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Pythagoras and the Ratios: The Mathematical Foundation of Harmony
"Pythagoras and his followers discovered that the physical phenomenon of musical harmony is fundamentally governed by simple numerical ratios. By experimenting with the lengths of vibrating strings on a monochord, they demonstrated that consonant musical intervals—the octave, the fifth, and the fourth—correspond precisely to the ratios 2:1, 3:2, and 4:3. This realization transformed music from a purely aesthetic experience into a rigorous branch of mathematics, establishing the foundation for Western music theory and the concept of a mathematical universe. The Discovery of the Monochord To understand the Pythagorean discovery, one must look at..."
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