I don't know the jazzers explanation for this, as they live on a parallel universe, but I can tell you a little about the 'half over five' concept that he says this is based on.
Another name is the flatted submediant. The submediant in a major key is the vi chord. In the key of A major that's F#minor. A chord sometimes built on the flatted submediant is F major (FAC). Two notes of this chord are chromatic to the key of A major that we're in, i.e. F and C.
Now, it's a general rule of harmony that if you chromatically alter a note it will assume a perceived tendency to move in the same direction in which its been altered.
So if the normal note of the key(of A) is F# but you chromatically alter it (in this case 'flat' it) to be F natural, you will hear (all things being equal) that it wants to continue in that direction and resolve to the scale note E. It doesn't want to go back to the scale note F#.
The chord built on the flatted submediant (bVI chord) is known for its split personality, especially when we add the flat seventh note Eb to make it a 7th chord (F7 in this case)
What happens here is that it seems to want to resolve in an unconventional way. Normally in a seventh chord, the seventh itself wants to fall a half step - but in the case of this chord we can hear that the seventh wants to rise. That indicates that what we're hearing isn't the 7th note Eb at all but the raised 6th D# rising to E.
Although the chord is called F7 (FACEb) - it's harmonic movement in this context reveals that it's actually F augmented 6th (F A C D#)
The chord has two standard resolutions - the first is to chord V
Note resolutions: (F7 to E)
F falls to E (because it's a chromatically altered scale note F#)
A falls to G#
C falls to B (same reason as F - this can be changed if the avoidance of parallel perfect fifths is important)
Eb rises to E (indicating that it's actually D#)
The resolution to chord I (F7 to A) is less common.
F falls to E
A stays the same
C rises to C# (here it acts more like B# than C because in any other context, a true C (if flatted from C#) would prefer to fall than rise.)
Eb rises to E (again showing that it's really D# rather than Eb, which like C would much prefer to fall)
As far as I can see - his use of the F melodic minor is following this principle and includes even one more note that has been chromatically altered and undergoes a similar personality change. The flat third of the melodic minor scale Ab, if heard as G#, will rise naturally to A.
This type of dual personality exhibited by chords such as the augmented 6th is a common tool in modulation, (called enharmonic modulation) You think you're hearing one thing only to realise you've been intentionally misled - and suddenly you're in a new key and wondering how you got there :lol:
