The way I have parallel keys in my head is that a major key is always three half-steps higher than a minor key. I was trying to evaluate this on the circle of fifths and also during an exam, but I realized that at some point this can actually fail, namely when enharmonic spellings are at work.
For example, during an exam I was given the two following keys and was asked to write their parallels;
- C minor
- D♭ Major
What I did was to follow the principle I had in my head:
- C minor + 3 half-steps gives the parallel major key = D♯ major
- D♭ Major - 3 half-steps gives the parallel minor key = B♭ minor
So I failed in the first case. The correct answer is actually E♭ major.
But in the second case, did I succeed? B♭ minor is their on the circle of fifths, but A♯ is there too!!
I do not understand how this works. Why is D♯ major wrong but E♭ major instead correct? So why is the enharmonic spelling NOT there in case of E♭ major but it's there in case of B♭/A♯ minor?!