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Watch the Relative Melodic Minor online guitar lesson by John Stowell from Modern Jazz Improv

If an augmented major sound is called for in a tune, you can use the relative melodic minor over the major: the #11 that this melodic minor generates over the major sounds fine as well, as long as you reference the #5. If the augmented major chord happens in a tune for a bar or more, there are some interesting possibilities with the implied V chord and the melodic minor substitutions of it (i.e., A mel mi/C maj #5#11 to Ab mel mi as G7 alt). The augmented major chord first appeared in jazz in the 1960's compositions of Wayne Shorter, Herbie Hancock and Keith Jarrett, among others.