Barry said: “Every major chord has one important major 6 chord (found on the 5th)”

The important major chords and important minor chords are always built on the 5th of a scale.

The ‘important majors and minors’ are important because they provide an additional way to create chord voicings that add color and movement within the chord.

The additional way to create movement on a major chord is to use the major 6 diminished scale on the important major chord (found on the 5th).

Here’s an example on a C major 6 chord:

So, whereas the major sixth diminished scale on the root of a major (or minor) chord introduces the 7, 9, 11 and #5 degrees, the major sixth diminished scale on the 5th introduces the 7, 9, # 9 and the #11 degrees. One could say that they are complementary, each providing a slightly different color palette.

A similar principle applies to dominant chords:

To create movement on a dominant chord, use the minor 6 diminished scale on the important minor of a dominant (found on the 5th).

Here’s an example on G7 chord:

The diminished notes highlight the 9, 13, #9 and #11.

There are other chord superpositions that Barry didn’t call important majors or minors, but were used in some of his exercises:

1.For 7sus chords, play a major sixth diminished scale on the 7th of the dominant chord.
For example, for G7sus, play F major 6 over G7.

Moving up and down the F major 6 diminished scale highlights the 9, #9, 11, #11 and 13:

2.For 7susb9, play a minor sixth diminished scale on the 7th of the dominant chord.
For example, for G7susb9, play F minor 6 over G7.
Moving up and down the F minor 6 diminished scale highlights b9, #9, 11, #11, 13.