I have taught guitar on & off since I was 21. At 40, shortly after a major shift in my life's direction, music became the focal point. I began teaching in a music store on the eastside of Cincinnati, Ohio. I noticed how many players at all levels of experience struggled with knowing where to go on the neck when it was time to take a solo.
I remember uttering what I called a non-prayer. I thought out loud that there has to be an easier way to explain scales & theory as it applied to the guitar neck. Within 2 weeks I saw the beginnings of what I now refer to as the system of "2s & 3s" (see chart). That early vision has grown & expanded to encompass much of what I now see when I look at the neck.
minor 2s & 3s
Using "2s & 3s", here's my shortcut for the minor pentatonic scale in the key of "A" minor. The big triangles are the minor root (the 2nd note of 2). The big red dots are the relative Major root (the 1st note of 3). The notes are "G" & "A" for the 2 notes plus "C", "D" & "E" for the 3 notes. Set up on the 6th string with your ring finger on the minor root. A good fingering to try would be: index & ring finger for the 2 note part. Then index, ring, ring for the 3 note part. This results in a kind of step or tiered alignment across the neck. (see chart)
Starting on the 3rd & 5th frets of the 6th string, you play the 1st 2 notes. Changing to the 5th string you play the 3 notes on frets 3, 5 & 7 using the index, ring, ring combo. This is your 1st "2 & 3" sequence & moves you down the neck. Now you are positioned over frets 5 & 7 for the next "2 & 3" sequence. On the 4th string you play frets 5 & 7 for the 2 note part. Then frets 5, 7 & 9 on the 3rd string for the next 3 note part. This "2 & 3" sequence moves you into the next octave of the scale.
Due to standard tuning, you now have to make a 1 fret adjustment to continue on to the next "2 & 3" sequence. So instead of frets 7 & 9, you are now on frets 8 & 10 of the 2nd string for the 2 note part, followed by frets 8, 10 & 12 on the 1st string for the 3 note part. This is a 3rd octave of the scale.
The traditional, individual pentatonic boxes generally give you a 4-5 fret glance at what notes are available. This 6 string pass reveals 10 frets of info for a better panorama of sonic possibilities.
Major 3s & 2s
Using "3s & 2s", here's my shortcut for the Major pentatonic scale in the key of A Major. The big red dot is the Major root (the 1st note of 3). The big triangle is the relative minor root (the 2nd note of 2). The notes are "A", "B" & "C#" for the 3 notes plus "E" & "F#" for the 2 notes. Set up with your index finger on the Major root. A good fingering to try would be: index, ring, ring for the 3 notes. Then index & ring finger for the 2 note part.
The Major "3s & 2s" has a similar tiered alignment as you move through the 3 & 2 note sequences. Even the 1 fret adjustment still applies as you cross over from the 3rd string to the 2nd. Once again you have 10 frets of info.