"Revitalizing Classic Illusions: Shepard-Tone Sequences and Shepard–Risset Glissandi, With Various Modifications"

The Shepard-tone sequence and Shepard–Risset glissando are classic auditory illusions in which pitch seems to inexhaustibly ascend or descend. Such stimuli have been used in scientific research, as well as for artistic purposes. This paper demonstrates several variations of those illusions, some of which do not appear to have been previously discussed in the literature. Most notably, hybrids of the two illusions are demonstrated, in which discrete Shepard-tone steps are connected by continuous glissandi. It is shown, using a sample of 91 listeners, that such hybrids can disambiguate the perceived direction of motion between two Shepard tones that are a tritone apart, thus overriding what has been called the tritone paradox . In other demonstrations, multiple layers of monaural and binaural beats are embedded into a Shepard– Risset glissando to produce Risset rhythms . Audio files for these and other examples are provided and discussed. Two original MATLAB functions (and equivalent functions in R) are also provided, which can be used to replicate the examples and explore additional variations.