Marin Mersenne
Encyclopedia
Marin Mersenne, Marin Mersennus or le Père Mersenne (8 September 1588 – 1 September 1648) was a French
theologian
, philosopher, mathematician
and music theorist
, often referred to as the "father of acoustics
" . Mersenne was "the center of the world of science and mathematics during the first half of the 1600s."
, Maine
(present day Sarthe
, France). He was educated at Le Mans
and at the Jesuit College of La Flèche. On 17 July 1611, he joined the Minim Friars
, and, after studying theology
and Hebrew
in Paris
received his full holy orders
in 1613.
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, with other kindred spirits such as René 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. 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 Quaestiones celeberrimae in Genesim (1623); L'Impieté des déistes (1624); La Vérité des sciences (Truth of the Sciences against the Sceptics, 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. In 1635 Mersenne met with Tommaso Campanella
, but concluded that he could "teach nothing in the sciences (...) but still he has a good memory and a fertile imagination." Mersenne asked if René Descartes
wanted Campanella to come to Holland to meet him, but Descartes declined. He visited Italy fifteen times, in 1640, 1641 and 1645. In 1643-1644 Mersenne also corresponded with the German Socinian Marcin Ruar
concerning the Copernican ideas of Pierre Gassendi
, finding Ruar already a supporter of Gassendi's position. Among his correspondents was Dekar, Galilei, Roberval, Pascal, Bekman and another scientists. Peter L. Bernstein in his book Against the Gods: the Remarkable story of risk writes: "The Académie des Sciences in Paris and the Royal Society in London, which were founded about twenty years after Mensenne's death, were direct descendants of Mersenne's activities."
He died through complications arising from a lung abscess
.
al and divinatory
arts, cabalism
, animistic
and pantheistic
philosophies. He mentions Martin Del Rio
's Investigations into Magic and criticises Marsilio Ficino
for claiming power for images and characters. He condemns astral magic and astrology
and the anima mundi a concept popular amongst Renaissance
neo-platonists. Whilst allowing for a mystical interpretation of the Cabala, he wholeheartedly condemned its magical application—particularly to angelology. He also criticises Pico della Mirandola, Cornelius Agrippa and Francesco Giorgio with Robert Fludd
as his main target. Fludd responded with Sophia cum moria certamen (1626), wherein Fludd admits his involvement with the Rosicrucian
s. The anonymous Summum bonum (1629), another critique of Mersenne, is an openly Rosicrucian text. The cabalist Jacques Gaffarel
joined Fludd's side, while Pierre Gassendi
defended Mersenne.
, introduced several innovating concepts that
can be considered as the basis of modern reflecting telescopes:
– Instead of using an eyepiece, as did Galileo who had to tilt the mirror to have easy access to the image, Mersenne introduced the revolutionary idea of a second mirror that would reflect the light coming from the first mirror. This allows one to focus the image behind the primary mirror in which a hole is drilled at the center to unblock the rays.
– Mersenne invented the afocal telescope and the beam compressor that is useful in many multiple-mirrors telescope designs.
– Mersenne recognized also that he could correct the spherical aberration of the telescope by using nonspherical mirrors and that in the particular case of the afocal arrangement he could do this correction by using two parabolic mirrors.
– Much earlier than Laurent Cassegrain
, he found the fundamental arrangement of the two-mirrors telescope combination, a concave primary mirror associated with a convex secondary mirror and discovered the telephoto effect that is critical in reflecting telescopes, although it is obvious that he was far from having understood all the implications of that discovery.
Unfortunately, because of the harsh criticism that he encountered, especially that of René Descartes, he made no attempt to build a telescope of his own invention.
s. The Mersenne twister, named for him, is used everyday in computer engineering, and is central to 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.
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 on First Philosophy
, 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 instrument
s. It is regarded as a source of information on 17th-century music, especially French music and musician
s, to rival even the works of Pietro Cerone
.
One of his many contributions to musical tuning
theory was the suggestion of
as the ratio
for an equally-tempered
semitone
(
). It was more accurate (0.44 cent
s sharp) than Vincenzo Galilei
's 18/17 (1.05 cents flat), and could be constructed using 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 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.
