[Retric]

First you are ignoring chords and note timing which is an option. Second there are only 1,327 named openings and variants in chess many of them are known to be inferior so you do see a lot of repition in the beginnings and endings of Master level games.

As an order of magnitude each note in a melody is from a low end estimate of ~1,000,000 completely valid options though musical style will limit this.

Thus from an encoding standpoint a chess game is theoretically a much lower entropy. But, a sufficiently constrained melody may be lower but probably not. Consider an easy example: https://m.youtube.com/watch?v=DtvNAQ8KOqI

[logicallee]

This is totally splitting hairs and I don't think we're adding to the discussion anymore. if you'll drop me an email (see my profile, since you don't list one) I'll spit back my analysis but it's really really pedantic and actually probably not worth our time. thanks for the exchange here.