The study of what are called illusions of the senses is, however, a very prominent part of the psychology of the senses; for it is just those cases which are not in accordance with reality which are particularly instructive for discussing the laws of those processes by which normal perception originates.
Our ears are very familiar with harmonic sounds and we are familiar with their properties. We use the arithmetical relationship between the partials of harmonic sounds (i.e. the pitch) as a channel for communicating musical thought. Harmonic sounds are one of the simplest type of sounds, whose spectrum we have been able to control by our acoustical instruments. With computers not only are we able to create sounds which do not have any correspondence to the natural physical word, but we can also control their spectrum in frequency and in time in almost any way. It is a rather different way of looking at the problem of composition. Before electronic music, a composer had a series of constraints dictating the type of sound and its control. These constraints are imposed on the composer in the physical domain of sound. However once we move into the domain of musical structures such constraints vanish. Here, it is only the psychological issues, such as culture, aesthetic, or style, which may impose a constraint on the mind of the composer. In other words, the composer is free to assume any structure he or she pleases on top of the time scale of the physical constraints of sound.
However, there are now practically no constraints in the relationships which exist in the domain of sound, and that in itself is probably the only constraint that the composer is faced with. The composer is now able to compose down to the smallest micro-structures of the sound. The Shepard tone is a sound whose internal constraints are not that of the harmonic relationship. It seems apparent that the internal constraints of such tones create an integrity in the sound which can be used as a tool for the communication of musical thought. Risset used different flavors of the Shepard tone for his composition Trois Moments Newtonians (1979). Risset also explains the work of Ken Knowlton regiarding this issue, showing how the same principles could be applied in the time domain to create rhythms which seem to become faster and faster while there is actually no change in speed. Such a rhythm can be created by superimposing several beats which have geometrical relationships to each other, and then slowly fading in the slow ones while fading out the fast ones. If, in fact, the reason for the illusion of the Shepard tone is the self-similar structure in the sound, we may be able to conclude that we can detect and relate to self-similarity in the auditory domain.