Hi all you AM insatiable learners,
As some of you are aware, I’ve been known to dabble in and dispense some of my cobbled together music theory. Every now and then you come across someone with a very thorough grounding such as one of our new members Jean-Michel G. He wrote this reply to a query in a post. I thought it deserved a wider audience so I asked his permission to repost it. Hope you find it a helpful overview.
John

Minor Scales and Harmonization
The minor world is a tad more complex than the major one…
To begin with, there is not one but three relative minor keys for any given major key (and I am not even talking about the modes here, just plain major/minor relationship).
Let’s take an easy practical example: C major.
The notes of the scale are, as you certainly know: C D E F G A B
In functional harmony, these notes are called “degrees” and on each degree we can build a chord. If we use triads, we get: C Dm Em F G Am Bm(b5)
So, the 1 chord is C, the 4 chord is F and the 5 chord is G.
Since all major scales are structurally equivalent, we can abstract their harmonization as follows:
I ii iii IV V vi vii(b5)
(uppercase roman numerals indicate major chords and lowercase roman numerals indicate minor chords)
If we start that scale from the 6th degree (or equivalently from a tonic located a minor third lower) we get the natural relative minor scale: A B C D E F G
whose chords (triads) are Am Bm(b5) C Dm Em F G
The 1 chord is now obviously Am, the 4 chord is Dm and the 5 chord is Em.
Again, in general we have: i ii(b5) III iv v VI VII
One big limitation of this scale is that there is a full step between the 7th degree and the octave (between G and A); put differently, there is no leading tone and therefore no perfect cadence.
If we raise the 7th degree one half step, we get the so-called harmonic relative minor scale whose notes are now A B C D E F G#; the chords on each degree of this scale are now Am Bm(b5) Caug Dm E F G#m
In general: i ii(b5) IIIaug iv V VI #vii
The 1 chord is Am, the 4 chord is Dm and the 5 chord is E. Now we have the very conclusive V –> i cadence (E –> Am) similar to the V –> I cadence in major.
As you can see, these chords are not the same as those from the relative major scale.
The issue with the harmonic minor scale is the one step and a half interval between the 6th and the 7th degree (F and G#) which is difficult to sing; so we raise the sixth degree one half step to get A B C D E F# G#, which is the melodic relative minor scale of C major. The triads are now: Am Bm Caug D E F#m(b5) G#m
In general: i ii IIIaug IV V #vi(b5) #vii
The 1 chord is Am, the 4 chord is D (not Dm) and the 5 chord is E.
Again, these chords are very different from those in the relative major parent. You will also note that the A melodic minor scale is very close to the A major scale; the only difference is the flat third.
The melodic minor scale and its modes are very important in jazz.
In fact, the only minor scale that has the same chords as its relative major parent is the natural minor scale. To summarize, taking only the 1, 4 and 5 chords:
Natural minor: i iv v
Harmonic minor: i iv V
Melodic minor: i IV V