Mersenne’s Laws (Edited from Wikipedia)

SUMMARY

Mersenne's laws are laws describing the frequency of oscillation of a stretched string, useful in musical tuning and musical instrument construction. The equation was first proposed by French mathematician and music theorist Marin Mersenne in his 1637 work Treatise on the Universal Harmony .

Mersenne's laws govern the construction and operation of string instruments, pianos, and harps, which must accommodate the total tension force required to keep the strings at the proper pitch.

Mersenne’s laws determine the frequency of a string. The three laws explain that:

1. Longer strings play lower notes, while shorter strings play higher notes. 2. Strings that are stretched tighter will play higher notes. Strings that are looser will play lower notes. 3. Heavier strings play lower notes, while lighter strings play higher notes.

These results don’t differ much from Galileo's, yet they are known as Mersenne's law, because Mersenne physically proved their truth through experiments. Galileo considered their proof impossible. Mersenne investigated and refined these relationships by experiment. Though he did not himself originate them, he receives the credit as their discoverer.

HISTORY

Marin Mersenne was born in 1588 and died in 1648 at the age of 59. He was a French theologian, philosopher, mathematician, and music theorist. He is often referred to as the "father of acoustics". Mersenne, an ordained priest, had many contacts in the scientific world and has been called "the center of the world of science and mathematics during the first half of the 1600s."

Marin Mersenne (pronounced Mehr-SENN) was born of peasant parents in France. He was educated at the Jesuit College of La Flèche. On 17 July 1611, he joined the Minim Friars, and, after studying theology and Hebrew in Paris was ordained a priest in 1613.

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Between 1614 and 1618, he taught theology and philosophy at Nevers, but he returned to Paris and settled at the convent of L'Annonciade in 1620. There he studied mathematics and music and met with other kindred spirits such as René Descartes and Étienne Pascal (the father of Blaise Pascal). He corresponded with scholars like Constantijn Huygens, Galileo Galilei, and other scholars in Italy, England and the Dutch Republic. He was a staunch defender of Galileo, assisting him in translations of some of his mechanical works.

For four years, Mersenne devoted himself entirely to philosophic and theological writing, and published Truth of the Sciences against the Sceptics in 1624. It is sometimes incorrectly stated that he was a Jesuit. He was educated by Jesuits, but he never joined the Society of Jesus.

In 1635 he set up the informal Académie Parisienne (Academia Parisiensis) which had nearly 140 correspondents including astronomers and philosophers as well as mathematicians. He was not afraid to cause disputes among his learned friends in order to compare their views, notable among which were disputes between Descartes and Fermat and Beaugrand. The Académie des Sciences in Paris and the Royal Society in London, which were founded about twenty years after Mersenne's death, were direct descendants of Mersenne's activities.

He published a commentary on the Book of Genesis in the Bible in 1623. It was written as a commentary on the Book of Genesis and comprises sections headed by verses from the first three chapters of that book. It is a polemic (argument) against magical and divinatory arts, cabalism, and animistic and pantheistic philosophies. He mentions Martin Del Rio's Investigations into Magic and criticisms Marsilio Ficino for claiming power for images and characters. He condemns astral magic and astrology and the anima mundi, a concept popular amongst Renaissance philosophers.

Mersenne is also remembered today thanks to his association with the Mersenne primes. The Mersenne Twister, named for Mersenne prime, is frequently used in computer engineering, and in related fields such as cryptography.

However, Mersenne was not primarily a mathematician; he wrote about music theory and other subjects. He edited works of Euclid, Apollonius, Archimedes, and other Greek mathematicians. But perhaps his most important contribution to the advance of learning was his extensive correspondence (in Latin) 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.

2 It has been argued that Mersenne used his lack of mathematical specialty, his ties to the print world, his legal acumen, and his friendship with the French mathematician and philosopher René Descartes (1596–1650) to manifest his international network of mathematicians.

His greatest service to philosophy was his enthusiastic defense 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 Descartes’ work, 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. In this connection, his best known work is Traité de l'harmonie universelle (also referred to as Harmonie universelle) of 1636, dealing with the theory of music and musical instruments. It is regarded as a source of information on 17th-century music, especially French music and musicians.

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