Extended Data Fig. 1: Details of auditory and visual stimulus design.

(a) Each auditory stimulus was composed of five pure tones at harmonic frequencies (octaves below and above other tones). The weight with which each tone contributed to the overall stimulus was taken from a Gaussian distribution across all possible tones. The example stimulus A in pink is composed of a tone of 2^13.25 Hz (center tone, highest weight) and two lower (at 2^11.25 and 2^12.25 Hz) and two higher harmonics (at 2^14.25 and 2^15.25 Hz). Tones followed scientific pitch and are expressed as powers of two: 2¹³ corresponds to 8.192 kHz, and C₉ in scientific pitch notation. During an auditory trial, the stimulus changed to a stimulus of five new harmonic tones with different weights (for example stimulus A to B). (b) The left polar diagram shows the circular arrangement of auditory stimuli. For each cardinal direction the insets show the tonal weights associated with these stimuli. Note how ever increasing the center tone frequency ultimately results in a circular shift back to the starting stimulus. This circularity can also be seen in panel a: going up and down half an octave from stimulus A always results in stimulus B. The auditory stimulus set is therefore circular. This feature is exploited in the Shepard illusion of eternal rise or drop in pitch. However, our stimuli were static so the illusory effect of continuously increasing or decreasing pitch was absent. The only illusory component was that half an octave change could be both experienced as an increase or decrease in pitch. This circular design of auditory stimuli mirrors the visual stimulus set (right part) with drifting gratings in all orientations. The amount of frequency change (expressed in partial octaves, red) or orientation change (expressed in degrees, blue) determined the saliency of auditory and visual changes. (c) Example stimuli during three consecutive trials. The upper spectrogram over time includes two auditory change trials. Auditory stimuli continued to be presented until the next auditory change, which could be identified based on a difference in spectral content, and experienced as a change in pitch. The example shows an easy auditory trial (salient change; stimulus A to B, half an octave) followed later by a difficult trial (subtle change; 1/32 of an octave). The lower schematic shows visual orientation over time including a visual trial. Note that the gratings were continuously drifting in the direction orthogonal to the grating orientation. An audiovisual trial would consist of a simultaneous change in both modalities (not shown). Note that this is only a schematic depiction, hence time is depicted in arbitrary units.