FR can measure changes in timbre, but not changes in the quality of the resolution of the note, including such things as the separation of the harmonics that make up the timbre.
I'm sorry Dave but that simply is not correct. A note is comprised of a fundamental and its harmonics, and the balance between those components does indeed fall under frequency response. Now, all of these components can and do vary over time. Harmonics of percussion and plucked string instruments typically decay over time faster than the fundamental decays. This is due to losses in the string (or metal in a triangle) that damp the highs more than lows. And when played softly, the harmonics are at a lower level than when playing loudly. But this does not change the basic relation of timbre to frequency response. That is, there's no such thing as "quality of the resolution of the note."
Wire has three properties - resistance, capacitance, and inductance. Together these three properties create a filter. And a filter affects frequency response. There is no way that a cable can do more than alter the frequency response (or possibly slew rate), and no way a cable can do anything that is not easily measured.