Hi Robert,
This is a very astute question, and one which needs careful consideration in the color correction process at the end of post production.
In fact, it’s a discussion you should have at the beginning as well.
Essentially, it’s in everyone’s best interest to know what the final exhibition will be for a motion picture project. This is important in order to determine the recording format, the aspect ratio, the frame rate and all the other things you mention; yet the answer is not always known or based in reality.
The fact is that most filmmakers aspire to theatrical exhibition in a dark movie theater with a screen 40′ wide, yet it’s the rare project that ultimately reaches such a venue. More likely is TV, Computer Screens or even Mobile Phones, and each of these requires a different gamma to faithfully reproduce the cinematographer’s intentions.
In practical terms, what happens is that once the color correction is finalized by viewing on a properly calibrated display (either computer, television or projector) then it it output through “transforms” designed for every intended use. Fortunately the makers of finishing platforms are aware and sensitive to the problems you mention and have built in solutions, just don’t forget about the multiple outputs at that moment.
In a pinch, LUT boxes can usually apply the same transforms on playback but only in an HD-SDI stream.
Another point you bring up is the difference between the film fest and a downtown digital cinema venue. This also is problematical, because there are so many different types of projectors out there; with different resolutions and especially brightness.
Motion picture projectors had standard which were established by industry groups to assure continuity from theater to theater, but now that our projects are shown in so many non-standardized venues all bets are off.
Consumer and Prosumer projectors, like the TV sets that proceeded them have a range of contract, brightness and color controls, so that if you’re forced to exhibit on one of these situations, it’s a good idea to get there early and preview the film and make some adjustments. Be careful though as the adjustments often default to the presets when the projector is power cycled, so make notes or record the settings if the unit has that capability and double check again before the actual show.
Hope this helps!
JS