During the many years from the age of Pythagoras to the nineteenth century, mathematicians and musicians alike, Greek, Roman, Arabian, and European, sought to understand the nature of musical sounds and to extend the relationship between mathematics and music. Systems of scales and theories of harmony and countnerpoint were dissected and reconstructed. The climax to this long series of investigations, from a mathematical standpoint, came with the work of the mathematician Joseph Fourier, who showed that all sounds, vocal and instrumental, simple and complex, are completely describable in mathematical terms. Because of Fourier's work not even the elusive beauty of a musical phrase escapes submission to mathematical formulation. Whereas Pythagoras was content to pluck the strings of a lyre, Fourier sounded the whole orchestra.
Morris Kline, Mathematics and Western Civilization
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