When the opening bars of Beethoven's Fifth thundered into the Apollo Rooms on lower Broadway in the wintry December of 1842, and the Philharmonic was born, New York was the seventh largest city in the Western world. Two earlier attempts to found a Philharmonic had failed, despite apparent success. The new orchestra ended its first season on a crest of enthusiasm -- its next hundred years would often be harder. American composers complained that the Philharmonic played only one American piece during its first ten years and that it leaned heavily on fashionable European music. By the turn of the century the Philharmonic's repertory was vastly Germanized. Competition sprang up not only in New York but Boston with rival orchestras. Then in 1909 came Gustav Mahler, composer and conductor, to revamp the orchestra and give it inspired new life. His death allowed a series of great reigns, among others those of Mengelberg and the supertemperamental Toscanini (most fascinating chapter). Argument over today's repertory abounds; American composers are still slighted, perhaps justly. Shanet gives a list of suggestions for enlivening our liveliest orchestra. His book is a labor of love, an enormous task attacked with brio and commonsensical humor.