Start with a definition of what you mean by "distortion", and at what point in what space you measure the speaker.
Issues around what point in space you measure the speaker have been weighing big on my mind lately. I've been measuring speakers as an amateur for quite a while now. But certain issues only became apparent to me more recently. Like the distortion issue. If your speaker is increasingly directional in the high frequencies and you measure off axis, you get really low distortion measurements. Many of you may be thinking, "Duh!" But I had never thought it through before until I stumbled upon it doing off axis measurements.
So how about I EQ it flat off axis, listen off axis, and enjoy the low distortion?
Doesn't sound so good. That bright on axis beam gets back to you viciously after a few bounces around the room.
But what if I put an absorber strategically placed on axis to reduce that high frequency energy before it bounces around too much? I don't know, haven't gone there yet. Seems like a precarious setup.
Another issue with measuring that's really been hitting me hard lately is how far back from the speaker you measure. If you have a speaker that gets highly directional as frequency goes up, like I do, there's an issue with fall off rate, and it should not be ignored! A speaker like this that measures flat on-axis at 1 meter will be tilted up on axis at 2 or 3 meters, and this is even if you use a long IR window that includes all the off axis lower frequency that bounces back to the measuring position. The highs don't fall off as fast as they get further from the speaker, including when they start bouncing. So the off axis energy gets strange, and despite the lower frequencies going out to hit more surfaces sooner, they're all falling off faster and they're losing the fight, at least in my room.
I've got an exponential horn that was naively designed (by me and my friend) to cover the range from 200 to 2000 Hz, with a tweeter horn coaxially mounted in the middle. After years of experimenting with this contraption I wrote it off as hopeless above about 600 Hz, which meant it had a really small useful range. The dispersion was the problem, I assumed. By 2k the mid horn was beaming like a laser, and when the tweeter took over it was going wide and bouncing off everything.
I got to thinking about this again recently and decided to take a long IR measurement at the listening position of the midrange horn by itself without EQ or crossover filters to see what it did. With smoothing it gave a remarkably straight line result from 300 Hz to 6000 Hz tilted at about 3 dB / Octave. Measuring up close it shows a 6 dB / Octave roll off over the same range, verifying the fact that indeed the frequency response is increasingly tilted up as you move back.
So what should the measured response be at the listening position with a speaker like this? If you make it flat at the listening position it'll be getting brighter further back when it starts reflecting off walls. 3 dB/ Octave at the listening position is too much, but it doesn't sound as bad as I expected. I think it's hard to calculate what the slope should be with speakers like this so it's good to try different slopes using EQ and listen. I've been doing that and I'm astounded how much better this horn is sounding than I've ever heard it before when I was trying to EQ it flat at 1 or even 2 meters using various methods to try to get a quasi-anechoic measurement. I actually really like it now! And, at 6000 Hz the tweeter is pretty beamy too so the coaxial horns actually work together nicely, beaming in harmony and producing a remarkably smooth, relaxed and detailed effect.