Today these harmonies are traced to the physics of vibrating strings, which move in patterns of waves. The Pythagoreans discovered these facts empirically by experimenting with strings of different lengths. And one three-fourths as long produces the fourth, also very harmonious. A string two-thirds as long produces the next most harmonious note, now called the fifth. A string (such as that on a violin) produces a note with a particular pitch a string one-half as long produces an extremely harmonious note to the first, now called the octave. Perhaps their most spectacular discovery was that musical harmony is related to simple whole-number ratios. The Pythagoreans were especially fascinated by the presence of numbers in the natural world. This terminology remains in use to the present day. The square numbers (1, 4, 9, 16,…) were arranged in squares, and the triangular numbers (1, 3, 6, 10,…) were arranged in triangles ( see figure). They represented numbers by arrangements of dots. Some Pythagorean speculations were mathematical. So important was the number 10 in their view of cosmology that they believed there was a tenth body, Counter-Earth, perpetually hidden from us by the Sun. The Pythagoreans recognized the existence of nine heavenly bodies: Sun, Moon, Mercury, Venus, Earth, Mars, Jupiter, Saturn, and the so-called Central Fire. Thus 10 also symbolized all possible spaces. A single point corresponds to 1, a line to 2 (because a line has two extremities), a triangle to 3, and space to 4. This number symbolized unity arising from multiplicity. The most perfect number was 10, because 10 = 1 + 2 + 3 + 4. All even numbers were female, all odd numbers male. The number 2 was symbolic of the female principle, 3 of the male they come together in 2 + 3 = 5 as marriage. The number 1 symbolized unity and the origin of all things, since all other numbers can be created from 1 by adding enough copies of it. The Pythagoreans invested specific numbers with mystical properties. It is not even known whether the Pythagorean theorem in geometry was actually discovered by him. Little is known of his life, and in fact he may be a composite figure to whom the discoveries of many different people have been attributed by his followers. Pythagoras was a Greek who thrived in the 6th century bce. The earliest known systematic cult based on the rule of numbers was that of the Pythagoreans. SpaceNext50 Britannica presents SpaceNext50, From the race to the Moon to space stewardship, we explore a wide range of subjects that feed our curiosity about space!.Learn about the major environmental problems facing our planet and what can be done about them! Saving Earth Britannica Presents Earth’s To-Do List for the 21st Century.Britannica Beyond We’ve created a new place where questions are at the center of learning.100 Women Britannica celebrates the centennial of the Nineteenth Amendment, highlighting suffragists and history-making politicians.COVID-19 Portal While this global health crisis continues to evolve, it can be useful to look to past pandemics to better understand how to respond today.Student Portal Britannica is the ultimate student resource for key school subjects like history, government, literature, and more.This Time in History In these videos, find out what happened this month (or any month!) in history.#WTFact Videos In #WTFact Britannica shares some of the most bizarre facts we can find.Demystified Videos In Demystified, Britannica has all the answers to your burning questions.Britannica Explains In these videos, Britannica explains a variety of topics and answers frequently asked questions. Britannica Classics Check out these retro videos from Encyclopedia Britannica’s archives.
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