Marin Mersenne Research Articles

Mean Curvature and Asymptotic Volume of Small Balls

Marin Mersenne (1588–1648) is remembered chieflyasaone-man scientific clearing house—the Internet of his day. During the first half of theseventeenth century, when mathematical physics was taking its first tentative stepsguided by Descartes and Galileo, “Mersenne did more to propagate emerging newsciences of acoustics, pneumatics, and ballistics than anyone else of his time” [

Six Unknown Letters from Mersenne to Vegelin

(ProQuest: ... denotes non-US-ASCII text omitted.)The published correspondence of the Minim friar Marin Mersenne (1588-1648) fills seventeen fat volumes, and constitutes one of the most important monuments of seventeenth-century intellectual life.1 Mersenne's appetite for information in almost every field of learning was extraordinary and unflagging; he corresponded with Italian mathematicians, Dutch and French musicians, Huguenot theologians, English philosophers and scientists, and a wide range of friars, Jesuits, savants and country gentlemen. However, the sheer bulk of the modern edition of his correspondence may give a somewhat misleading impression of the quantity of Mersenne's own letters that have survived. A significant proportion of those seventeen volumes consists, in fact, of letters between third parties which mention Mersenne or relate in some way to his own correspondence. For the year 1641, for example, exactly 100 letters are printed: 54 are letters between third parties, 39 are letters to Mersenne, and only seven are letters by him.2 The discovery of six hitherto unknown autograph letters by Mersenne - addressed to Philip Ernst Vegelin, and located among the Vegelin papers in the Provincial Archive of Friesland at Leeuwarden - therefore amounts to a significant addition to the corpus of Mersenne's own letters.3The recipient of these letters was a talented young Dutchman of German origin, who shared some of Mersenne's scientific and musical interests, and had become acquainted with Mersenne personally in Paris. His name is not unknown to Mersenne scholars: one letter from him to Mersenne is contained in the published correspondence, and the Minim friar occasionally referred to him in letters to a mutual acquaintance.4 However, almost nothing has been written about him, apart from the brief entry in the Nieuw nederlandsch biografisch woordenboek, and virtually no attention has been given to the small but significant role he played as an intellectual intermediary between the Netherlands, France and England.5Philip Ernst Vegelin was born on 10 October 1613; his father, who bore the same name, came from a Protestant family, originally from Fribourg in Switzerland, which had moved to the Rhineland town of Neustadt, in the Palatinate. (The family name was probably derived from 'Vogelin'; the recipient of these letters normally signed himself 'Vegilin', but sometimes used 'Vegelin' - or, when writing in French, 'Veguelin', to indicate the hard 'g'. In later generations the spelling became fixed as 'Vegelin', which is the form used in this article.) Philip Ernst Vegelin senior served under Gustavus Adolphus, and was rewarded with an estate at Claerbergen, in the southern part of Friesland; the full family name therefore became Vegelin van (or 'de') Claerbergen.6Nothing is known of Philip Ernst Vegelin junior's education or early adulthood until the late 1630s, when he evidently spent some time in Paris: before he visited England in 1639 he was already well acquainted with the French engineer and musical theorist Jean Le Maire. This visionary but secretive inventor had developed a new form of musical notation, using individual symbols for notes of different pitch (instead of placing them on a stave); he also designed a new type of lute, called an 'Almerie' (an anagram of his name).7 No doubt it was Vegelin's own passion for music that drew him to Le Maire; it may also be a testimony to his personal charm that this notoriously unforthcoming inventor did apparently share some of his secrets with him. Whether Vegelin had also made the personal acquaintance of Mersenne by this stage is not known, though it does seem likely; he certainly knew of Mersenne's own work as a musical theorist (published in his huge folio volume, the Harmonie universelle) - as one of his later comments, noted by Samuel Hartlib and quoted below, makes clear. Nor is it known how long Vegelin spent in Paris at this time. …

The harmonious hand. Marin Mersenne and the science of memorized music.

The harmonious hand. Marin Mersenne and the science of memorized music.

Schenker's Mysterious Five

This article focuses on Schenker's role in what Milton Babbitt has called the occupational malady of theorists of music, namely the desire to search for the origin or proof of a theory outside its own system.1 Babbitt uses the seventeenth-century theorist Marin Mersenne to illustrate his point. In seeking to explain the derivation of the major triad, Mersenne claimed that one must proceed through six divisions of the string; but he need only have busied himself with the first five divisions, whose notes CCGCE already yield the requisite pitches. If five were enough, why choose six? For consis-

Infinite Degrees of Speed Marin Mersenne and the Debate Over Galileo's Law of Free Fall

AbstractThis article analyzes the evolution of Mersenne's views concerning the validity of Galileo's theory of acceleration. After publishing, in 1634, a treatise designed to present empirical evidence in favor of Galileo's odd-number law, Mersenne developed over the years the feeling that only the elaboration of a physical proof could provide sufficient confirmation of its validity. In the present article, I try to show that at the center of Mersenne's worries stood Galileo's assumption that a falling body had to pass in its acceleration through infinite degrees of speed. His extensive discussions with, or his reading of, Descartes, Gassendi, Baliani, Fabri, Cazre, Deschamps, Le Tenneur, Huygens, and Torricelli led Mersenne to believe that the hypothesis of a passage through infinite degrees of speed was incompatible with any mechanistic explanation of free fall.

