Along with moving a note between strings, knowing how to move between octaves will be another useful tool in our kit.
Let's take a look at how we can get comfortable doing this.
Below, we have marked off every E note on the fretboard, up to the 15th fret. Take a moment and play all the notes, from lowest to highest. Then, work your way back down from the top to the open low E.
Next, start moving between two different E's. Can you tell the difference between moving up or down an octave, or playing the same note in a different spot?
Get a feel for the different octave shapes on the fretboard. Try to visualize these E notes on your own fretboard.
When you're ready, choose a new note. G, for example. Try to find as many G notes as you can on the fretboard, and then try to see the relationships between them. We want to be able to go up or down an octave at a moment's notice.
Below is a color coded chart marking off the most important octave relationships. (Extra credit - what did I omit?)
Blue - no octave difference, these are literally the same note.
Red - one octave apart.
Green - two octaves apart.
If you change the note in question from E to anything else, the positions on the fretboard will shift up or down, but the relationship between the notes will stay the same. These octave relationships hold true no matter what note you are playing!
Learning to see these shapes on the fretboard is the next step of your visualization journey. This is a step towards that sort of open-ended playing that seems to effortlessly flow around the fretboard. Be patient and keep at it! It will all pay off.