It was a surprise to me to learn that octaves have a physical. mathematical basis. I discovered this as a teen reading about how to make music on a computer, w

It was a surprise to me to learn that octaves have a physical. mathematical basis. I discovered this as a teen reading about how to make music on a computer, where the relationship of notes to frequency was explained. To my ear moving up an octave had always sounded like an arbitrary increase in pitch.