In the Barry Harris method, we tend to view all chords in their major or minor 6th chord presentation:
▪ Major 7th chords we will typically turn into major 6th chords (or we treat the 7th as a borrowed diminished note from its scale of chords (details in the next chapter).
Minor 7th chords are already inversions of a major 6th chords (e.g: Dmin7 = Fmaj6).
▪ Dominant chords can be substituted by the minor 6th chord on their 5th scale degree (not always, it is a matter of style). Barry Harris calls this minor 6th chord the important minor.
A minor7♭5 chord (from now on I will call these ♭5 chords) is already an inversion of a 6th chord 3 half steps above it (e.g: D♭5 = Fm6).
A major triad is a usually a simplified version of a major-6.
A minor triad is usually a simplified version of a minor-6 or a minor-7 (context dependent).
Remember: diminished chords, ♯5 chords and ♭5 chords are by definition not chords – as they are not intervals on the major or dominant scale.
▪ When playing a 6th chord, you can use the root of the original chord or the new root (e.g: Dm7 = F6. Play Either D or F in the bass).
▪ The Major 6th chords on the I and the V are interchangeable (e.g: Cmaj6 and Gmaj6). It sounds better to keep the original root in the bass if choosing the major on the 5th.
▪ The pentatonic major and pentatonic minor scales are in essence an arpeggiated 6-chords. They should be viewed in this context.
A sus 4 is a triad with a raised 3rd that typically resolves back to the third (e.g: C+E+F > C+F+E).
▪ Dominant ♭9 chords should be viewed as an elegant voicing of a dominant chord. Use the root of the dominant chord in the LH and place a diminished chord – a half step above it, on top of it (e.g: LH C, RH C♯°).