Pythagoras, philosopher: “There is geometry in the humming of the strings, there is music in the spacing of the spheres”

The story has it that one day Pythagoras happened to hear a blacksmith hitting metal with hammers of different weights and he noticed each one created a certain tone. Form his observations, the ancient Greek philosopher and mathematician, who played the lute, discovered the principles of consonance and dissonance.

The father of numbers saw that two of the hammers made what seemed to be the same note but an octave apart. One happened to weigh six pounds and the other twelve pounds, and he realized that octaves must then correspond to a 1:2 ratio.

The other two hammers weighed eight and nine pounds, and they produced a perfect fourth note and fifth note, respectively, above the note produced by lightest hammer. This gave him the ratios of 3:4 and 2:3 for those two notes.

The harmony of math

With this information he went home to test his theory using strings. He was thus able to prove the mathematical principles of harmony and reportedly said: “there is geometry in the humming of the strings.”

He then thought about how the planets and stars are constantly in motion and concluded that they too must be making sound like the vibrating strings. “There is music in the spacing of the spheres,” he is quoted as saying.

This idea trickled down through the centuries and was picked up by later thinkers such as Johannes Kepler. The astronomer, astrologer, and mathematician from the seventeenth century, tried to explain the mathematical harmony of the universe in relation to music in his 1619 Harmonices Mundi (The Harmony of the World).

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