ItwasexactlyfromasmiththatPythagoraslearned-by"thedifferentsoundsfromhittingspotsondifferentdistancesontheanvil"-sohecouldconstructhismathematicallybaseddistinctionandstructureofthenotesofmusic.
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It was exactly from a smith that Pythagoras learned - by "the different sounds from hitting spots on different distances on the anvil" - so he could construct his mathematically based distinction and structure of the notes of music.