Marin Mersenne

For the primes named after Marin Mersenne, see Mersenne prime.

Marin Mersenne, Marin Mersennus or le Père Mersenne (September 8, 1588 – September 1, 1648) was a French theologian, philosopher, mathematician and music theorist.

Life

Marin Mersenne (pronounced Mayr-senn) was born of peasant parents near Oizé, Maine (present day Sarthe). He was educated at Le Mans and at the Jesuit College of La Flèche, where he was a schoolmate and friend of René Descartes. On July 17, 1611, he joined the Minim Friars, and, after studying theology and Hebrew in Paris received his full holy orders in 1613.

For a time, he taught philosophy at Nevers but returned to Paris in 1620 at the convent of L'Annonciade. There, with other kindred spirits such as Descartes, Étienne Pascal, Gilles de Roberval and Nicolas-Claude Fabri de Peiresc, he studied mathematics and music. He corresponded with Giovanni Doni, Constantijn Huygens and other scholars in Italy, England and Holland. For four years he devoted himself entirely to philosophic and theological writing, and published Quaestiones celeberrimae in Genesim (1623); L'Impieté des déistes (1624); La Vérité des sciences (1624). It is sometimes incorrectly stated that he was a Jesuit. He was educated by Jesuits, but he never joined the Society of Jesus. He taught theology and philosophy at Nevers and Paris. He visited Italy three times, in 1640, 1641 and 1645.

He died through complications arising from a lung abscess.

Work

Mersenne is remembered today thanks to his association with the Mersenne primes. However, he was not primarily a mathematician; he wrote about music theory and other subjects. He edited works of Euclid, Archimedes, and other Greek mathematicians. But his perhaps most important contribution to the advance of learning was his extensive correspondence (in Latin, of course) with mathematicians and other scientists in many countries. At a time when the scientific journal had not yet come into being, Mersenne was the center of a network for exchange of information.

His philosophical works are characterized by wide scholarship and the narrowest theological orthodoxy. His greatest service to philosophy was his enthusiastic defence of Descartes, whose agent he was in Paris and whom he visited in exile in the Netherlands. He submitted to various eminent Parisian thinkers a manuscript copy of the Meditations, and defended its orthodoxy against numerous clerical critics. In later life, he gave up speculative thought and turned to scientific research, especially in mathematics, physics and astronomy. Of his works in this connection the best known is L'Harmonie universelle (1636) dealing with the theory of music and musical instruments.

One of his many contributions to musical tuning theory was the suggestion of

\sqrt{\sqrt{2\over3-\sqrt2}}

as the ratio for a semitone. It was more accurate (0.44 cents sharp) than Vincenzo Galilei's 18/17 (1.05 cents flat), and could be constructed with straightedge and compass. Mersenne's description in the 1636 Harmonie universelle of the first absolute determination of the frequency of an audible tone (at 84 Hz) implies that he had already demonstrated that the absolute-frequency ratio of two vibrating strings, radiating a musical tone and its octave, is as 1 : 2. The perceived harmony (consonance) of two such notes would be explained if the ratio of the air oscillation frequencies is also 1 : 2, which in turn is consistent with the source-air-motion-frequency-equivalence hypothesis.

His Traité de l'harmonie universelle (1627) is regarded as a source of information on 17th century music, especially French music and musicians, to rival even the works of Pietro Cerone.

See also: 53 equal temperament.

Bibliography

Works by Mersenne

Euclidis elementorum libri, etc. (Paris, 1626)
Les Mécaniques de Galilée (Paris, 1634)
Questions inouies ou recreations des savants (1634)
Questions théologiques, physiques, etc. (1634)
Harmonie universelle (Paris, 1636-7)
Nouvelles découvertes de Galilée (1639)
Cogitata physico-mathematica (1644)
Universae geometriae synopsis (1644)

Works about Mersenne

Adrien Baillet, Vie de Descartes (1691)
Poté, Éloge de Mersenne (1816)
Gehring, F. (1922) "Mersennus, Marin (le Père Mersenne)", Grove's Dictionary of Music and Musicians (ed. J.A. Fuller Maitland)