Number as the Principle of All Things

The best known account of how the Pythagoreans found number in music is a story about a blacksmith's forge, reported centuries later by Nicomachus, Pythagoras is said to have passed a smithy, noticed that hammers of different weights struck an anvil in intervals that sounded consonant or dissonant together, and worked out from the weights the whole number ratios that later grounded the doctrine. Riedweg's study is direct about the problem with the tale. The physics does not hold. A hammer's pitch when it strikes an anvil is not governed by its weight in the way the story requires, so the ratios the legend has Pythagoras reading off four hammers could not actually have produced the consonances it credits him with discovering, and modern scholarship treats the whole scene as a later illustrative fiction rather than a preserved memory of an actual event. What the Pythagoreans almost certainly used instead was a stretched string, a monochord, where length and pitch really do stand in the simple ratios the tradition celebrates, a far less colourful but physically sound method that never produced a story worth retelling for two thousand years. The blacksmith tale survived anyway because it dramatises the doctrine better than the true method does, an anvil and four hammers making a more vivid scene than a single string, which leaves this discovery resting on evidence the story itself cannot supply.