Final answer:
Pythagoras impacted our understanding of sound by developing the theory of harmonics and recognizing the relationships between numbers and sounds. His belief that all of nature is generated according to mathematical regularities led to the idea that musical tones and harmonies have healing powers.
Step-by-step explanation:
Pythagoras impacted our understanding of sound by developing the theory of harmonics. He recognized the relationships between numbers and sounds, specifically through harmonics and the intervals between notes. Pythagoras believed that all of nature is generated according to mathematical regularities, including the harmonics produced by the movement of planets and stars. This belief led to the idea that musical tones and harmonies could have healing powers and that sound could be understood and explained through mathematical principles.