Marin Mersenne (1588-1648): apologética tradicional cristiana frente a la crisis religiosa de 1623

La problemática tratada en este artículo versa acerca de la crisis religiosa del X V I I, así comosobre la respuesta que la misma provocó entre la reacción católica del momento, entre la quese encontraba Marin Mersenne, aspecto muy poco tratado hasta ahora por parte de la historiografíafilosófica.

Early American Wind and Ceremonial Music, 1636-1836: Phase 2 of the National Tune Index

Some years ago Kate Keller was having difficulty matching the titles of some eighteenth-century fife tunes to the actual melodies. Quite frustrated by the lack of any reference tools, Keller made an index of the melodies and titles in whatever original sources she had at hand. Her working index was very limited since the field was far too large and the sources were scattered in libraries all over the United States and Europe. She discussed her idea of a larger and more comprehensive index with several colleagues, and then, with Carolyn Rabson and this writer, submitted an application to the National Endowment for the Humanities. The NEH looked favorably on the project, and the National Tune Index was born. To make the index as broadly based as possible, an effort was made to choose representative and available works from six categories: American imprints, ballad operas and British theater works, dance collections, British instrumental collections, British song sheets and song collections, and manuscripts. The first phase of the National Tune Index, 18th-Century Secular contains about 38,500 titles, taken from over five hundred original sources, and has been available on microfiche since 1980. But the NEH did not grant full funding, and most of the wind band and ceremonial music had been omitted. The author went back to the NEH to seek additional funding. Happily, the NEH was so pleased with the results of the first project that it was willing to provide additional support, though not enough to complete the project without help. Finally, after ten years of slow work, the second phase was published in 1989. Early American Wind and Ceremonial Music, 1636-1836 is a computer-generated seven-part index of 20,733 citations taken from 1,077 pieces of sheet music and 298 collections found in the United States, Canada, United Kingdom, Ireland, Germany, Belgium, Sweden, and France. Fully compatible with phase 1 (18th-Century Secular Music), phase 2 places a primary emphasis on the roots of early American wind band, field music, percussion, and ceremonial music. For that reason, Hessian, French, and British sources form a major portion of the data base. The period covered runs from 1636 (Marin Mersenne's Harmonie Universelle, the earliest printed source located for trumpet and drum signals) to 1836 (Samuel Cooper's A Concise System of Instructions and Regulations for the Militia and Volunteers of the United States). There are some exceptions: to aid those interested in early hunting signals the titles of the unmeasured horn calls in Turbevile's The Noble Art of Venerie or Hunting of 1575 are included, as are later field music signals, thus allowing a logical survey and comparison. Three genres are represented in phase 2: American imprints, European instrumental collections, and manuscripts. Within the boundaries of wind band and ceremonial music dating from 1636 to 1836, comprehensive coverage is the goal. The flute, a gentleman's leisure-time instrument not included in the band, is omitted, but all known published tutors for oboe, clarinet, bassoon, horn, keyed bugle, trumpet, fife, and drum are included. Besides instrumental tutors, phase 2 includes collections of social and ceremonial music; arrangements for wind band; field music manuals and collections; individual marches and pieces relevant to the wind band; military regulations containing bugle, trumpet, fife and drum signals; and horn signals for the hunt. These musics played a vital role in the life of early America, combining social, religious, military, and ceremonial experiences and traditions. In this regard, the manuscripts are especially important, since they freely crossed social barriers and because they provide a measure of popularity. The National Tune Index is a bibliographical finding tool. Because the index is so large, it had to be published in microfiche form, but that medium should pose no problem for most researchers. …

Descartes's Theory of Modality

Descartes propounded the allegedly strange, peculiar, curious, and incoherent doctrine that necessary truths are made true by God's voluntary act.' It seems to imply that God could have made necessary truths false, which entails that they are not necessary after all. Some of Descartes's interpreters have taken him in that way, as firmly implying that nothing is absolutely necessary or impossible.2 We all know, however, that if this doctrine runs free through Descartes's philosophical work it will do untold damage: many of his arguments have to be protected somehow from the thesis that socalled necessary truths are really contingent. Discussing an argument of Descartes's for the real distinction between body and mind, for example, Curley writes: If we were to invoke the doctrine of the of eternal truths, we might say that a really omnipotent being could cause the mind and body to exist apart even if that were not logically possible. But in the Meditations Descartes is careful not to invoke that extravagant conception of omnipotence, and we would do him no service by bringing it in.3 That typifies the kind of thing Cartesian scholars have felt forced to say, charitably shielding Descartes from his own splatter. This creation or voluntarism doctrine does not appear in the Meditations, the Discourse on the Method, or the Principles of Philosophy. Descartes first declared it in three private letters to Marin Mersenne, most of a decade before his first published work ap-

