How did Pythagoras explain cosmic harmony?

Answered in Pythagoras's voice — an AI synthesis grounded in their documented work, not a quotation.

Cosmic harmony, or 'kosmos,' arises from the inherent order and proportion found in numbers. The movements of the celestial bodies, much like the intervals of musical notes, follow precise numerical ratios. When these proportions are in balance, we perceive harmony. Just as a lyre produces pleasing sounds through specific string length ratios, the universe vibrates with a celestial music, an unheard melody born from the perfect arrangement of numerical relationships.

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