For every key on the piano, we have a scale. However, the number of scales we commonly see in music does not match the number of keys we have to play them with. We have twelve keys in total, but we have fifteen major scales (I’ll also address minor scales a bit in this post) and could easily have more. The reason for this is something called enharmonic notes.
Enharmonic notes are much easier to visualize with a piano, so here ya go:
Take a look at the black keys first, they’re simpler. Any one of those black keys above can be called by two different names, in terms of flats or sharps. Sharps are for black keys above their namesake. Flats are for black keys below their namesakes. For instance, as you can see, the black key above C and below D is called either C-sharp or D-flat. (You can also express the white keys B, C, E, and F like this; B is C-flat, C is B-sharp, E is F-flat, and F is E-sharp.)
With five black keys, we now have ten “keys” because of their nomenclature. Unfortunately, things get even more confusing, because we don’t use every new key. For major keys, we have all the flats (Db, Eb, Gb, Ab, Bb) but only two sharp keys (C# and F#). The reason for this is that we have a pattern to all major scales. Just because the scale is moved up or down on the piano does not change the way it is formed. When you try to adhere to that pattern in the wrong key (D#, for instance), you’ll find it impossible unless you use special accidentals, and traditionally, we don’t like these special accidentals to be in major scales. So we simply eject inconvenient scales like D# and stick to more familiar ones like Eb, which sound the same but are spelled differently.
For the same reason of sticking to a pattern, minor scales include only some enharmonic keys. In minor, we have all the sharp keys (c#, d#, f#, g#, a#) and only a few flat minor keys (eb, ab, bb). So, if you want to use the parallel minor of Db major, you can’t use Db minor – you always move to C# instead. Similarly, if you’re in A# minor and want to use the parallel major, you have to use Bb.
So, what if we wanted to break the rules and use special accidentals in a major key anyway? What would happen? Well, you would be in what we call a “theoretical” key.
But firstly, I’d like to define “special accidental”: it is not a normal sharp or flat but a double sharp or double flat. Theoretical keys are, by definition, keys which would not be possible without double sharps or flats. They are highly impractical when it comes to understanding, composing, and playing the music. They also beg the question, why use a new, contrived key when it sounds exactly the same as its counterpart with a different name?
Well, that’s an interesting question, and surprisingly, it does not have a straightforward answer. Most musicians think they hear a difference between two keys that sound the same but are spelled differently. They say you play sharps differently than flats. And I do have to agree with that. It is a fact that the way you spell a chord or scale can change its function, its harmonic direction, and even its atmosphere. But is this mostly our imagination, that we can hear differences between keys?
I don’t want to get caught up in an overly academic conversation about our equal temperament tuning method and whether it makes theoretical keys different from their enharmonic keys. But whether or not they sound different based on their spelling, theoretical keys are limited in two ways: concerning the human ear and concerning the human mind. At a certain point, I don’t really care if a piece is in C-flat-flat-flat (a very theoretical key!) or A major because I wouldn’t hear much of a difference, and I wouldn’t want to play in it because it’s just too complicated. That’s why it’s theoretical. Honestly, if you completely transposed a piece from Ab major (four flats) to F# major (six sharps), changing the actual pitches, most musicians wouldn’t really care. So, no one is going to concern themselves with theoretical keys much, although it is an interesting concept which offers an original way of thinking about an “average” key.
Very few composers have ventured into theoretical keys. All they do is hint at them, really. Debussy hinted at, or at least meant, the theoretical key of D-flat minor when he moved from D-flat major to C-sharp minor in his Clair de Lune.
That should have been a parallel minor modulation, but since D-flat minor does not exist except as a theoretical key, Debussy was forced to move to the enharmonic key of C-sharp instead.
To conclude, I think my main point is that music isn’t perfect! (And theoretical keys are cool. I’m geeking out over them, to be honest.) There will always be certain aspects of music that are impossible to box up into neat packages.