Mersenne on Vocal Diminutions

Marin Mersenne's Harmonie universelle (Paris, 1636-37) provides a rare insight into French vocal practice of the early 17th c. Although he approaches singing as a teacher or composer, his comments also provide the performer with clues about ornamentation in early-17th-c. French vocal music. His examples of diminutions and explanations of individual ornaments reveal that the practice was significantly different from that of the later part of the century, with which most modern singers are more familiar.

A Tale of Two Fishes: Magical Objects in Natural History from Antiquity Through the Scientific Revolution

With Marin Mersenne and Rene Descartes, Pierre Gassendi was eminent among generation of European thinkers who decisively discredited what previous century called the occult When Henry Cornelius Agrippa used that phrase in title of his famous book of 1510, he could take for granted a philosophical theory of natural magic as part of a larger system of natural philosophy. More than a hundred years later Gassendi and his colleagues shook foundations of natural magic by displacing its chief philosophical supports, replacing hylemorphic apparatus of matter and form, substance and accident as taught in Peripatetic school philosophy with new corpuscular and mechanical paradigms. 1 Just as these new theories had an empirical basis in actual or putative experience-when Descartes meditated on bouncing tennis balls or when Pascal's brother-in-law carried a tube of mercury up Puy-deDome-so was theory of natural magic instantiated by reference to a set of material objects, objects odd enough to count as magical and bearing properties that eluded matter-theory that prevailed in Europe from

René Descartes

René Descartes (1596–1650) was born at La Haye, near Tours in France. He entered the Jesuit School at La Flèche in 1606, where he studied Latin and Greek and the classical authors, and acquired respect for the certainty of mathematics and distaste for the theories of Aristotle as developed by medieval commentators. In 1616, he took a degree in law at the University of Poitiers. There followed a period during which he travelled, for some of the time as a gentleman-officer in the armies of Maurice of Nassau, Prince of Orange, and Maximilian, Duke of Bavaria. In 1625 he returned to Paris and renewed his acquaintance with Father Marin Mersenne, who was later instrumental in making his views known to many of the famous intellectuals in Europe. From 1628 to 1649 he lived in Holland and worked out in detail the scientific, philosophical and mathematical ideas that had engaged him during his travels. His main philosophical works are Rules for the Direction of the Mind, written in 1629–30 but not published until 1684, Discourse on Method, 1637, Meditations, 1641, Principles of Philosophy, 1644, and The Passions of the Soul, 1649. In 1649, Descartes accepted an invitation to visit the Queen of Sweden and instruct her in philosophy. He succumbed to the rigorous climate, and died in February 1650.

René Descartes

René Descartes (1596–1650) was born at La Haye, near Tours in France. He entered the Jesuit School at La Flèche in 1606, where he studied Latin and Greek and the classical authors, and acquired respect for the certainty of mathematics and distaste for the theories of Aristotle as developed by medieval commentators. In 1616, he took a degree in law at the University of Poitiers. There followed a period during which he travelled, for some of the time as a gentleman-officer in the armies of Maurice of Nassau, Prince of Orange, and Maximilian, Duke of Bavaria. In 1625 he returned to Paris and renewed his acquaintance with Father Marin Mersenne, who was later instrumental in making his views known to many of the famous intellectuals in Europe. From 1628 to 1649 he lived in Holland and worked out in detail the scientific, philosophical and mathematical ideas that had engaged him during his travels. His main philosophical works are Rules for the Direction of the Mind, written in 1629–30 but not published until 1684, Discourse on Method, 1637, Meditations, 1641, Principles of Philosophy, 1644, and The Passions of the Soul, 1649. In 1649, Descartes accepted an invitation to visit the Queen of Sweden and instruct her in philosophy. He succumbed to the rigorous climate, and died in February 1650.

