The Basis for my query was that, Mode Scales' can be interpreted in either 'Series and/or 'Parallel... It turns out That, 'C (over )Aeolian, starts in the 6th degree, therefore counting backwards from C, is, Bb, Ab, G, F, Eb. The chords over the steady C bass note are the vi, IV & V in the key of Eb major, which are Cm, Ab & Bb. Used as a Mode Drone backing to compliment the Aeolian C:.
Usually when people talk about 'parent major scales' they are referring to the relationship between modes and keys. For example, D-dorian is all natural notes starting with D, or in other words a key signature of no flats or sharps. The major scale with no flats or sharps is C-major making C major the parent major scale of D dorian.
With that in mind, it doesn't make sense to ask what the parent major scale of a major scale is. The major scale that shares a key signature with A major is, well, A major. There is a mode - the Ionian mode - that is identical the major scale, so you might ask what the parent major scale of A Ionian is, and that would be A major.
It's nor clear how you ended up with E-flat.
The parent major of A IS A! I think what you're getting at is to, say, take a phrygian mode of E, for example, and calculate what the key sig., or major scale notes, it possesses.In this example, phrygian starts on the 3rd note of its parent scale, thus that will be C major. All the notes in E phrygian are those found in C.
It may be less complicated to consider the formula a different way."I don't play like my aunty Lou" works for me. No, I'm not ga-ga! It's a mnemonic for Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian.
Let's go back to E Phrygian.Using the above list, it's the third on it. Always going back to Ionian, that will give us C major (E>D>C). It will work for all the modes of majors, or come to think, all modes.
Your problem, I think, stems from not knowing the notes which make up key signatures. I say this, as you mixed up a key with 3# and one with 3b. Any mode of a particular key MUST have the same notes as its parent, obviously, otherwise they can't belong together.