An OCTAVE is a note that is the same note but only notes higher or lower. 3

8

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An OCTAVE is a note that is the same note but only 8 notes higher or lower.

Explanation:

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to answer your question:

f(x)= a^x.  if x=0, f(x)=1  if x=1, f(x)=a  if x=1, f(x)=a^a