Attempted solutions to the Enigma commonly propose a well-known melody which is claimed to be either a counterpoint to Elgar's theme or in some other way linked to it. Musical solutions of this sort are supported by Dora Penny and Carice Elgar's testimony that the solution was generally understood to involve a tune, and by the evidence from an anecdote describing how Elgar encoded the solution in a numbered sequence of piano keys. A rival school of thought holds that the "larger theme" which "goes" "through and over the whole set" is an abstract idea rather than a musical theme. The interpretation placed on the "larger theme" forms the basis of the grouping of solutions in the summary that follows.