What Greek mathematician came up with the idea of the octave and first focused on the pleasing sounds that some notes make together

Pythagoras

Explanation:

A tripling of frequency gives a perfect fifth one octave higher. They didn't know this in terms of frequencies, but in terms of lengths of vibrating strings. Pythagoras, who experimented with a monochord, noticed that subdividing a vibrating string into rational proportions produces consonant sounds.

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