The source of these ratios, in the pattern of vibrations known as the harmonic series, was exposed by Joseph Sauveur the early 18th century and even more clearly by Helmholtz in the 1860s.
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Circa 1694 Étienne Loulié, a musician who had recently collaborated with mathematician Joseph Sauveur on the education of Philippe, Duke of Chartres, was asked by Chartres to work with Sauveur on a scientific study of acoustics sponsored by the Royal Academy of Science.