Imagine you have an scene with shutter speed 1/60, f/8 and ISO 200. Then you change the configuration to get an equivalent exposure: speed 1/120, f/5.6, ISO 200 (plus one stop in speed, minus one stop in aperture).
My question is, apart from the obvious changes in the depth of field due to the aperture change, and less blur for the speed change, would there be any effect in brightness, contrast, color or other? And what if the change is 3 or more stops?
Answer
In a theoretical sense, these things are perfectly interchangeable. See the second half of my answer to What is the "exposure triangle"? (after I get done ranting about the terminology). This is actually exactly the point of the "stops" system — you can think in terms of Exposure Value (measured in stops) and not need to worry about any complicated conversions between factors. So, in one sense, by definition, yes.
There are two wrinkles, though.
The first is that each of the adjustable factors can have effects beyond exposure and beyond the obvious ones that people learn first. That is, while aperture affects depth of field, it also affects other aspects of lens rendering, including aberrations (which are often worse wide open) and diffraction (which becomes a practical limit on sharpness as you stop down. Or, long shutter speed obviously increases the possibility of subject motion blur, but also might include camera shake blur — or of noise from warmer electronics.
The second is that the theoretical doesn't always match reality. This is particularly apparent in film, where longer exposures suffer from "reciprocity failure", which is basically defined as "whoops — stops stop being equivalent like they're expected to be". This particular problem is not the case with digital photography, but there are other areas where the imperfections of the real world may get in the way of theory, like the imprecision of measurements as Guffa mentions. And the nominal aperture and shutter speed scales don't actually perfectly halve/double every stop, but are generally within real-world tolerance. (Remember, the point is to make photographs, not scientific measurements, and in practice, these are rarely relevant.)
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