After some internet research, I've chosen Roberto's suggestion of Fugue
as the name of the new game. While the fugue as a musical form originated
in the Baroque period, it continued through the Rococo period and into the
Classical period. Seems fine for a Rococo/Ultima blend.
Classical Music's 'holy trinity' (J.S Bach, Mozart, Beethoven) have all
used the fugue form.
