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 (M6) chords (or we treat the 7th as a borrowed diminished note from its scale of chords – details in the next chapter).
Minor 7th (m7) chords are already inversions of M6 chords (e.g: Dm7 = F6).
▪ Dominant (Dom / V) chords can be substituted by the minor 6 (m6) chord on their 5th scale degree (not always, it is a matter of style). Barry Harris calls this m6 chord the important minor.
A m7♭5 chord is already an inversion of a m6 chord 3 half steps above it (e.g: Dm7♭5 = Fm6).
A major triad is usually a simplified version of a M6.
A minor triad is a simplified version of a m6 or a m7 (context dependent).
Remember: diminished chords, dominant ♯5 chords and dominant ♭5 chords are not chords by definition – as they are not intervals on the major or dominant scale. Also note that dominant ♯5 and dominant ♭5 function as a dominant chord in tunes.
▪ 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 M6 chords on the I and the V are interchangeable (e.g: C6 and G6). 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 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.
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 its origin diminished chord (a half step above it), on top of it (e.g: LH C, RH D♭°).
In the Barry Harris method we focus on the octave, no extentions. So the extentions need to have a rationale within the octave.
♯9 = ♭III
♯11 = ♭V
♭13 = ♯V