Here is an excellent, interactive chart on instrument frequency responses. Hover over each instrument graph bar & it will give additional specific info in small windows to the right:

http://www.independentrecording.net/irn/resources/freqchart/main_display.htm

It seems that the higher end 'Yellow Bars' are all harmonics & according to this site, nothing in the musical instruments listed here exceed 16Khz. Synthesizers probably can go higher, but most of us on this planet couldn't hear it.

So at 12-13 Khz, I don't think that I'm missing a lot.

Having said all that, woe be to any speaker or amp designer that willfully cuts off their high end at around 16Khz even though above it, that capability is largely wasted...

TAM