driver size vs distortion

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I got a pair of new JBL Control 1 Pro (5" 2-way) and did some listening and also some measurements with REW. For my instrument application there is a problem with distortion, just at certain frequencies. For example, right around 200 Hz is bad spot, where I measure about 25% THD with a pure 200 Hz tone at around 90 dB SPL @ 1 meter. This is when driving about only 1 watt. You can hear the harmonics pretty readily. I tested both speakers of the pair. If you back off the level, the distortion goes away. Offhand seems unreasonable for a quality speaker rated at 150W RMS.

But maybe I'm wrong. Is this normal? Are all drivers around this size going to perform this poorly distortion-wise, or is the JBL design just an anomaly? If I were to build a cabinet (e.g. stock parts from parts-express), would stepping up to a 6.5" or 8" solve this issue? Or is it not related to size?

Background: I'm selecting speakers for an 8-channel+sub audio system for a virtual pipe organ at home. All channels with have full parametric EQ available. Because of the quantity, I was hoping to spend only around $80-$150 per speaker, and also I have space constraints. In this application, too much distortion would color individual notes and ruin the realism. I need about 105 dB SPL output per speaker, similar to the JBL spec. The sub will handle everything 100 Hz and below.
 
No they were new out of the box. I should clarify - I don't think the JBLs sound bad. For normal music listening conditions, you would probably never notice this issue nor have all that energy at one frequency. It's just that for my application I need less distortion.
 
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