then centuries old.)
The single most important develop- ment in the history of European music, according to Joseph Machlis in The En- joyment of Music (Norton, 5th ed., 1984), was the emergence between 850 and 1150 A.D. of polyphony-the use of two or more melodic lines. Polyphony re- quired ever more precise forms of nota- tion. Music, says Machlis, "took a long step from being an art of improvisation and oral tradition to one that was care- fully planned and that could be preserved accurately."...