He also performed extensive experiments to determine the acceleration of falling objects by comparing them with the swing of pendulum
s, reported in his Cogitata Physico-Mathematica in 1644. He was the first to measure the length of the seconds pendulum
, that is a pendulum whose swing takes one second, and the first to observe that a pendulum's swings are not isochronous
as Galileo thought, but that large swings take longer than small swings.
in his second suite of Ancient Airs and Dances
.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
theologian
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...
, philosopher, mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and music theorist
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...
, often referred to as the "father of acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
" . Mersenne was "the center of the world of science and mathematics during the first half of the 1600s."
Life
Marin Mersenne was born of peasant parents near OizéOizé
Oizé is a commune in the Sarthe department in the region of Pays-de-la-Loire in north-western France.-References:*...
, Maine
Maine (province)
Le Maine is one of the traditional provinces of France . It corresponds to the old county of Maine, with its center, the city of Le Mans.-Location:...
(present day Sarthe
Sarthe
Sarthe is a French department, named after the Sarthe River.- History :The department was created during the French Revolution on March 4, 1790, pursuant to the law of December 22, 1789, starting from a part of the province of Maine which was divided into two departments, Sarthe to the east and...
, France). He was educated at Le Mans
Le Mans
Le Mans is a city in France, located on the Sarthe River. Traditionally the capital of the province of Maine, it is now the capital of the Sarthe department and the seat of the Roman Catholic diocese of Le Mans. Le Mans is a part of the Pays de la Loire region.Its inhabitants are called Manceaux...
and at the Jesuit College of La Flèche. On 17 July 1611, he joined the Minim Friars
Minim (religious order)
The Minims are members of a Roman Catholic religious order of friars founded by Saint Francis of Paola in fifteenth-century Italy...
, and, after studying theology
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...
and Hebrew
Hebrew language
Hebrew is a Semitic language of the Afroasiatic language family. Culturally, is it considered by Jews and other religious groups as the language of the Jewish people, though other Jewish languages had originated among diaspora Jews, and the Hebrew language is also used by non-Jewish groups, such...
in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
received his full holy orders
Holy Orders
The term Holy Orders is used by many Christian churches to refer to ordination or to those individuals ordained for a special role or ministry....
in 1613.
Between 1614 and 1618, he taught theology and philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
at Nevers
Nevers
Nevers is a commune in – and the administrative capital of – the Nièvre department in the Bourgogne region in central France...
, but he returned to Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
and settled at the convent of L'Annonciade
Annunciation
The Annunciation, also referred to as the Annunciation to the Blessed Virgin Mary or Annunciation of the Lord, is the Christian celebration of the announcement by the angel Gabriel to Virgin Mary, that she would conceive and become the mother of Jesus the Son of God. Gabriel told Mary to name her...
in 1620. There, with other kindred spirits such as René Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...
, Étienne Pascal
Étienne Pascal
Étienne Pascal was the father of Blaise Pascal. His father and mother were Martin Pascal, the treasurer of France, and Marguerite Pascal de Mons. He also had three daughters, two of whom survived past childhood: Gilberte and Jacqueline...
, Gilles de Roberval
Gilles de Roberval
Gilles Personne de Roberval , French mathematician, was born at Roberval, Oise, near Beauvais, France. His name was originally Gilles Personne or Gilles Personier, that of Roberval, by which he is known, being taken from the place of his birth.Like René Descartes, he was present at the siege of La...
and Nicolas-Claude Fabri de Peiresc
Nicolas-Claude Fabri de Peiresc
Nicolas-Claude Fabri de Peiresc was a French astronomer, antiquary and savant who maintained a wide correspondence with scientists and was a successful organizer of scientific inquiry...
, he studied mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and music. He corresponded with Giovanni Doni, Constantijn Huygens
Constantijn Huygens
Constantijn Huygens , was a Dutch Golden Age poet and composer. He was secretary to two Princes of Orange: Frederick Henry and William II, and the father of the scientist Christiaan Huygens.-Biography:...
and other scholars in Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
, England and Holland. 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 Quaestiones celeberrimae in Genesim (1623); L'Impieté des déistes (1624); La Vérité des sciences (Truth of the Sciences against the Sceptics, 1624). It is sometimes incorrectly stated that he was a Jesuit. He was educated by Jesuits, but he never joined the Society of Jesus
Society of Jesus
The Society of Jesus is a Catholic male religious order that follows the teachings of the Catholic Church. The members are called Jesuits, and are also known colloquially as "God's Army" and as "The Company," these being references to founder Ignatius of Loyola's military background and a...
