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The short answer is 10 octaves.

A human with normal hearing (it declines with age) can hear frequencies ranging from 20 to 20,000 hertz. Octaves increase as frequencies double. So for instance is you started at 6,000 Hz, the next octave up would be 12,000 Hz. It takes ten times to double the frequency starting at 20 Hz to get to 20,480 Hz (20,40,80,160, etc.), which is about the highest a normal ear can perceive. Therefore a normal person's hearing spans 10 octaves.

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