Tempo can be made to loop infinitely via layered sped-up copies with faded amplitudes
Evidence
In a similar vein to the Shepard tone pitch illusion described in Section 5.5.4, Risset (1986) introduced a rhythm-based phenomenon described as an eternal accelerando in which playing a rhythmic sequence is perceived as continually increasing in speed. Instead of using harmonics that are spaced in octaves as found in the Shepard tone (see Figure 5.19), a rhythmic sequence, along with copies of itself sped up to be in “tempo octaves” (twice as fast, four times as fast, eight times as fast, sixteen times as fast etc.) such that at the end of the sequence each has sped up by a factor of two (the tempo “octave”) so the sequence can be repeated. The amplitudes of the patterns at the low and high time extremes are gently faded such that the sequence toward the center of the set (the four-times-as-fast sequence in the example here) dominates what is perceived. If the sequences slow down rather than speed up, an eternal deccelerando can be produced. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1658
Categorization
- XREF: Mirrors the Shepard tone octave illusion described earlier in this same chapter; cross-domain parallel to Escher-style infinite ascent structures.
- SEED: Angle for an article: the eternal accelerando as a musical illustration of the Shepard illusion transplanted from pitch to rhythm, and what that reveals about auditory streaming architecture.
- SHARE: A friend into generative/ambient music would enjoy the Risset eternal accelerando and Stowell’s audio implementation reference.