Comment by Stenzel

There is no illusion of pitch, and it is a common misconception that the fundamental frequency must be present in a tone. Pitch is the perceived periodicity of a tone, which is roughly the greatest common divisor of the harmonics. If perceived pitch without fundamental is considered an auditory illusion with, common pitch detection techniques should fail if the fundamental is not present, but they work quite well in the absence of the fundamental. So either there is no illusion of pitch or algorithms have illusions too.