In the same vein as the study of paradoxes and ambiguities in visual perception (i.e. optical illusions, for example M C Escher), auditory illusion as an area of research has contributed significantly to our understanding of perceptual and cognitive processes in decoding sonic and musical sensory inputs. With the work of Jean-Claude Risset and R. N. Shepard (creator of Shepard tones), it has also contributed to the development of electroacoustic techniques and means, in particular in the field of sound synthesis. Auditory illusions may frequently be caused by paradoxes in our perception of pitch/frequency and spatial location of sound.
Closely allied is the notion of analysis through synthesis, significant in the development of techniques such as Frequency Modulation synthesis, developed by John Chowning. For recent research in the field refer to the work of Diana Deutsch. http://deutsch.ucsd.edu/