Theoretical key

In music theory, theoretical keys or impossible keys are keys with key signatures that contain one or more double-flats or double-sharps.

Double-flats and double-sharps are used in music as accidentals, but they are rarely placed in the key signature (in music that uses equal temperament), because it would make reading the key signature very difficult.

For example, the key of G♯ major is rarely used to write music down, because its key signature has an F. An equal-tempered scale of G♯ major has exactly the same notes as the A♭ major scale. Key pairs like this are called enharmonically equivalent. So the theoretical key of G♯ major is usually written with the key signature of A♭ major.

G♯ major:	G♯	A♯	B♯	C♯	D♯	E♯	F
A♭ major:	A♭	B♭	C	D♭	E♭	F	G