I'd also contest the point that listening tests are irrelevant here as speaker measurements are only valuable insofar as we can correlate them to listening tests. Put another way, I'd argue everyone here knows that distortion matters to some extent! The problem is that 'some' extent. The audibility of frequency response problems and how they relate to preference is very well documented. Meanwhile speaker designers and acousticians are still trying to figure out how much distortion actually matters in music and the best way to measure it in a relevant manner.
I'll add to this that it doesn't seem that hard to setup a controlled blind test experiment to correlate non-linear distortion in loudspeakers and subjective impressions. You just need a high quality loudspeaker of known low distortion, a typical room, and a "virtual" (software) distortion generator that is capable of adding the same kind of non-linear distortion that a loudspeaker driver would introduce. Then get some test subjects and off you go.
Are there any published studies that have tried the above?
(Though I guess one limitation of that protocol is that you wouldn't be able to test the case where the non-linear distortion depends on off-axis angle.)
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