The jazz or “real” melodic minor scale is simply a major scale with a lowered 3rd degree. Notice how this scale gives us a combined major and minor effect.
By lowering the 3rd of the A major scale, this scale becomes an A jazz minor scale.
RULE: Play a jazz melodic minor scale one half-step higher than the root of the dominant 7th chord (i.e. for G7, play Ab melodic minor scale).
Because this scale contains a B (C ) note (the 3rd of G7), it gives us a strong G7 chordal sound.
Starting on the root of the jazz minor scale, the arpeggio we derive is an A m(maj7) arpeggio. Remember, this is simply an A maj7 or 9 arpeggio with a lowered 3rd degree.
Tension and Resolution with Jazz Minor