I recall a certain amount of annoyance in Music Theory class (granted it was a long time ago) when we were rewarded for identifying the functionality of a note in terms of its place within a harmonic progression. How extraordinarily dull!
In the tone circles I devised for the tones in the Mozart G minor Piano Quartet lies a much more to-the-point image of what must concern us as players and as listeners: what happens to this tone, or that?
There are many ways in which a composer may call attention to the volatility of a given tone, the most obvious being to change it soon after introducing it, as Mozart often does with C, turning it into C# soon after the opening of a movement in C major. Another, more subtle way, is to do as Mozart does in K.478, to invert its logical placement by descending, rather than rising, to D. Whereas the rise would affirm G as a reliable fundamental, that critical descent does the opposite.
There are so many subtle ways to untune a tone.