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<title> SUMMARY </title>The leit-motiv of the present description of the relationship between music and natural philosophy in Italy in the seventeenth century is a recurrent theme: the mathematical or « Pythagorean » approach to music as opposed to the experimental or « Aristoxenian » approach. During the sixteenth and seventeenth centuries this opposition, rendered pertinent by the cultural transformations that accompanied the consolidation of modern science, gained in complexity and took on original forms and meanings. The present paper, in the first instance, outlines the major traditions of classical musical thought and its medieval heritage. Secondly, it provides a survey of the more significant attempts at renewing musical theory that were carried out during the second half of the Cinquecento in the light of the Italian renaissance of mathematics of the XV and XVI centuries. It continues with an examination of the musical ideas of Galileo and offers a primary documentation of the interest displayed by representatives of the Galilean school in the science of sound during the first half of the Seicento.Finally it discusses, for the first time, the theories of sound of F. M. Grimaldi and D. Bartoli and the musical doctrines of P. Mengoli within the framework of the principal philosophical elements of Italian culture between 1660 and 1680.

In: Nuncius
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title SUMMARY /title The publication of La Corrispondenza di Pietro Mengoli (Florence 1986), for the ' Archives of the Correspondence of Italian Scientists ' edited by the Istituto e Museo di Storia della Scienza, draws attention to a little-known mathematician and natural philosopher of the Galileian School, who was active in Bologna from 1625-1686. Mengoli was trained at the school of Bonaventura Cavalieri (1598-1647), and, after his teacher's death, became professor of mechanics (from 1649-50) and then mathematicis (from 1678 to 1685) in the Bolognese Studium. Today Mengoli's name is known mainly to Italian historians of mathematics interested in his Novae quadraturae arithmeticae (1650) and Geometria (1659). Only recently have his several works on ' mixed mathematics ', metaphysics, cosmology and Biblical chronology come to the attention of scholars. During his lifetime, however, the ' Bolognese Mathematician ' was widely known in Europe, especially in the years 1660-1680. His Speculationi di musica (1670) was eagerly awaited by members of the Royal Society, and was reviewed and partly translated in the Philosophical Transactions (1674). Oldenburg, in his review, pointed out for future historians of musical science the main points of interest of this uncommon musical treatise: 1) the peculiar theory of sound; 2) the refusal of the so-called ' coincidence-theory of consonance '; and, 3) the amazing physiology of hearing, which Mengoli based on his assumption of the existence of two drums in the human ear.

In: Nuncius