Giambattista Benedetti
Encyclopedia
Giambattista Benedetti (August 14, 1530 – January 20, 1590) was an Italian
mathematician from Venice
who was also interested in physics, mechanics, the construction of sundials, and the science of music.
doctrine at that time was that the speed of a freely falling body is directly proportional to the total weight of the body and inversely proportional to the density of the medium. Benedetti's view was that the speed depends on just the difference between the specific gravity
of the body and that of the medium. As opposed to the Aristotelian theory, his theory predicts that two objects of the same material but of different weights would fall at the same speed, and also that objects of different materials in a vacuum would fall at different though finite speeds.
In a second edition of the Demonstratio (also 1554), he extended this theory to include the effect of the resistance of the medium, which he said was proportional to the cross section or the surface area of the body. Thus two objects of the same material but of different surface areas would only fall at equal speeds in a vacuum. He repeated this version of his theory in his later Diversarum speculationum mathematicarum et physicarum liber (1585). In this work he explains his theory in terms of the then current theory of impetus
.
It is thought that Galileo derived his initial theory of the speed of a freely falling body from his reading of Benedetti's works. Thus the account found in Galileo's De motu, his early work on the science of motion, follows Benedetti's initial theory as described above. It omits the later development which included the resistance of the medium and not just its density. In this early work, Galileo also subscribes to the theory of impetus.
In 1572, the Jesuit Jean Taisner
published from the press of Johann Birkmann of Cologne
a work entitled Opusculum perpetua memoria dignissimum, de natura magnetis et ejus effectibus, Item de motu continuo. This is considered a piece of plagiarism
, as Taisnier presents, as though his own, the Epistola de magnete of Peter of Maricourt
and the second edition of Benedetti's Demonstratio.
dated from around 1563, Benedetti proposed a new theory of the cause of consonance
, arguing that since sound
consists of air waves or vibrations, in the more consonant intervals the shorter, more frequent waves concurred with the longer, more frequent waves at regular intervals. Isaac Beeckman
and Marin Mersenne
both adopted this theory in the next century. In the same letter, he proposed the consonance measure of taking the product of the numerator and the denominator of a rational interval, which has been associated with the name of James Tenney
. When they sought Descartes' opinion on Benedetti's theory, Descartes declined to judge the goodness of consonances by such a rational method. Descartes argued that the ear
prefers one or another according to the musical context rather than because of any concordance of vibrations.
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...
mathematician from Venice
Venice
Venice is a city in northern Italy which is renowned for the beauty of its setting, its architecture and its artworks. It is the capital of the Veneto region...
who was also interested in physics, mechanics, the construction of sundials, and the science of music.
Science of motion
In his works Resolutio omnium Euclidis problematum (1553) and Demonstratio proportionum motuum localium (1554), Benedetti proposed a new doctrine of the speed of bodies in free fall. The accepted AristotelianAristotelian physics
Aristotelian Physics the natural sciences, are described in the works of the Greek philosopher Aristotle . In the Physics, Aristotle established general principles of change that govern all natural bodies; both living and inanimate, celestial and terrestrial—including all motion, change in respect...
doctrine at that time was that the speed of a freely falling body is directly proportional to the total weight of the body and inversely proportional to the density of the medium. Benedetti's view was that the speed depends on just the difference between the specific gravity
Relative density
Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity usually means relative density with respect to water...
of the body and that of the medium. As opposed to the Aristotelian theory, his theory predicts that two objects of the same material but of different weights would fall at the same speed, and also that objects of different materials in a vacuum would fall at different though finite speeds.
In a second edition of the Demonstratio (also 1554), he extended this theory to include the effect of the resistance of the medium, which he said was proportional to the cross section or the surface area of the body. Thus two objects of the same material but of different surface areas would only fall at equal speeds in a vacuum. He repeated this version of his theory in his later Diversarum speculationum mathematicarum et physicarum liber (1585). In this work he explains his theory in terms of the then current theory of impetus
Theory of impetus
The theory of impetus was an auxiliary or secondary theory of Aristotelian dynamics, put forth initially to explain projectile motion against gravity...
.
It is thought that Galileo derived his initial theory of the speed of a freely falling body from his reading of Benedetti's works. Thus the account found in Galileo's De motu, his early work on the science of motion, follows Benedetti's initial theory as described above. It omits the later development which included the resistance of the medium and not just its density. In this early work, Galileo also subscribes to the theory of impetus.
In 1572, the Jesuit Jean Taisner
Jean Taisner
Jean Taisner was a priest. In 1572, Taisner published from the press of Johann Birkmann of Cologne a work entitled Opusculum perpetua memoria dignissimum, de natura magnetis et ejus effectibus, Item de motu continuo...
published from the press of Johann Birkmann of Cologne
Cologne
Cologne is Germany's fourth-largest city , and is the largest city both in the Germany Federal State of North Rhine-Westphalia and within the Rhine-Ruhr Metropolitan Area, one of the major European metropolitan areas with more than ten million inhabitants.Cologne is located on both sides of the...
a work entitled Opusculum perpetua memoria dignissimum, de natura magnetis et ejus effectibus, Item de motu continuo. This is considered a piece of plagiarism
Plagiarism
Plagiarism is defined in dictionaries as the "wrongful appropriation," "close imitation," or "purloining and publication" of another author's "language, thoughts, ideas, or expressions," and the representation of them as one's own original work, but the notion remains problematic with nebulous...
, as Taisnier presents, as though his own, the Epistola de magnete of Peter of Maricourt
Peter of Maricourt
Pierre Pelerin de Maricourt , Petrus Peregrinus de Maricourt or Peter Peregrinus of Maricourt; was a 13th century French scholar who conducted experiments on magnetism and wrote the first extant treatise describing the properties of magnets...
and the second edition of Benedetti's Demonstratio.
Music
In a letter to Cipriano de RoreCipriano de Rore
Cipriano de Rore was a Franco-Flemish composer of the Renaissance, active in Italy...
dated from around 1563, Benedetti proposed a new theory of the cause of consonance
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
, arguing that since sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
consists of air waves or vibrations, in the more consonant intervals the shorter, more frequent waves concurred with the longer, more frequent waves at regular intervals. Isaac Beeckman
Isaac Beeckman
Isaac Beeckman was a Dutch philosopher and scientist, who, through his studies and contact with leading natural philosophers, may have "virtually given birth to modern atomism".-Biography:...
and Marin Mersenne
Marin Mersenne
Marin Mersenne, Marin Mersennus or le Père Mersenne was a French theologian, philosopher, mathematician and music theorist, often referred to as the "father of acoustics"...
both adopted this theory in the next century. In the same letter, he proposed the consonance measure of taking the product of the numerator and the denominator of a rational interval, which has been associated with the name of James Tenney
James Tenney
James Tenney was an American composer and influential music theorist.-Biography:Tenney was born in Silver City, New Mexico, and grew up in Arizona and Colorado. He attended the University of Denver, the Juilliard School of Music, Bennington College and the University of Illinois...
. When they sought Descartes' opinion on Benedetti's theory, Descartes declined to judge the goodness of consonances by such a rational method. Descartes argued that the ear
Ear
The ear is the organ that detects sound. It not only receives sound, but also aids in balance and body position. The ear is part of the auditory system....
prefers one or another according to the musical context rather than because of any concordance of vibrations.