Also wondering if the musical essence alluded to might be something not necessarily captured in a Distortion measure.
Its not hard to imagine a white noise process like Brownian Motion having a fairly small distortion level distributed around the input signal.
but an amp also with low distortion but “smoother” (less jagged) plot of output vs frequency might be nicer to the ear.
then some measure of a calculus like rate of change ‘smoothness’ might be more important, within an acceptable level of distortion.
EDIT : didn’t Arnie say he’d done (nearly) String Theory level Math - there’d be enough stochastic calculus in there … ?
also consistent with the idea that parts per billion distortion (halcro) sounds good, since the distortion is so low it ceases to matter how that level of absolute performance is achieved.
and possibly why Class D is less loved with its likely scatter gun of error terms around the input signal, even if the separation in time becomes vanishingly small (switching 500,000 times a second).
perhaps it is these “discontinuities” the ear can pick up.
reportedly CTC (Curl Thompson Crump) had one of trio able to improve their amps by ear, by listening to existing design, & picking the appropriate replacement component to improve the sound.
Just idle speculation. Usually the things that are “magic” day become science in later times (sometimes decades / centuries later).