@noske So far, for me this is a most relevant forum to discuss this since am not aware of other possibilities and i know nothing about electronics. As i have already mentioned, i was not aware of these things before i had a look on the article which seems to be very useful and well written.
An average is no good if you wish to have an information about the distortion of the harmonics of a particular degree, unless you adjust the weights respectively,. but then you will have different functions, i.e., using current terminology different "THD" for different harmonics. If ones wishes to have a single universal measure, we may give a large weight to the gain and relatively small or 0 weight to the second and third degree harmonics. But then we will practically ignore the higher order harmonics, which we know are good for may people (who likes tube stuff)! Or a manufacturer may decide which of the "THD"s specify in their products.
@snapsc , you may be correct about the design strategies of the Cherry amps, Tommy also liked tubes. I think these are second and/or third order harmonics that made me enjoy so much the Megaschino, and my tube SET amp as well. I suggest that it is precisely this tube-like effect of the higher order harmonics that makes the sound so enjoyable.
Creating alternative "THD" measures seems to me to be a best simple solution to reflect a more precise picture of what is really happening. In fact, we have here a kind of multiobjective and threshold optimization problem. Our first objective is to minimize the first order harmonics that is also referred to as the gain if i am not mistaken, and also we aim at somehow maximize (!) the distortion in higher order harmonics. Or we may try to maximize the distortion of 2nd and 3rd degree harmonics where we wish to keep the distortion of the first degree harmonics (the gain) no larger than a certain claimed threshold (for example, 0.001%). Redefining THD in this way, the producers of the tube amplifiers will bravely be able to put real distortions that their equipment have. I don't know about electronics and the limits of the distortions, i.e., would a very large distortion of the 2nd and 3rd order harmonics be good, and what is an ``ideal'' balance between the second and the third order harmonics?
At this point, with my humble knowledge, i suggest that all this THD (and perhaps other spec parameters) theory is just a b*****t (created by engineers who do not know much about mathematics). It is a non-relevant and non-informative parameter which does not disclose actual balance between the harmonics of different orders.
Electric engineers succeed to develop exceptionally sounding equipment, but the existing parameter for measuring their ``distortion'' seem to me to be useless.