. He taught theology and philosophy at Nevers and Paris. In 1635 Mersenne met with Tommaso Campanella
Tommaso Campanella
Tommaso Campanella OP , baptized Giovanni Domenico Campanella, was an Italian philosopher, theologian, astrologer, and poet.-Biography:...
, but concluded that he could "teach nothing in the sciences (...) but still he has a good memory and a fertile imagination." Mersenne asked if René Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...
wanted Campanella to come to Holland to meet him, but Descartes declined. He visited Italy fifteen times, in 1640, 1641 and 1645. In 1643-1644 Mersenne also corresponded with the German Socinian Marcin Ruar
Marcin Ruar
Marcin Ruar , pseudonym Aretius Crispinus) was a Socinian writer, advocate of religious tolerance, and rector of the Racovian Academy from 1620 to 1622....
concerning the Copernican ideas of Pierre Gassendi
Pierre Gassendi
Pierre Gassendi was a French philosopher, priest, scientist, astronomer, and mathematician. With a church position in south-east France, he also spent much time in Paris, where he was a leader of a group of free-thinking intellectuals. He was also an active observational scientist, publishing the...
, finding Ruar already a supporter of Gassendi's position. Among his correspondents was Dekar, Galilei, Roberval, Pascal, Bekman and another scientists. Peter L. Bernstein in his book Against the Gods: the Remarkable story of risk writes: "The Académie des Sciences in Paris and the Royal Society in London, which were founded about twenty years after Mensenne's death, were direct descendants of Mersenne's activities."
He died through complications arising from a lung abscess
Lung abscess
Lung abscess is necrosis of the pulmonary tissue and formation of cavities containing necrotic debris or fluid caused by microbial infection....
.
Quaestiones celeberrimae in Genesim (1623)
It was written as a commentary on the Book of Genesis and comprises uneven sections headed by verses from the first three chapters of that book. At first sight the book may appear to be a collection of treatises on various miscellaneous topics. However Robert Lenoble has shown that the principle of unity in the work is a diatribe against magicMagic (paranormal)
Magic is the claimed art of manipulating aspects of reality either by supernatural means or through knowledge of occult laws unknown to science. It is in contrast to science, in that science does not accept anything not subject to either direct or indirect observation, and subject to logical...
al and divinatory
Divination
Divination is the attempt to gain insight into a question or situation by way of an occultic standardized process or ritual...
arts, cabalism
Christian Kabbalah
The Renaissance saw the birth of Christian Kabbalah/Cabbalah , also spelled Cabbala/Cabala...
, animistic
Animism
Animism refers to the belief that non-human entities are spiritual beings, or at least embody some kind of life-principle....
and pantheistic
Pantheism
Pantheism is the view that the Universe and God are identical. Pantheists thus do not believe in a personal, anthropomorphic or creator god. The word derives from the Greek meaning "all" and the Greek meaning "God". As such, Pantheism denotes the idea that "God" is best seen as a process of...
philosophies. He mentions Martin Del Rio
Martín del Río
Martín del Río is a municipality located in the province of Teruel, Aragon, Spain. According to the 2010 census the municipality has a population of 469 inhabitants.Road N-211 crosses the eastern side of Martín del Río....
