Nope, I’m quite prepared to accept there are harmonics that are not directly audible to the majority of humans. I’ve seen them on a scope when playing my Sax 

Still not convinced that a decent “ordinary” tweeter won’t reproduce these harmonics up to say 30kHz and I’m extremely skeptical of any sort of human perception beyond this 
Anyway, I certainly wont be forking out £300 to £400 to find out if anything above 30kHz makes my brain go, Ahhhh, bat music. 
Edit. I cant help wondering if these harmonics are perceptible then why aren't we all running around clutching our heads because the natural world produces them in abundance never mind all the electronically generated high frequencies that we've surrounded ourselves with.
Single spur balanced Mains. Self built music server with 3 seperate linear PSU, Intel i5, 16 GB RAM no hard drive (various Linux OS). Benchmark Dac2 HGC, single ended XLR interconnects/Belkin cable. Exposure 21RC Pre, Super 18 Power (recap & modified). Modded World Audio HD83 HP amp. Hand built Monitors with external crossovers , Volt 250 bass & ABR, Scanspeak 13M8621 Mid & Scanspeak D2905/9300 Hi. HD595 & Beyer 880 (600 ohm) cans.
The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.
-Bertrand Russel
John.