Pythagoras might not have figured out what was going on if he used the weights. Also, the frequency is not simply related to the length when it comes to vibrating bars, like you find on a xylophone or a marimba the frequency is inversely proportional to the square of the length.
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If Pythagoras had studied a xylophone, instead of a lyre, things, again, might have turned out quite differently! Although these possibilities may seem a bit far-fetched, they are not as can be seen from a famous woodcut made in the Middle Ages to explain the theories of Pythagoras:. The purpose of the wood cut was to illustrate the Pythagorean ratios and how they applied to musical instruments. The lower right panel shows flutes whose lengths correspond to the Pythagorean ratios. 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.
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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.
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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.
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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. News Space 15 January Citizen scientists combine to identify longest chain of synchronised exoplanets ever discovered — and best described by the language of music.
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Richard A Lovett reports. In Johannes Kepler calculated the "divine" musical scales of the planets in the solar system. Now citizen science has found a strong musical equivalence in a chain of newly discovered exoplanets. Explore exoplanets citizen science astronomy.
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Richard A. Lovett is a Portland, Oregon-based science writer and science fiction author.
With the help of citizen scientists, exoplanet hunters have made one of their most unusual discoveries yet: a system called K that contains five planets orbiting in near-perfect resonances so close to their star that all five orbits are less than 13 days. Orbital resonances occur when planetary orbits are spaced so that they circle their star in numerically related patterns. In the case of K, this resonance is close to , which means that each planet makes three circuits of the star in the time it takes the next one out to make two. But K is the most dramatic example of this yet, with five planets — all between 1.
Specifically, their orbits are 2. Moreover, there are hints of a sixth planet, which, if it exists, would orbit in about 42 days. That raises the possibility that there might be as-yet unobserved planets in the gaps between Christiansen agrees. The fact that the planets wound up in such a smooth arrangement, she says, suggests that they migrated inward to their present positions very sedately, rather than via chaotic gravitational interactions.
That is, instead of having orbital resonances that are exactly in a ratio or 1. But even more exciting than the science, says Bryson, is the way in which the find was made.