Vincenzo Galilei was among the first music theorists to advocate for a new system of tuning based on performance, instead of the mathematical principles of music set fourth by Pythagoras. Pythagorean music theory bases pitch on the mathematical proportions of dividing a string. Vincenzo's primary problem with this system is that, although it is great for the mathematician and the music theorist, it is impractical for the performer. All music based on this particular system of tuning would inevitably sound out of tune and unpleasant. In this learning leaflet learn about the tuning systems in the late-Renaissance period.
Why were experimental variables (like tilt) so important?
Galileo described his experiment with an inclined plane in Two New Sciences. In this work, Galileo furthered a research tradition in physics known as "impetus." This tradition, begun in the 6th century CE with John Philoponos, sought to explain motion. A body falling straight down accelerates too fast to be measured, so Galileo constructed his inclined plane in order to study it in slow motion. Galileo's inclined plane provided experimental confirmation of the law of free fall.
Giambattista della Porta was one of the most widely known European Renaissance magicians. In 1558, at the age of twenty three, the first edition of his book Natural Magic was printed. Due to its popularity and Della Porta's increased fame, he published an expanded second edition in 1589, increasing the original four books to twenty books. Learn more in this learning leaflet.
Is there a mathematical basis of the universe?
Johann Kepler's "Mystery of the Universe" is one of the brilliant illustrations in the history of astronomy. Kepler used the five regular Pythagorean solids to refute the major objections to Copernicanism. In this work he demonstrated that vast empty regions lying between the planetary spheres, which were required by Copernicus, were not wasted space. Rather, these gaps perfectly matched, within the limits of observational error, the geometry of the 5 regular Pythagorean solids.
How did knowledge spread in Galileo’s world?
Johann Schreck joined the Jesuit order in 1611, the same year that he used Galileo's telescope to observe the satellites of Jupiter. Upon becoming a Jesuit, Schreck joined the Jesuit mission in China, taking with him a scientific library of approximately 7,000 volumes as well as a Galilean telescope. Schreck's story is the beginning of a century-long exchange of scientific ideas between Europe and Asia.
Are they talking about physics as they stroll through the garden?
At a time when very few scientists were capable even of reading Newton's masterwork of physics, the "Mathematical Principles of Natural Philosophy," Madame du Châtelet mastered it and translated it into French. She also defended Newton in the Newton-Leibniz controversy.
How important in science is usability?
Prior to Newton, perhaps half a dozen astronomers accepted Kepler s three laws. Galileo was typical in ignoring Kepler s accomplishments. Yet this beautiful book is an exception. Maria Cunitz was not only one of the first astronomers to adopt Johann Kepler's astronomy, but because of the usability of her tables, she made the accuracy of Kepler's laws easy to grasp.
Can you identify the five regular solids?
Throughout history the regular solids were studied with keen interest by astronomers, mathematicians, artists, architects and philosophers. The Pythagoreans proved that there are only five regular solids: the cube, triangle, octahedron, dodecahedron, and icosahedron.