My limited experience here is that speakers can and will produce measurable harmonic distortion starting below 80dB at a 10 foot listening position, which isn't terribly loud at the driver in a typically reflective residential room.
I don't have nor am I building any specialized speakers/drivers, but here's a 1998 MartinLogan electrostat vs 2016 JBL LSR 305.
I leave it to you to guess which is which, for now.
I figure since the observed SPL is the same, the frequency is the same, but the distortion products are quite different, it isn't the mic -- UMIK-1 ---that is causing the distortion in the readings.
Plus, you can hear the more distorting speaker distort vs the lesser distorting unit...
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Were I designing drivers, I suppose a quiet microphone would be handy, surely quieter than the UMIK-1, and, of course, a quiet room, as the residential low frequency ambient noise messes with lower SPL low frequency measurements.