Music and Mathematics: A Pythagorean Perspective | University of New York in Prague
Pythagoras and the Theory of Music Intervals. The Move This made me think that it truly is an important relationship to study! I quickly discovered that the connection between mathematics and music is huge, with a wealth of . Plato was a Pythagorean who lived after the Golden Age of Ancient Greece. Plato. The mathematician, philosopher, scientist Pythagoras believed that the study of music and mathematics enabled a person to understand and. The Pythagorean, Quadrivium and Platonic classifications of mathematics Why study at UNYP . Based on his careful observations, Pythagoras identified the physics of intervals, or distances between notes, Within this harmonic or overtone series, there is a mathematical relationship between the frequencies – they are.
Starting from this argument and from the observation that their speeds, as measured by their distances, are in the same ratios as musical concordances, they assert that the sound given forth by the circular movement of the stars is a harmony.
Since, however, it appears unaccountable that we should not hear this music, they explain this by saying that the sound is in our ears from the very moment of birth and is thus indistinguishable from its contrary silence, since sound and silence are discriminated by mutual contrast. What happens to men, then, is just what happens to coppersmiths, who are so accustomed to the noise of the smithy that it makes no difference to them. But, as we said before, melodious and poetical as the theory is, it cannot be a true account of the facts.
There is not only the absurdity of our hearing nothing, the ground of which they try to remove, but also the fact that no effect other than sensitive is produced upon us. Excessive noises, we know, shatter the solid bodies even of inanimate things: But if the moving bodies are so great, and the sound which penetrates to us is proportionate to their size, that sound must needs reach us in an intensity many times that of thunder, and the force of its action must be immense.
The three branches of the Medieval concept of musica were presented by Boethius in his book De Musica: Harmonices Mundi Musica universalis, which had existed since the Greeks, as a metaphysical concept was often taught in quadrivium and this connection between music and astronomy intrigued Johannes Kepler, and he devoted much of his time after publishing the Mysterium Cosmographicum Mystery of the Cosmos looking over tables and trying to fit the data to what he believed to be the true nature of the cosmos.
The scales of each of the six known planets, and the moon, placed on five-line staffs.
- Musica universalis
- Music and Mathematics: A Pythagorean Perspective
Harmonices is split into five books, or chapters. The first and second books give a brief discussion on regular polyhedron and their congruencesreiterating the idea he introduced in Mysterium that the five regular solids known about since antiquity define the orbits of the planets and their distances from the sun. Book three focuses on defining musical harmonies, including consonance and dissonanceintervals including the problems of just tuningtheir relations to string length, and what makes music pleasurable to listen to.
In the fourth book Kepler presents a metaphysical basis for this system, along with arguments for why the harmony of the worlds appeals to the intellectual soul in the same manner as the harmony of music appeals to the human soul. Here he also uses the naturalness of this harmony as an argument for heliocentrism.
In book five, Kepler describes in detail the orbital motion of the planets and how this motion nearly perfectly matches musical harmonies.
The Connection Between Music and Mathematics | Kent State Online Master of Music in Music Education
Finally, after a discussion on astrology in book five, Kepler ends Harmonices by describing his third lawwhich states that for any planet the cube of the semi-major axis of its elliptical orbit is proportional to the square of its orbital period. Furthermore, the ratios between these extreme speeds of the planets compared against each other create even more mathematical harmonies. This works out because, like a string, the frequency of an air column e.
However, the panel on the lower left has a problem. As discussed above, the weights on the ends of the strings will change the tension in the strings.
But, the frequency of the strings is not simply related to the tension, and the strings will not sound according to the Pythagorean intervals. The examples in the upper panels are even more complicated, but suffice it to say, the bells, water glasses, and anvils will not produce the correct intervals. One of the defining features of the Middle Ages was a reverence for the knowledge passed down from the ancient Greek philosophers.
This knowledge was then applied to situations where it did not apply, but there was also no tradition of actually trying something out to see if it was correct.
Had anyone bothered to build any of the instruments except for the flute in the ratios prescribed in the woodcut, they would have found that the intervals were all wrong. A crucial step for the development of modern science was the willingness to test the theories of other to see if they really were correct or not. This period marked the beginning of the Renaissance, and we will hear more about Vincenzo later. However, he certainly set the stage for his son to come along and challenge the most basic beliefs about the Universe at the time.
While Pythagoras was making lost of progress in mathematics, geometry and music, the Greek astronomers of the time were not doing quite so well. They realized that there were certain "fixed" stars — stars whose relative position in the sky did not change through the seasons. They also noted that there were "wanderers" or planets planet is the Greek word for wanderer. These planets moved around relative to the background stars. To explain these observations, the astronomers figured that the fixed stars were attached to a large black sphere that defined the edge of the universe.
The planets had to be attached to moving spheres, with each planet on its own sphere. However, these spheres could not be black, otherwise, one could not see through to the stars in back.
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So, the spheres that the planets were attached to had to be crystal spheres. The "planets" that the astronomers knew about were: Seven, in all, so there were seven crystal spheres. The big question was: To the Greeks, the answer was obvious: Pythagoras just had his big breakthrough that mathematics could explain phenomena in nature and he now understood why there were seven notes in the musical scale. Thus, there must be the same reason for why there are seven crystal spheres.
The astronomers were so convinced of this that they called it the Music of the Spheres. This concept was so powerful that it led astronomy astray for years!How to Understand Music Intervals (What are Intervals?)
Even many great physicists were taken in by this vision that universe had an order that was musical in nature. The astronomer Kepler became obsessed with trying to fit the orbits of the planets to a musical scale!