Patrick; My apologies if misunderstanding. Your question is what happens when changing a signal by 0.1dB at 16 bit. This can be broken down to two separate effects.
First, the practical implementation. In this case, digital. It's not mumbojumbo.
It's a calculation with associated word length expansion, dither and truncation back to 16 bit. There's no distortion or altered frequency balance - except for the added dither noise. Unless something is broken. This is the issue I feel the original post was about..?
Secondly, there's the intended 0.1dB change. This is a separate issue from the actual means of accomplishing the task. Even if it may somehow be detectable in clinical conditions, it can't have any practical value. That's the least of worries in audio, especially compared to the side effects of doing the gain change (truncation distortion, dither noise or analogue noise).
Eric; all DSP's are created equal and have the unalienable right to avoid truncation distortion. Even gain! Hehe.. An example: Multiplying, say, 300 by 1,023293 is 306.9879. Multiplication have a habit of creating more decimal numbers. If the operation does not have enough footroom, the sum will truncate
as the result is calculated. Therefore longer word length in the calculation and another round of dither. It's the only option to truncation distortion! Dither does not add chaos to the mix, it's actually the straight opposite. Truncation gives (non musical) spurious frequencies, some relatively high in level, while dither spreads this energy across the spectra as a noise floor. Word length expansion is not only for comp and EQ.
The sound forge program springs to mind. The version I tried had the nasty habit of opening and editing all files in their original bit depth. To avoid truncating these results, the user had to manually select a higher bit depth, do the calculations and then select the proper way to reduce bit depth with dither prior to saving. I don't know how many accumulative truncations I did before discovering that little fact. It may not bother much in a single truncation, but hey, this is mastering! Details count.
Cheers,
Andreas Nordenstam