To answer your question we need to understand how you look upon scales, chords, arpeggios. etc. When I think of a scale I think in A, B, C's and 1, 2, 3's. For example:
Let's use the G scale. OK the G scale has one sharp, namely the F# so we are looking at these notes............................................G, A, B, C, D, E, F#, G
It's scale degree numbers are......... 1,. 2, 3, 4, 5, 6,. 7,.. 8
I use the major scale box pattern for everything I do.
Major scale box showing scale degree numbers.
G~~|---2---|-------|---3---|---4---| 1st string
D~~|---6---|-------|---7---|---8---|
A~~|---3---|---4---|-------|---5---|
E~~|-------|---R---|-------|---2---|4th string
And I play from fake chord sheet music transposed to Nashville numbers.
So to move on the fly from F to E is not a big deal. Instead of me using my Major scale box with the "R" root note placed on the 4th string first fret, which is an F note -- I just move my box to the 4th string 12th fret as that is an E note. Probably should have a fretboard chart about here as there is an E @ the 3rd string 7th fret you could use.
But to know all that I had to spend a lot of time with my major scale box. Running it up and down my fretboard till I could do any key in my sleep. Here is the box again:
Major scale box showing scale degree numbers.
G~~|---2---|-------|---3---|---4---| 1st string
D~~|---6---|-------|---7---|---8---|
A~~|---3---|---4---|-------|---5---|
E~~|-------|---R---|-------|---2---|4th string
Want the G major scale. Put the box's R on the G at the 4th string 3rd fret and all the G major scale notes await me in the box. Notice the F# is with in the box's pattern. As chords are made from a scale all seven of the chord's root notes await me within the box. On top of that If you think of chords having R-3-5-7 or R-3-5-b7 notes, help yourself they two are inside the box waiting on you.
Yep I think in A, B, C's to know where to place my box and then from there I think in scale degree numbers, aka 1, 2, 3's.
As Nashville numbers are the same as the scale degree numbers - Nashville numbers are in 1, 2, 3's. Yep I transpose my fake chord A, B, C's over to 1, 2, 3's. If the chords used are in the key of C I mark through all the C's with a 1. All the F's with a 4 and the G with a 5. Takes about two minutes to transpose a sheet of fake chord over to Nashville numbers. As the box is a major scale box if your song is in a minor key you transpose to the relative minor.
Yes I know you are saying, but, I'd like to add more than just the root. Fine where is the 5? From the root a 5 is always up a string and over two frets, or just below the 5 on the next string down. Some thing you can work on in your spare time... where can I find the 3? It going to be up a string and back a fret from your root note. How about a flat 3 or b3? Yes some things to work on...
So when the vocalist wants the song in something other than what our sheet music has, it's not a big deal, I just move my box, and ever thing I need awaits me within the box.
Ask specific questions....