6th Intervals are Inverted 3rds
Playing a major scale in thirds is often confused with sixths on guitar. This is because thirds are often inverted on the fretboard with the third in the lower, or bass, position and the root on top. When this occurs the interval appears to be a sixth because you’re looking at it backward.
The guitar tab below illustrates a G major scale played along the string 2 (B) with third intervals following over on string 1 (E). In the scale, the notes are three steps away from each other, hence the term “3rds.” For example, G-B is a third interval because the G scale is G-A-B-C-D-E-F# with G-A-B being 1-2-3 or 1 and 3, a 3rd. Third interval shapes like those you see below are used in songs such as “Heaven” (intro) by Los Lonely Boys, “Wanted Dead or Alive” (intro) by Bon Jovi, and “Tequila Sunrise” (solo) by The Eagles.
E----7---8-----10-----12-----14-----15-----17-----19--|
B----8---10----12-----13-----15-----17-----19-----20--|
G-----------------------------------------------------|
D-----------------------------------------------------|
A-----------------------------------------------------|
E-----------------------------------------------------|
In the next set of tabs, the thirds from string 1 (E) have been transposed down an octave and placed on string 4 (D). But if you view the notes along string 4 as the roots, then the notes along string 2 appear to be a sixth away. G-B has become B-G. B to G is six steps when you count in the G scale (B-C-D-E-F#-G), hence the term “6th.” In actuality, these notes still produce third harmony because they are essentially inverted 3rds, but it musical vernacular they are technically referred to as sixths. Shapes like these are used in songs such as “Your Body is a Wonderland” (solo) by John Mayer, “Peace Train” (intro) by Cat Stevens and “Have You Ever Really Loved a Woman?” (verse) by Bryan Adams.
E-----------------------------------------------------|
B----8---10----12-----13-----15-----17-----19-----20--|
G-----------------------------------------------------|
D----9---10----12-----14-----16-----17-----19-----21--|
A-----------------------------------------------------|
E-----------------------------------------------------|
In this final guitar tab example you can see the same notes from the previous example with the roots on string 1 (E) and the thirds on string 3 (G). Shapes like this are used in songs such as “Brown Eyed Girl” (verse) by Van Morrison, “Patience” (intro) by Guns and Roses and “Finish What You Started” (solo) by Van Halen.
E----3----5-----7-----8-----10-----12-----14-----15---|
B-----------------------------------------------------|
G----4----5-----7-----9-----11-----12-----14-----16---|
D-----------------------------------------------------|
A-----------------------------------------------------|
E-----------------------------------------------------|
So you can see that 3rds on the guitar can take on many different forms. Some of the inverted shapes above are referred to as 6ths because guitar players are counting the interval from low to high. Using interval shapes for guitar is covered in Fretboard Theory Chapter 9: Intervals.
in the second example we accept that you mean string 4 (D)
Updated! Thanks, Patrick.