If you did a change of variables
Consider the two groups as permutations of points on a plane or something.
You could visualise A6 as all the even permutations of the points of a hexagon.
Take 4 of the points on a hexagon, then can you get all permutations of those 4 points in A6?
All the even permutations are obvious, and the odd ones can be made even by swapping the extra 2 points you didn't choose!
Would you even need an auditory organ to get music? It would be transmitted as an electromagnetic wave, so it isn't a given that it should be converted into sound. It could be converted into a visualisation or vibrations or something else. It's conceivable that a biological organ could exist which can directly pick up radio waves.
I don't think music could send any practical message other than- hey we exist and we like this kind of patterns. It's not even necessary that an ETI would appreciate music...