Octaves: accounting for the multiple notes of the same key
We said earlier that the fifth string played open is an A note. We also established earlier that the name "A note" is a representation of the sound the string makes when it vibrates at 440 hertz.
Now look at the twelfth fret on that 5th string. You see this is also designated A. If you fret this string at the 12th fret it will not vibrate at 440 hertz. You have cut the string in half, so it will now vibrate at 880 Hz, or twice the frequency of the open string. If you will compare the two notes you will hear that they both share the A sound, though the one on the 12th fret is higher in pitch. The A on the 12th fret is one octave above the A, 5th string open. Notice also the A on the third string, 2nd fret. This A has the same pitch as the one on the fifth string, 12th fret, and is also one octave above the A of the fifth string open position.
Now play the A note on the first string, 5th fret. Notice that this A note has a higher pitch than either of the others we have looked at so far. This A on the first string is two octaves higher than the A on the open fifth string, and one octave higher than the A on either the fifth string 12th fret or the second string, 2nd fret.
Now, if you will look at your fretboard notation chart you will see that the other notes are all repeated on the fretboard in a similar manner. So anytime you play the major scale pattern, you will hit each of the notes within the particular keyed scale you are playing two or three times.