Theoretical key

In music theory, a theoretical key or "impossible key" is a key whose key signature has at least one double-flat or double-sharp.

Double-flats and double-sharps are frequently used as accidentals, but placing them in the key signature (in music that uses equal temperament) make the music generally impractical to read.

For example, the key of F♭ major is a key of this type, because its corresponding key signature would contain a B (on its subdominant degree). An equal-tempered scale of F♭ major comprises the same pitches as the E major scale, so that the two scales sound exactly the same; such key pairs are said to be enharmonically equivalent. Consequently, the theoretical key of F♭ major is usually notated as E major.

Even when enharmonic equivalence is not resorted to, it is more common to use either no key signature or one with single-flats and to provide accidentals as needed for the Bs, than to incorporate double-flats into the key signature. Nevertheless, examples of the latter can be found (see below).

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