Actually, the fact that nearly all transistor amps are push/pull is the main reason they are primarily generating odd order harmonics. Push/pull cancels even orders by design. Push/pull tube amps do so as well but there is more residual even order harmonics in most designs (tube matching issues??). Negative feedback tends to suppress all harmonics but it suppresses the low orders more and has the side effect of generating new, higher order harmonics. This can lead to a signal modulated "noise" floor that looks like noise but is really a myriad of distortion products. Being signal modulated and correlated it is not something one can "hear below" like one can with true noise.
The correct weighting of harmonics has been the subject of a number of papers over the decades and at least one thesis. One of the first serious attempts was a BBC engineer named D.E.L Shorter who though the weighting would be the square of the harmonic order but Cheever found that this didn't actually go far enough and that there is also an SPL dependency that needs to be accounted for.
Yet an SS/PP amplifier can do it all , bandwidth, drive , Low TIM/THD , et al , time you start focusing on those bad speakers and less so the Amp delivering the bad news..
Match load to any quality amplifier and targeted results will be met no matter type ..
Regards