This is really helpful and interesting. But what do the three relationships, Melodic, Harmonic and Formal mean?
I think you wanted to say that F was a perfect fifth below C - or have I got it wrong?
First, yes, I meant that F was a P5 below.
As far as the three common forms of minor -- Melodic, Harmonic, and Natural (Aeolian mode), those are basically inflections of the minor idea. Minor has always been less stable and more chromatic than Major.
The basis of keyness in tonal music has been the two 5th relationships to "tonic" -- the 5th above called "dominant" and the 5th below called "sub-dominant" (the names are mired in the murkiness of Medieval modal chant theory). To establish that we are in the key of C (major or minor) music often establishes either or both of the 5ths (F and G) as temporary or large scale tonal areas. This is true whether we are in major or minor.
These two 5ths are often called the "Tonal Degrees" of the scale because they are constant regardless of most modes (Major, Mixolydian, or most of the minors.)
the other scale degrees are much more flexible, particularly the 3rd above and below tonic.
The 3rd above tonic is the one that determines major or minor -- a major 3rd above (E nat. in C) makes the key major (as long as the two 5ths remain perfect), and a minor 3rd above (Eb in C) makes it minor. Thus
C major: C D E F G A B C
C minor: C D Eb F G A B C (melodic minor [ascending in classical use])
For the key of C -- as long as we have C F G and E nat., it is major; and as lon as we have C F G and Eb, it is minor.
Now if we lower the 3rd below (Ab here) we get:
C minor: C D Eb F G Ab B C (Harmonic minor).
If we lower the 7th degree to Bb, we get "natural minor" or Aeolian mode. This, by the way, has been used much less (regardless of what the old theory books say -- its importance was a figment of Rameau's imagination) -- than the Dorian minor or even phrygian (which I'll get to in a minute.)
C minor: C D Eb F G Ab Bb C (Aeolian minor or "Natural minor")
It does happen to be the "descending form" of classical Melodic Minor, but I have come to realize that that is possibly a false premise, but that's for a different discussion.
The next common minor scale (even Bach used it and identified it's basis in the preface to the "Well-Tempered Clavier") is Dorian minor. This keeps the maj 6th of major, but lowers the 7th (Bb here)
C minor: C D Eb F G A Bb C (Dorian minor)
This scale actually occurs frequently in pieces that are said to be in "Melodic Minor" as well as one of the common modern modal areas for improvisation and is the most common scale to use for the II in a II - V progression.
Finally, we can take the "Natural minor" and lower the 2nd step (Db in C) and we get the Phrygian mode:
C minor: C Db Eb F G Ab Bb C (Phrygian minor).
While phrygian is not often used classically, the lowered 2nd step has often been borrowed in other modes (major or minor). Classically it was the "Neapolitan" and some refer to it as the "phrygian 2".
In any case, All of these can be referred to as minor, and, while some more than others, they have all been used as a tonal basis for a piece or section.
We can almost say that a minor key is:
C Db D Eb F G Ab A Bb B C (not too far from a chromatic scale) (only C, F, and G can not be altered.)
In reality, "borrowing" between Major and minor became commonplace starting at least with Beethoven.
As I said at the beginning, Major is more stable and it has had little variation -- the most common being Mixolydian (Major with a b7 - C D E F G A Bb C), which is found frequently in folk music and, as a cross with Dorian (giving E and Eb), is related to Blues.
I hope that this gives you some food for thought.
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