How the measurements reflect the sound that we perceive?
I described that above.
Since the ear uses higher ordered harmonics to sense sound pressure, its keenly sensitive to them since the ear has a +120dB range. If these harmonics are not masked by the lower orders (2nd and 3rd) they will contribute to harshness and brightness, since the ear assigns tonality to all forms of distortion.
That is why you don't hear it outright as breakup in any amplifier that isn't being overloaded. You sense it as tonality instead. For example, the 'dry' quality some amplifier have is due to their distortion signature, which audiophiles call the 'sonic signature' of the amplifier.