's Investigations into Magic and criticises Marsilio Ficino
Marsilio Ficino
Marsilio Ficino was one of the most influential humanist philosophers of the early Italian Renaissance, an astrologer, a reviver of Neoplatonism who was in touch with every major academic thinker and writer of his day, and the first translator of Plato's complete extant works into Latin...
for claiming power for images and characters. He condemns astral magic and astrology
Astrology
Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...
and the anima mundi a concept popular amongst Renaissance
Renaissance
The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...
neo-platonists. Whilst allowing for a mystical interpretation of the Cabala, he wholeheartedly condemned its magical application—particularly to angelology. He also criticises Pico della Mirandola, Cornelius Agrippa and Francesco Giorgio with Robert Fludd
Robert Fludd
Robert Fludd, also known as Robertus de Fluctibus was a prominent English Paracelsian physician, astrologer, mathematician, cosmologist, Qabalist, Rosicrucian apologist...
as his main target. Fludd responded with Sophia cum moria certamen (1626), wherein Fludd admits his involvement with the Rosicrucian
Rosicrucian
Rosicrucianism is a philosophical secret society, said to have been founded in late medieval Germany by Christian Rosenkreuz. It holds a doctrine or theology "built on esoteric truths of the ancient past", which, "concealed from the average man, provide insight into nature, the physical universe...
s. The anonymous Summum bonum (1629), another critique of Mersenne, is an openly Rosicrucian text. The cabalist Jacques Gaffarel
Jacques Gaffarel
Jacques Gaffarel was a French scholar and astrologer. He followed the family tradition of studying medicine, and then became a priest, but mainly developed his interests in the fields of natural history and Oriental occultism, gaining fluency in the Hebrew, Persian, and Arabic languages.His...
joined Fludd's side, while Pierre Gassendi
Pierre Gassendi
Pierre Gassendi was a French philosopher, priest, scientist, astronomer, and mathematician. With a church position in south-east France, he also spent much time in Paris, where he was a leader of a group of free-thinking intellectuals. He was also an active observational scientist, publishing the...
defended Mersenne.
L’Harmonie Universelle (1637)
In this book, Mersenne, a disciple of René DescartesRené Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...
, introduced several innovating concepts that
can be considered as the basis of modern reflecting telescopes:
– Instead of using an eyepiece, as did Galileo who had to tilt the mirror to have easy access to the image, Mersenne introduced the revolutionary idea of a second mirror that would reflect the light coming from the first mirror. This allows one to focus the image behind the primary mirror in which a hole is drilled at the center to unblock the rays.
– Mersenne invented the afocal telescope and the beam compressor that is useful in many multiple-mirrors telescope designs.
– Mersenne recognized also that he could correct the spherical aberration of the telescope by using nonspherical mirrors and that in the particular case of the afocal arrangement he could do this correction by using two parabolic mirrors.
– Much earlier than Laurent Cassegrain
Laurent Cassegrain
Laurent Cassegrain was a Catholic priest who is notable as the probable inventor of the Cassegrain reflector, a folded two mirror reflecting telescope design.-Biography:...
, he found the fundamental arrangement of the two-mirrors telescope combination, a concave primary mirror associated with a convex secondary mirror and discovered the telephoto effect that is critical in reflecting telescopes, although it is obvious that he was far from having understood all the implications of that discovery.
Unfortunately, because of the harsh criticism that he encountered, especially that of René Descartes, he made no attempt to build a telescope of his own invention.
Other
Mersenne is remembered today thanks to his association with the Mersenne primeMersenne prime
In mathematics, a Mersenne number, named after Marin Mersenne , is a positive integer that is one less than a power of two: M_p=2^p-1.\,...
s. The Mersenne twister, named for him, is used everyday in computer engineering, and is central to fields such as cryptography.
However, Mersenne was not primarily a mathematician; he wrote about music theory
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...
and other subjects. He edited works of Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
, Apollonius
Apollonius of Perga
Apollonius of Perga [Pergaeus] was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes...
, Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...
, and other Greek mathematicians. But perhaps his most important contribution to the advance of learning was his extensive correspondence (in Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
) with mathematicians and other scientists in many countries. At a time when the scientific journal
Scientific journal
In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. There are thousands of scientific journals in publication, and many more have been published at various points in the past...
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
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
. He submitted to various eminent Parisian thinkers a manuscript copy of the Meditations on First Philosophy
Meditations on First Philosophy
Meditations on First Philosophy is a philosophical treatise written by René Descartes and first published in 1641 . The French translation was published in 1647 as Méditations Metaphysiques...
