The octave on guitar
On guitar, the octave is seven frets up and eight frets up when you cross to the next string, and twelve frets up along one string.
One pair of strings is the odd one out, because the gap between those two strings is different from the rest. Most players learn that exception as a rule of its own.
You do not have to memorise all 132 frets. You need two strings and one shape. First learn the natural notes, the ones without sharps or flats, on the low E string: E open, F at fret 1, G at 3, A at 5, B at 7, C at 8, D at 10 and E again at 12. Then learn the same walk up the A string, starting from A.
The octave shape does the rest. From any note on the sixth string, move two strings across and two frets up, and you have the same note an octave higher. From the fifth string the move is the same. When the shape crosses onto the top two strings it becomes two strings across and three frets up, because of the uneven gap before the B string.
Together, the two anchor strings and the octave shape reach every note on the neck, and neither asks you to count up from the nut.