I have heard that bassoons have a weird property: when they play a note, their fundamental frequency is nearly absent. The ear-brain system fills in this frequency, making the bassoon sound very low pitched without actually containing much of the very low frequencies.
How can I verify this? (Google is failing me here.) How can I find whether it's possible to have the reverse - a sound that seems high-pitch without actually containing high frequencies? This seems pretty impossible to me right now, but then again, so does the bassoon thing. There's probably some weird perception stuff going on in the brain that I don't understand. If there is such a thing, I wonder if I can find a way to put that as an "instrument" on my digital piano so I can actually hear my right hand play.