M.F. Burnyeat, 22 February 2007
It is hard to let go of Pythagoras. He has meant so much to so many for so long. I can with confidence say to readers of this essay: most of what you believe, or think you know, about Pythagoras is fiction, much of it deliberately contrived. Did he discover the geometrical theorem that bears his name? No. Did he ponder the harmony of the spheres? Certainly not: celestial spheres were first excogitated decades or more after Pythagoras’ death. Does he even deserve credit for his most famous accomplishment, analysing the mathematical ratios that structure musical concordances? Possibly, but there is little reason to believe the stories about his being the first to discover them, and compelling reason not to believe the oft-told story about how he did it. Allegedly, as he was passing a smithy, he heard that the sounds made by the hammers exemplified the intervals of fourth, fifth and octave, so he measured their weights and found their ratios to be respectively 4:3, 3:2, 2:1. Unfortunately for this anecdote, recently rehashed in the article on Pythagoras in Grove Music Online, the sounds made by a blow do not vary proportionately with the weight of the instrument used.