In a piston engine, an 8:1 engine has the same volume of air in the combustion chamber as a 12:1 compression ratio engine.
Are you sure about this?
we are talking about two identical engines, same size, same fuel flow, same RPM, same EVERYTHING - except one has a higher compression ratio -
I can see that you are talking theoretical engine, as some parameter of the engine has to be changed to alter compression ratio; combustion bowl size, head height, or piston stroke.
From work on performance engines, it is the compression pressures and not really the comp ratio that is important. Compression pressures are related to the comp ratio but are more influenced by valve and ignition timing. Of course the dynamics of the intake and combustion chambers has a direct affect.
I work on the practical side, so is interesting talking to a theorist - unless of course you are just a sciolist.