What is your explanation of ability to sense the existance or absence of frequencies higher than measured sine wave sensitivity?
Huh? Not sure I understand you. I don't think there is evidence that we hear higher frequencies.
A square wave is made up of all odd harmonics...you hear the odd harmonics up to the point where you can no longer hear them (around 15 KHz for most people)...so you do not hear the "slope" of the square wave but within your audible hearing range you hear the harmonic content that makes up the square wave.