AN AMERICAN SOUND
RED AND HOT The Fate of Jazz in the Soviet Union 1917-1980. By S. Frederick Starr. Illustrated. 368 pp. New York: Oxford University Press. $16.95. When Rasputin was poisoned in Petrograd in 1916, the deed was done, according to Prince Felix Yussupov, the poisoner, to the accompaniment, on a gramophone, of ''Yankee Doodle.'' This was one of the more curious intrusions of American popular music into Russian culture, but by no means the first or the last. By the turn of the century, Russians were listening to Tin Pan Alley hits, and the hectic years between the failed revolution of 1905 and World War I found the orchestra of the Czar's own regiment playing ragtime and a sophisticated urban elite dancing the cakewalk. After the October Revolution of 1917 and the upheaval of the civil war came another influx of American music: jazz, the exuberant, seductive form that would delight the Soviet masses and cause ideological headaches for their leaders for decades to come.