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 major 6th chords (e.g: Dm7 = F6).
▪ 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 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 not chords by definition – 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: 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♭°).
Extension chords (♯9,♯11,♭13, . Instead: ♯17 etc)
In the Barry Harris method we focus on the the octave, no extensions. So the extentions need to have a rationale within the octave.
Rationale: Extension chords can be understood through the tritone context. For example, when C is the root note, G♭ is its tritone (dominant), and D♭m6 is the min 6th on the 5th (= a half step above I). Now, the D♭m6 + its diminished chord (C-E♭-G♭-A) provide us with the right context and rationale for the extension chords.
So:
♯9 = ♭III
♯11 = ♭V
♭13 = ♯V