But when a relative key is on the opposite side of the circle from its home key , then in theory modulating to that key would involve adding so many sharps or flats that double-sharps and double-flats would have to be written in the key signature . But when a relative key ascends the opposite side of the circle from its home key , then theory suggests that double-sharps and double-flats would have to be incorporated into the notated key signature .