, 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
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...
and musical instrument
Musical instrument
A musical instrument is a device created or adapted for the purpose of making musical sounds. In principle, any object that produces sound can serve as a musical instrument—it is through purpose that the object becomes a musical instrument. The history of musical instruments dates back to the...
s. It is regarded as a source of information on 17th-century music, especially French music and musician
Musician
A musician is an artist who plays a musical instrument. It may or may not be the person's profession. Musicians can be classified by their roles in performing music and writing music.Also....* A person who makes music a profession....
s, to rival even the works of Pietro Cerone
Pietro Cerone
Pietro Cerone was an Italian music theorist, singer and priest of the late Renaissance. He is most famous for an enormous music treatise he wrote in 1613, which is useful in the studying compositional practices of the 16th century.-Life:...
.
One of his many contributions to musical tuning
Musical tuning
In music, there are two common meanings for tuning:* Tuning practice, the act of tuning an instrument or voice.* Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases.-Tuning practice:...
theory was the suggestion of
as the ratio
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
for an equally-tempered
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
semitone
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
(
). It was more accurate (0.44 centCent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
s sharp) than Vincenzo Galilei
Vincenzo Galilei
Vincenzo Galilei was an Italian lutenist, composer, and music theorist, and the father of the famous astronomer and physicist Galileo Galilei and of the lute virtuoso and composer Michelagnolo Galilei...
's 18/17 (1.05 cents flat), and could be constructed using 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
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
, is 1 : 2. The perceived harmony (consonance
Consonance
Consonance is a stylistic device, most commonly used in poetry and songs, characterized by the repetition of the same consonant two or more times in short succession, as in "pitter patter" or in "all mammals named Sam are clammy".Consonance should not be confused with assonance, which is the...
) 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.
He also performed extensive experiments to determine the acceleration of falling objects by comparing them with the swing of pendulum
Pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position...
s, reported in his Cogitata Physico-Mathematica in 1644. He was the first to measure the length of the seconds pendulum
Seconds pendulum
A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 1/2 Hz....
, that is a pendulum whose swing takes one second, and the first to observe that a pendulum's swings are not isochronous
Isochronous
Isochronous : From Greek iso, equal + chronos, time. It literally means regularly, or at equal time intervals. In general English language, it refers to something that occurs at a regular interval, of the same duration; as opposed to synchronous which refers to more than one thing happening at the...
as Galileo thought, but that large swings take longer than small swings.
Music
An air attributed to Mersenne was used by Ottorino RespighiOttorino Respighi
Ottorino Respighi was an Italian composer, musicologist and conductor. He is best known for his orchestral "Roman trilogy": Fountains of Rome ; Pines of Rome ; and Roman Festivals...
in his second suite of Ancient Airs and Dances
Ancient Airs and Dances
Ancient Airs and Dances is a set of three suites composed by Italian composer Ottorino Respighi.- Suite No. 1 :Suite No. 1 was composed in 1917...
.
See also
- Mersenne primeMersenne primeIn mathematics, a Mersenne number, named after Marin Mersenne , is a positive integer that is one less than a power of two: M_p=2^p-1.\,...
- Catalan–Mersenne number/Catalan's Mersenne conjecture
- Equal temperamentEqual temperamentAn equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
- Mersenne twister
- Mersen
- List of Roman Catholic scientist-clerics
Works by Mersenne
- Euclidis elementorum libri, etc. (Paris, 1626)
- Les Mécaniques de Galilée (Paris, 1634)
- Questions inouies ou récréation des savants (1634)
- Questions théologiques, physiques, etc. (1634)
- Harmonie universelle (Paris, 1636-7). Translation to English by Roger E Chapman (The Hague, 1957)
- Nouvelles découvertes de Galilée (1639)
- Cogitata physico-mathematica (1644)
- Universae geometriae synopsis (1644)
Works about Mersenne
- Adrien BailletAdrien BailletAdrien Baillet was a French scholar and critic. He is now best known as a biographer of René Descartes.-Life:He was born in the village of Neuville near Beauvais, in Picardie...
, 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)
Other resources
- Marin Mersenne—The Birth of Modern Geometry (UK Open UniversityOpen UniversityThe Open University is a distance learning and research university founded by Royal Charter in the United Kingdom...
TV documentary made in 1986 and transmitted on BBC2)
External links
- "Marin Mersenne", Mathematics Genealogy ProjectMathematics Genealogy ProjectThe Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...
.