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# Marin Mersenne

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

Marin Mersenne (September 8, 1588 - September 1, 1648) was a French theologian, philosopher, mathematician and music theorist.

Born of peasant parents near Oize (Sarthe), he was educated at the Jesuit College of La Flèche , where he was a schoolmate and friend of Descartes. In 1611 he joined the Minim Friars, and devoted himself to philosophic teaching in various convent schools, including Nevers. He settled eventually in Paris in 1620 at the convent of L'Annonciade. For the next 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.

Mersenne is today remembered 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 Holland. 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 major contributions to musical tuning theory was the suggestion of $\sqrt\sqrt{2\over3-\sqrt2}$ as the ratio for a semitone. It was more accurate than Vincenzo Galilei's 18/17, and could be constructed with straightedge and compass. Mersenne's description in the 1636 Harmonic 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.

## Selected works

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