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 developments indicated the increase of that searching intellectual handling of musical structure, methods, products and workers which in the later 18th century and still more in the 19th was to become prominent.

Joseph Sauveur (d. 1716) was the founder of the modern science of acoustics, which he first called by that name. His work is astonishing, since he was a deaf-mute from infancy, hearing never but a little and acquiring but a partial use of his voice. Early evincing mathematical genius, he came to Paris in 1670, taught mathematics, from 1680 in the Dauphin's household, and from 1690 was employed by the government upon fortification-plans. From about 1696, with the aid of musical assistants, he became absorbed in acoustics, joined the Académie, and published in its Transactions several epoch-making studies (1700-13). He fully established the vibrational character of all sound, examined the phenomena of vibrating bodies, elaborated the theory of partial-tones and sought to base a system of consonance on them, determined the vibration-numbers of tones of fixed pitch, suggesting 256 as a standard number for middle C, studied the range of audibility, etc. Contemporaneous with him in the Académie was Louis Carré (d. 1711), a pupil of the metaphysician Malebranche, with essays on sound and instruments (1702-9). The contending views of temperament were reviewed by Johann Georg Neidhardt of Königsberg (d. 1739) in several works (1706-34), that of 1724 containing the first use of logarithms in calculating intervals, and by Christoph Albert Sinn, a Brunswick surveyor, advocating the equal system (1717). Louis Bertrand Castel (d. 1757) attempted the futile task of presenting musical effects to the eye by the use of colors (1725-35), besides other essays. Leonhardt Euler (d. 1783), from 1727 a prolific mathematical writer at St. Petersburg, reëxamined the general physics of sound, and sought to frame a fresh theory of harmony from numerical principles, with rather grotesque results in part, though his studies of vibrations were valuable (about 25 works, 1727-74). Useful additions were made in 1732 by Johann Bernoulli of St. Petersburg (d. 1747), and in 1753 by his son Daniel Bernoulli (d. 1781). Georg Andreas Sorge (d. 1778), from 1722 court-organist at Lobenstein, wrote extensively (from 1741) upon sound, intervals, temperament, instrument-making, etc., often with ability, but in an obscure style and a contentious spirit; his work on composition (1745-7) led about 1760 to a bitter debate with Marpurg. Levens of Bordeaux sought (1743) to readjust scales by a theory of reciprocal overtones and undertones, followed by others. Robert Smith (d. 1768), professor of astronomy at Cambridge, published a good general treatise (1749). Both the chief editors of the famous Encyclopédie (1751-80), Denis Diderot (d. 1784) and Jean le Rond d'Alembert (d. 1783), were acousticians, the former known (from 1748) through essays, including one on a mechanical organ, and the latter (from 1747) through many articles and an exposition of Rameau's theory of harmony (1752); both contributed musical articles to the Encyclopédie. Tartini (d. 1770), the violinist, was an original investigator, as his theoretical works (from 1754) show, being the discoverer of combination-tones, as also Sorge (above), Romieu of Montpellier (1751) and Jean Adam Serre of Geneva (1753) claimed to be.