A looping rhythm in tempo octaves with faded extremes sounds endlessly accelerating
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: The rhythm analogue of the Shepard tone illusion, which the reader already tracks from Section 5.5.4 — same trick of octave-spaced copies plus amplitude fade. — connects to: Tempo can be made to audibly accelerate forever by layering tempo octaves; Tempo can be made to loop infinitely via layered sped-up copies with faded amplitudes; Aperiodic sounds emerge when continuous in-between frequencies cancel periodic repeats — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 459 (+13 more)
- SEED: An essay on musical illusions that never resolve — Shepard tones, Risset rhythms, barber-pole melodies — and why the brain accepts impossible perpetual motion.
- CANDY: A rhythm that speeds up forever yet repeats is a great elevator fact for music-minded friends.
- SHARE: Perfect for one electronic-music or percussionist friend who would actually build the Risset rhythm in a DAW.
Broader Connections
- Tempo can be made to audibly accelerate forever by layering tempo octaves
#corroborates(1.00) - Tempo can be made to loop infinitely via layered sped-up copies with faded amplitudes
#corroborates(1.00) - A Shepard tone creates an endlessly ascending pitch while staying within one octave
#exemplifies(0.90) - Aperiodic sounds emerge when continuous in-between frequencies cancel periodic repeats
#complicates(0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 459 - Even steady musical notes constantly change in their sound
#complicates(0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1485 - Pitch of periodic sounds is determinable from the waveform’s cycle period
#complicates(0.80) — David Howard, Jamie Angus, coustics and Psychoacoustics, 909 - Timbre depends on staggered harmonic entry times and spectral extent
#complicates(0.80) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1475 - Clear musical pitch arises from regularly repeating acoustic waveforms
#complicates(0.75) - Half-period delay of a tone cancels odd partials and raises pitch an octave
#complicates(0.75) - A gated tone sounds continuous at a level called the pulsation threshold
#complicates(0.75) — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 590 - In-filling components between harmonics cancel wave repetition to represent aperiodic sounds
#complicates(0.75) — David Howard, Jamie Angus, coustics and Psychoacoustics, 455 - Consecutive intervals of equal magnitude and opposite sign create repeated tones in pitch sequences
#complicates(0.75) - Note onsets have staggered harmonic entry times that define each instrument’s timbre
#complicates(0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1449 - The sustained field does not distinguish melodic from tonic sequences
#complicates(0.75) - Musical instrument notes have a gradual onset before steady state
#complicates(0.70) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1478