Marin Mersenne and the Probabilistic Roots of "Mitigated Scepticism"

Marin Mersenne and the Probabilistic Roots of "Mitigated Scepticism"

An early critique of Bacon's Sylva Sylvarum: Edmund Chilmead's treatise on sound

Summary Edmund Chilmead (1610–54), a little-known scholar and musician, was the author of a possibly unique testimony to the interest among English natural philosophers in the nature of sound and philosophical music theory during the years following the publication of Francis Bacon's Sylva Sylvarum (1626). Chilmead's ‘An Examination … of the Naturall History’ is a manuscript treatise which takes the form of twenty ‘Quaeres’ on the second and third centuries of experiments of the Sylva which are concerned with the nature of sound. In the treatise, Chilmead reveals his familiarity with the developments in the field of musical acoustics made by the French natural philosopher Marin Mersenne (1588–1648) and his circle. The paper falls into two complementary sections. In the first, Feingold gives an account of Chilmead's life and career (which has hitherto never been fully documented) in order to place him in the context of the intellectual and social milieu of Oxford and London during this period. In the secon...

Acoustics in the early Royal Society 1660-1680

The early Royal Society has been the focus of much attention by historians of science over many years, (1) but strangely enough there is no really detailed account to be found of the activities and discussions which took place in the weekly meetings, although there is ample information available on the subject. This study of the Royal Society’s collective interest in acoustics aims to provide a detailed analysis of an important subject that has not been dealt with elsewhere, at the same time as providing a case study of the way in which experiments were suggested and sometimes undertaken in meetings during the first twenty years of the Society’s existence. Apart from the article published forty years ago in this journal by Lloyd, in which the author is concerned only with articles in the Philosophical Transactions relating to music theory and acoustics in the years 1677—1698 (2), the contribution of members of the Royal Society to the topic of acoustics has been treated as subsidiary to that of more famous individuals in the seventeenth century; namely Galileo Galilei, Marin Mersenne, Isaac Newton and Joseph Sauveur. The comparative neglect of the activities of the Royal Society has arisen because writers have been concerned with tracing the ‘progress’ of acoustics as a scientific discipline, in which events in the seventeenth century merely set the scene for the triumphs of John and Daniel Bernoulli and Euler in the eighteenth century.

An Early Eighteenth-Century Discussion of Musical Acoustics by Étienne Loulié

An Early Eighteenth-Century Discussion of Musical Acoustics by Étienne Loulié. Un article de la revue Canadian University Music Review / Revue de musique des universités canadiennes (Numéro 2, 1981, p. 1-240) diffusée par la plateforme Érudit.

Swift's Laputians as a Caricature of the Cartesians

The prevalent view that Book III of Gulliver’s Travels satirizes the Royal Society overlooks the fact that this book contains two satires, one on the Laputians and one on the Balnibarbians. The first of these satires gains point if we regard it as aimed at the Cartesians, interpreting Laputa as France, the land of the Cartesians, and Balnibarbi as England, the land of the Newtonians, characterizations made by Voltaire in his Lettres philosophiques. The Laputians’ fear of the extinction of the sun is fully justified by the cosmology of Descartes’s Principes; their musical mania exaggerates only slightly that of the Cartesian popularizer Marin Mersenne; their influence on the Balnibarbians, inspiring them to build the Academy of Lagado, represents the influence of Descartes on the Royal Academy, an influence that has been hitherto underestimated.

Mersenne and Vanini

Although many scholars have cited Marin Mersenne's Quaestiones celeberrimae in Genesim for his critical remarks about the life of Julius Caesar Vanini, none of them has realised the extent to which Mersenne dealt with Vanini's works. They have found in Mersenne only a story about Vanini's intention to teach atheism, his execution, and one or two criticisms of his ideas. Far from making here and there a few comments about Vanini, however, Mersenne devoted a large portion of the volume to a critical analysis of the view of nature and religion which Vanini presents in his two books. The purpose of this article is, first, to explain why no one has hitherto discovered the extent of Mersenne's preoccupation with Vanini and, secondly, to examine briefly his basic attitude to Vanini's life and works.

Mersenne and Evolving Tonal Theory

Marin Mersenne, one of the most prolific writers to have devoted his attention to music, pursued his interest in the subject during a time which was critical in the development of tonal, harmonic theory. It was in the seventeenth century the century between Zarlino and Rameau that the first steps were taken by theorists to formulate the basic principles which were to culminate in Rameau's epochal treatises. The present study is an examination of Mersenne's conception of harmonic theory, with a particular focus on those ideas which seem to point toward future developments in tonal theory.

Music and computing: The present situation

There may be those who find that the terms music and computing form an unlikely pair. We remind them that the monochord, a device usually associated with music, was one of the first scientific measuring instruments. We need not stop there. In virtually any historical period one finds an interaction between music and science and mathematics. With respect to the seventeenth century, for example, Claude Palisca has observed:In any discussion of science in the seventeenth century, among the names that inevitably arise are those of Galileo Galilei, Marin Mersenne, Rene Descartes, Johannes Kepler, and Christian Huyghens. It is no mere coincidence that these... were all trained musicians and authors on musical subjects... because music until the seventeenth century was a branch of science and held a place among the four mathematical disciplines of the quadrivium beside arithmetic, geometry, and astronomy.