Genius Mathematician Pythagoras Was Wrong About This One Thing in Music

Pythagoras is known in Mathematics for his theorem on right-angle triangles. However, the genius was reportedly wrong about something in music.

Pythagoras Was Reportedly Wrong About Musical Consonance

Pythagoras, the Greek philosopher, made a well-known attempt to apply mathematics to studying the beauty of music. He claimed that basic "integer ratios" in the sounds' frequencies, or tones, were necessary for the harmonic groupings of notes known as musical consonance to sound pleasing. Furthermore, the philosopher insisted that this was valid regardless of the instrument.

An international team of researchers conducted a study involving 4,272 volunteers. The participants were asked questions regarding their responses to specific chords. Mathematically speaking, those responses indicated a predilection for slightly flawed musical compositions.

"We prefer slight amounts of deviation," said music psychologist Peter Harrison from the University of Cambridge. "We like a little imperfection because this gives life to the sounds, and that is attractive to us."

Additionally, the team discovered that when it came to instruments that Western listeners are less familiar with-such as bells, gongs, xylophones, and a set of gongs known as the bonang-the integer ratios that Pythagoras loved so much might be ignored totally.

This Indonesian instrument revealed whole novel patterns of consonance and discord in study answers. These patterns could not be precisely mapped onto the scales chosen in the US and Europe but matched the musical scale utilized in Indonesian culture.

Harrison noted that certain percussion instruments were shaped so that when they resonated, the frequency components (tone) didn't follow the conventional mathematical connections. That was when they discovered intriguing events taking place.

This relationship between consonance and timbre may explain why note scale systems in various cultures differ from what those from the West are accustomed to.

Did Pythagoras Plagiarize His Right Angle Theory?

In related news, a new study suggests that the Pythagorean theory may not be Pythagoras' original idea. According to a modern mathematician, the theorem may have been known more than a millennium before the Greek philosopher was born, having been discovered on an old Babylonian tablet. This tablet introduces a notion akin to the theorem, prompting inquiries into its actual source.

Pythagoras is credited for the Pythagorean theorem after he noticed square tiles in a palace hall forming right triangles. He saw that the area of the square on the longest side, the hypotenuse, was equal to the areas of the squares on the two shorter sides. He then created a formal demonstration since he felt this principle applied to all right triangles based on this intuitive intuition.

Bruce Ratner, a mathematician with a doctorate in mathematical statistics and probability from Rutgers University, has carried out studies that refute the conventional belief that Pythagoras is the author of the theorem. The study published in 2009 resurfaced recently and presented proof from a clay tablet known as YBC 7289 that dated from 1800 to 1600 BC, suggesting that the Pythagorean theorem was known by Babylonian mathematicians more than a millennium before Pythagoras was born.

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