In the interest of my own learning, would you please point out which measurements correspond to what people hear?
Sure- two measurements that have not got the attention they deserve- first, distortion vs frequency, which ideally should be a straight line or decreasing with increased frequency.
If the amp has problems with feedback due to insufficient Gain Bandwidth Product, the distortion will rise with frequency above a certain point (often between 1 and 3KHz). If this happens the amp could be perceived as bright due to how our ears perceive higher ordered harmonics and the Fletcher Munson curve.
The other measurement is the distortion spectra. Its not enough that the distortion be low. The ear has a masking principle; the way that tube amps sound nice and smooth is because they have enough 2nd and 3rd harmonic that those harmonics are able to mask higher orders. If those harmonics are insufficient, the amp may be perceived again as harsh and bright. This measurement is a bit open to interpretation as you have to know what you are looking at to be able to say how the amp is going to sound when you listen to it.
Quite often this last measurement is done with the fundamental at a low frequency - like 50 or 100Hz. If this is so and there isn't a measurement with the fundamental at 1KHz or higher then the measurement isn't all that helpful if distortion rises with frequency! IOW at a low frequency the distortion spectra might appear benign but above a certain frequency things could be considerably different.
So now you can see how an amplifier with 0.005% harmonic distortion might sound harsh and bright if those harmonics are not masked and the THD was measured at a low frequency- this can hide problems in the design. OTOH a zero feedback tube amp might have much higher distortion, but because it does not rise with frequency and the lower orders dominate, it might sound smooth and musical.
Class D offers a means to eliminate the first problem of rising distortion as well as allowing for a more benign distortion spectra.