A history of American music; Music in the New World, by Charles Hamm. New York: W.W. Norton & Co. 722 pp. $25 .

This informative and entertaining semi-scholarly history studies all varieties of American music, from ''Native American'' forms through ''The Age of Rock.'' Its best features are a lively chapter on ''The Music of Tin Pan Alley, '' an appreciative treatment of ''Hillbilly and Country-Western Music,'' and a helpful brief bibliography and discography.

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