Your ears can be fooled. Pitch, which is related to the frequency of sound, is a subjective sensation in which you - the listener - assign perceived tones to relative positions on a musical scale. The relative perception of pitch can be fooled, resulting in auditory illusions, which are the aural equivalent of optical illusions.
First up, here are some optical illusions that are equivalent to the auditory illusions you are about to hear:
These two illusions occur because we are presented with ambiguous two-dimensional information, but our brains assume the shapes are three-dimensional and assigns a direction to the apparent rotation. This direction is artificial and can, with practice, be made to change direction at will.
Now, for the auditory illusions:
The tritone paradox is the auditory equivalent of the above optical illusions. The perceived changes in pitch are artificial, and depend in part on where the listener grew up. Also, people with a musical background tend to hear them differently than non-musical listeners. Again, with practice the perceived changes in pitch can be made to reverse. In the Shephard scale, a continuous sequence of specially formed tones can be made to sound as if it continues ascending or descending forever.
Finally, one of my favorite auditory illusions is the speech-to-song illusion, where a section of a spoken sentence, when repeated often enough, suddenly appears to be sung.
Have fun!