When we described a note as being high or low it is the pitch of
the note we are referring to. Pitch works in exactly the same way as
frequency, which is the rate of vibration of the material making the
sound (in this case the guitar string).
Take a look at these two different C notes as they appear on the guitar:
You can see that doubling the frequency produces the same note but
in a higher register. It is easy to see this on the guitar.
If you play your open E string then
play the note half way along the string (at fret 12) the note at fret
12 is another E. Halving the length of the string doubles the frequency:
In music, the distance between two sounds is called the interval. The
interval between the two Cs or the two Es is called an octave. In
terms of frequency, doubling the frequency of any note increases the
pitch by an octave.