A couple of suggestions: it might be interesting to try different types of scales like a pentatonic scale and maybe add a way to disallow certain intervals such as 2nds for example.
Consider adding percussion tied to certain kinds of moves. For example, you could have a distinct sound when someone is put in check, so there’s an auditory cue.
This last one would be a bit trickier, but you might also experiment with changing the timbre to create a sense of suspense as the material advantage (or some engine's eval score) starts to favor one player or the other.