The Shepard sound effect

This activity allows students to discover auditory illusions and understand how our perception can be deceived by complex acoustic phenomena. It develops the spectral analysis of sounds and the understanding of the mechanisms of perception.

Imagine a sound that seems to rise in pitch forever, climbing higher and higher without ever reaching a limit, like an acoustic staircase with no top. This is the Shepard tone, one of the most famous auditory illusions in psychoacoustics, first described by cognitive scientist Roger Shepard in 1964. It is the sonic equivalent of M.C. Escher's impossible staircases or the optical barber pole illusion. The trick lies in the clever superposition of multiple sine waves spaced exactly one octave apart, with their amplitudes carefully shaped so that as the highest frequencies fade out, new low frequencies fade in. The listener's brain tracks the overall upward trend without noticing the recycling of frequencies at the bottom. The Shepard tone has been used extensively in film (Christopher Nolan's Dunkirk uses it to create relentless tension) and video games. This experiment uses FizziQ's spectral analysis tools to deconstruct the illusion, revealing the simple mathematical structure behind a deeply deceptive perceptual experience.

Learning objectives:

The student analyzes a Shepard sound (auditory illusion of an infinite continuous rise) using FizziQ sound analysis tools. Using the frequency meter and the frequency spectrum the student observes that despite the impression of infinite rise the sound is in reality composed of several sinusoids spaced an octave apart whose amplitude gradually varies, thus creating the illusion.

Level:

High school

FizziQ

Author:

Duration (minutes) :

30

What students will do :

- Listen to and experience the Shepard tone illusion of endlessly rising pitch
- Use spectral analysis to identify the multiple frequency components of the Shepard tone
- Observe that the components are spaced exactly one octave apart
- Understand the amplitude modulation that creates the illusion of infinite ascent
- Connect the acoustic analysis to the principles of auditory perception and psychoacoustics

Scientific concepts:

- Auditory illusions
- Spectral analysis
- Pitch perception
- Wave superposition
- Psychoacoustics

Sensors:

- Microphone (frequency analysis)
- FizziQ spectrum analyzer (FFT)
- FizziQ frequency meter

What is required:

- Smartphone with the FizziQ application
- 'Shepard' recording from the sound library
- Headphones (recommended) for better perception
- FizziQ experience notebook

Experimental procedure:

Open FizziQ and load the 'Shepard' recording from the sound library. Put on headphones for the best perceptual experience.
Listen to the recording without looking at any analysis tools. Note your impression: does the sound appear to rise continuously in pitch?
Now open the Spectrum Analyzer (FFT) in FizziQ and replay the recording.
Observe the spectrum. You should see several peaks at different frequencies, not just one.
Identify the frequencies of the peaks. Verify that they are separated by approximately octave intervals (each is roughly double the previous one).
Watch how the peaks evolve over time as the tone appears to rise. Note that high-frequency peaks fade out while new low-frequency peaks fade in.
Use the Frequency Meter to track the apparent fundamental frequency over time. Does it truly increase indefinitely?
Pause the recording at several moments and record the frequencies and amplitudes of all visible spectral peaks.
Create a table showing the evolution of each frequency component over time.
Verify that each component rises in frequency while its amplitude follows a bell-shaped envelope: growing from silence, reaching maximum intensity, then fading out.
Sketch or describe the amplitude envelope shape that makes the illusion work.
Discuss: why does the brain perceive a continuous rise when the spectrum is actually recycling frequencies?

Expected results:

The spectrum should reveal 4-8 simultaneous sine wave components spaced one octave apart (frequency ratios of 2:1). At any given moment, the middle components are loudest while the highest and lowest are near silence. As time progresses, all components shift upward in frequency, but when a high component reaches the upper amplitude cutoff, a new low component emerges from silence at the bottom. The frequency meter may show a steadily increasing value (tracking the dominant component) or may jump unpredictably as different components alternately dominate. The key observation is that despite the impression of infinite ascent, the frequency range of the entire signal remains bounded within approximately 2-3 octaves.

Scientific questions:

- Why does the brain perceive a single rising tone rather than multiple separate frequencies?
- What role does the amplitude envelope play in creating the illusion?
- How is the Shepard tone similar to the visual illusion of the Penrose staircase?
- Could you create a descending Shepard tone? What would need to change?
- How has the Shepard tone been used in film and music to create emotional effects?
- What does this illusion tell us about how the auditory system processes pitch?

Scientific explanations:

The Shepard effect, discovered by Roger Shepard in 1964, is a fascinating auditory illusion where the listener perceives a sound that appears to rise or fall indefinitely without ever reaching a limit. This paradoxical “acoustic Penrose staircase” is based on an ingenious superposition of sinusoidal sounds.

The mechanism is as follows: several sinusoids are generated at frequencies separated by exactly one octave (2:1 ratio). When all frequencies increase simultaneously, the amplitude of each component is modulated: higher-pitched sounds gradually attenuate while new lower-pitched components appear.

Because our brain primarily interprets the direction of melodic movement rather than absolute frequencies, we perceive a continuous rise, even if the frequencies return cyclically to the same values. The spectrogram reveals this structure: rising parallel lines that vary in intensity, creating a perfect cycle.

Analysis with the FizziQ frequency meter shows that the detected fundamental frequency does not rise indefinitely but falls periodically, while the frequency spectrum reveals the simultaneous presence of several components. This illusion exploits a fundamental characteristic of our auditory perception: the pitch of a sound is perceived in a relative and circular way (notes separated by an octave are perceived as similar).

Variants like the Shepard-Risset glissando (continuous version) or the Deutsch effect (tritone paradox) exploit similar principles. These illusions have applications in electronic music, cognitive psychology and sound interface.

Extension activities:

Frequently asked questions:

Q: I do not perceive the illusion of endless rising. Is something wrong?
R: The illusion works best with headphones at moderate volume. Some listeners are more susceptible than others. Try closing your eyes and focusing on the overall pitch impression rather than individual components.

Q: The spectrum shows many peaks but I cannot identify octave spacing. How do I verify?
R: List the frequencies of the peaks from lowest to highest. Each should be approximately double the previous one. For example: 100, 200, 400, 800, 1600 Hz. Small deviations from exact doubling are due to measurement precision.

Q: Why are there more peaks at some moments than others?
R: The number of audible peaks depends on the amplitude envelope. At any given time, some components are fading in or out and may be too quiet to appear above the noise floor in the spectrum analyzer.

Q: Can this illusion work with non-octave spacing?
R: The classic Shepard tone uses octave spacing because the brain tends to fuse octave-related frequencies into a single percept. Non-octave variants exist but produce different and generally weaker illusions.