In a fixed pitch aircraft the RPM is an output not an input. It reflects the amount of power being added to the prop and dissipated by the prop in the air.
Because the air is less dense higher up, less power can be dissipated at any given RPM - therefore the RPM will increase with altitude if you maintain a content power output (hence to dissipate 75% at 7000 ft is 2700 rpm and at sea level may be 2350). Fortunately for a given throttle setting power declines at about the same rate as the ability to dissipate power - hence BPs comment about achieving max rpm at most altitudes.
There are only three things that control power output, the fuel burned per hour, the mixture and the engine geometry (which is of course fixed).
The throttle controls the air volume flow (broadly) and the carb meters fuel to match to volume. So at a fixed altitude the throttle controls the amount of fuel and hence the power.
If you change altitude but not throttle setting, the same volume of air will move so the same mass of fuel will flow, however the mixture will be richer and therefore power will be less. This then results in the prop slowing down (so the power dissipated matches the engine power) and this slower pumping reduces air volume flow (and via the carb fuel flow), further reducing power until we are back in balance (engine power out = power dissipated by prop).
You can see therefore, that you must both advance the throttle to increase the volume of airflow and 'lean the engine' to ensure you retain the same fuel flow rate and combustion mixture (and therefore power ) as you climb.
Last edited by mm_flynn; 27th October 2012 at 18:57.