(from "Pythagoras and the Discovery of Irrational Numbers" by Daniel Vikum)
"It was within the field of music that Pythagoras first discovered a special correlation between numbers and the physical world.
According to historical accounts, Pythagoras was walking past a blacksmith when he became aware of the different sound pitches produced by pieces of metal being hit by hammers. He went on to experiment with other materials and found a consistent relationship between mass and sound pitch.
When measuring the pitches of vibrating strings he found that the sound pitch it produced was inversely proportional to its length. When he put two strings together and produced two tones he could describe intervals (the distance between two consecutive or simultaneous pitches) using numerical ratios.
He did however not merely discover that there existed a relationship between ratios and musical intervals, but that the intervals most pleasing to the ear also had the simplest ratios. He would call these intervals perfect intervals"
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