Also rather interesting that you should point out the relationship distortion has with harmonics and how you consider "weighting".There is always more to it...
We all know about Fletcher-Munson. The Fletcher-Munson curves show where our ears are most sensitive, which is birdsong frequencies. This is because birds are the first indication of a predator in the vicinity and their calls activate other birds to spread the alarm. It does not matter if you are predator or prey, if you can't hear birdsong you're likely hungry or eaten.
The harmonics of a good number of instruments happen to fall into this region which is up to 7KHz. So the instruments that are making the most energy in music have harmonics that fall in the range to which our ears are most sensitive. This is likely not coincidence, but it presents a daunting challenge to engineers if the goal is to get audio systems to sound like real music and not an audio system!
Traditional engineering tends to ignore this, although we've known the Fletcher-Munson curves for decades.
One example of this is the use of loop feedback in amp and preamplifier designs. Feedback is known to bifurcate the input signal and thus generate harmonics of its own while also suppressing distortion. For this reason feedback usually contributes to brightness in all amps in which it is used; this brightness is caused by distortion rather than frequency response error. Our ears use the higher ordered harmonics to sense sound pressure, so any addition to these harmonics (or their presence where none was before) is easily heard, despite not being all that easy to measure.
The audio industry is a long ways from acknowledging this fact so we can expect amps to have a tendency to brightness for some time to come. One of the few areas where there are deviations from this norm is in high end audio. Its a weird world...
