For those of you trying to find some theme to this whole exercise, maybe this will clear it up for you a little, might want to look at the chart while I explain it, since I myself and still working on it.
The easiest way I can explain what I see is by using the E on the 12th fret. if you count back down the fretboard 5 frets, and drop down one string, you will be on the same root note. so on the A string your now on the 7th fret. 5 more frets and one string lower, your on the D string 2nd fret. This leaves you with one more fret to count before the cycle repeats again from the 12th fret on the next string, so counting D string 1st fret, starting over on G string 12th fret we need to go 4 more frets to make it equal 5 frets total again.
the exception is of course the B string which the distance will only be 4 frets distance.because all of the strings are a perfect 4th away from each other in tuning, and the B string is a (major 3rd?). take a look at the picture and count back 5 frets and drop down a string.
I understand the terminology is incorrect as the strings start on the little e and go "down" to the big E but I'm talking perspective from your face looking down at the strings. This observation doesn't change no matter what note you pick anywhere on the board. you can alternatively count "up" 5 frets and "up" one string (except for the B string where the distance will still always be 4 frets) and it never changes. Pretty slick I think, as long as you can do simple math this will work out perfectly. (assuming my ability to explain what I'm seeing is clear enough). Pop up the image in a new window and check out what im talking about, after checking it out you should see exactly what I'm talking about. Hope it helps make it "click" for some of you.