When I hear a melody in my head - the first thing I want to know is: Where's 'Do' (the Tonic)? This tells me whether I'm hearing a Major or a Minor Key Center [this is determined by whether I'm hearing 'me' (b3) or 'mi' (natural 3rd)] - with/against the Tonic.
When I first started doing this - I would reference (in my head) any Major sounds to 'C' Major -- and any Minor sounds to 'A' Minor. The reason I chose this reference was because it was comfortable. I used this method - even at times when I was hearing both - Major and Minor sounds (in relation to the same Tonic). I would spare anyone the confusion this caused by suggesting that we become comfortable with the Key Center of 'C' Minor (to get to know the sounds of the direct contrast between a Minor Key Center and a Major Key Center -- that share the same Tonic... the same perspective.
Realize that what we're doing here is combining the harmony of Two Major Scales ['C' Major and 'Eb' Major] into a single palette (with a single Tonic) to train the ear.
We begin by asking the question: In which Major Scale does the 'C' note reside as the sixth degree? The answer (in the case of Aeolian) is always one whole step + one half step up from the note in question -- this translates to the Eb Major Scale:
From the 'Relative Minor Tonic of 'C' - we see: 'C' Minor
Now we compare the 'C' Minor Key Center to the 'C' Major Key Center:
Here - we begin to move the chords (from 'C' Minor) that offer unique root movement (in relation to 'C' Major) 'up' into a new palette to explore:
I find it interesting that the chords in 'C' Minor (Aeolian) that offer 'unique' root movement (in relation to the key of 'C' Major) happen to be the I,IV, and V chords of its Relative Major (Eb Major).
As outlined in a previous post - the diminished triad can be heard as an extension of a Vma triad function - as a V7 (Dominant Chord). We can eliminate the diminished triads in our palette by adding the 7th (extension tone) to the V Chords of the two Major Keys we are combining: 'Eb' Major (Bb7) and 'C' Major (G7):
So that finally we end up with a palette (of likely chord types - and new possibilities for root movement) that looks like this: