a mature craftsman.