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Well, that's what it would look like on an infinite fretboard tuned in 4ths...obviously, in the real world, you have to step around the G-B string transitions
So I knew the names of the open strings ... that's the beginning
Next I realised starting on the top E string the 7th fret is an octave of the string before it. Except the B string, it's 8th fret.
The 12th fret is the octave, that was obvious
Then I applied this simple rule, all notes have sharps except B and E and so just filled in the gaps.
That's how I teach it to my students and most of them grasp it within a couple of weeks. I firmly believe you can over complicate things in an effort to make learning easier when really it just takes a bit of common sense.
I well remember in the early days of having lessons, that I was simply trying to improvise using A minor pentatonic whilst my teacher played some chords for me to play over. I knew the pattern at 5th fret level. I knew that I was perfectly capable of playing the pattern fretting with fingers 1,3, and 4.
Whilst improvising, I managed to fret the 7th fret on the D string with my middle finger, and became completely lost because the pattern I'd learnt didn't involve the middle finger. Panicking, I played the fret above with my third finger (it sounded horrid), so I then played the fret below with my index finger (again it sounded horrid). I just had to stop, and go back and restart on the bottom string playing A at the 5th fret. It taught me that I needed to know the fretboard properly.
Oh ... you mean the *actual fretboard* ...
JM build | Pedalboard plans
I started out on acoustic and know chords really well so that helps with the CAGED system.
I am quite good with notes on the fretboard as I have some mnemonics and patterns for the octaves that help. I also know scales going up and down strings but not across as well. I am not sure how we classify vertical and horizontal on the fretboard but I have no problem going per string but still struggle in the way we do pentatonics,across as I call it.
You need to look at the systems and decide which is the most efficient and easy to manage over a range of applications.
I could present a very strong argument for the system I use but others would disagree.
Slightly different in the classical world where things are taught a lot more uniformly.