The Shepard Tone: a sound illusion to explore with FizziQ
- Christophe Chazot
- Nov 15
- 4 min read
Updated: 7 days ago
The Shepard Tone : an infinite rise… or almost
You're surely familiar with the Penrose staircase illusion, the seemingly endless staircase popularized by the artist M.C. Escher. But are you familiar with the Shepard Tone, an acoustic illusion conceived in the 1960s by the American psychologist Roger Shepard, which creates the impression that a sound rises—or falls—without ever reaching a peak? Let's explore and analyze this astonishing sound effect with the FizziQ app.
The Origins of Illusion
Roger Shepard earned his PhD in psychology from Yale in 1955 and joined Bell Labs, where he set out to create a sonic equivalent of the Penrose illusion popularized by Escher.
Using a newly invented tool—the digital sound synthesizer developed by Max Mathews—Shepard demonstrated that it is possible to create the impression of an endlessly rising or falling pitch by superimposing several tones an octave apart and playing them cyclically [1]. This is the Shepard effect.
A few years later, the French composer and researcher Jean-Claude Risset extended this discovery by creating a continuous version of the illusion [2][3]. Instead of a sequence of discrete notes, Risset produced an infinite “glissando” in which the frequencies appear to rise or fall without interruption. This is known as the Shepard–Risset scale, which has become the most widely recognized form of this acoustic illusion.
How does the Shepard Tone work?
The idea is elegant. Several pure sine waves, spaced octaves apart, are superimposed. When their frequency is increased together:
The most acute ones gradually diminish until they disappear.
Meanwhile, at the lower end of the spectrum, new bass sounds are appearing,
and that the intermediate sounds — those that the ear perceives best — rise steadily.
This carefully orchestrated mechanism gives the impression that the sound rises endlessly, while the sequence actually describes a perfectly camouflaged loop .
Listen to and analyze the Shepard Tone with FizziQ
In FizziQ, the Shepard effect is easily accessible from the FizziQ app's Sound Library. From the main menu, go to Tools > Sound Library > Shepard. Pressing Play immediately produces the "infinite" build-up.
The sequence is produced using only three octaves. Recordings with more octaves can be found online for an even more pronounced effect. This version, however, is easier to analyze, which we will do in the rest of this article.
The fundamental frequency: proof that everything is an illusion
A sound that actually rises to infinity has no physical reality. To see this for yourself, simply display the fundamental frequency in FizziQ. After launching the sequence from the library, go to Measure > Microphone > Fundamental Frequency
What we observe is very instructive:
The fundamental frequency rises steadily.
Then, around 650 Hz , it drops sharply.
And the cycle begins again.
In other words: the frequency doesn't rise indefinitely. The sound starts again... but our brain doesn't see it coming.
The spectrum: where everything becomes clear
Spectral analysis reveals the hidden mechanics. To do this, let's return to the Measurements > Microphone > Frequency Spectrum screen.
If we study the dynamics of the spectrum in FizziQ, we observe different phenomena:
a dominant component that gradually increases and gains in intensity,
then which begins to subside,
while another, more serious one, gently takes over.
This transition is so gradual that you only hear one thing: a continuous rise , when in reality a new wave is replacing the previous one. It's a perfectly orchestrated sonic crossfade effect that deceives the ear.
To go even further
A particularly powerful analytical tool is the spectrogram , which shows the evolution of frequencies over time: the horizontal axis represents time, the vertical axis represents frequencies, and the colors represent their intensity.
The FizziQ mobile app doesn't yet allow you to plot the spectrogram, but you can use FizziQ Web (the browser version) for this analysis. The spectrogram then reveals the entire mechanics of the illusion: you can clearly see the high tones fading at the top of the spectrum while new low tones appear at the bottom.
This is the perfect visualization to understand the "crossfade" that creates the impression of an infinite rise!
Why does our brain fall into the trap?
The illusion exploits three weaknesses in our brain:
1. Our attention is selective: We follow what changes most clearly: here, the local rise. Everything that appears or disappears at the periphery goes into the background.
2. The ear does not hear everything with the same intensity: Very low and very high sounds are faint. Mid-range sounds — those that rise continuously — are the most present. This is precisely the area where the illusion is most effective.
3. Tonal ambiguity: The different tones that make up the illusion are separated by a cotave. However, because the frequency distribution changes rapidly, the brain cannot clearly identify the octave, nor pinpoint when the loop restarts. This confusion creates a virtually invisible "join" and deceives our ear.
Other sound illusions to explore with FizziQ
The Shepard effect is just one example among many other fascinating acoustic illusions:
McGurk effect : what we see alters what we think we hear.
Binaural beats : two different tones in each ear create a phantom frequency.
Missing fundamental : the brain reconstructs a missing low note.
The paradox of the tritone : the same pair of notes can seem to rise or fall depending on the listener.
These phenomena provide numerous opportunities to explore acoustics, psychoacoustics, and the workings of our perception, with a playful dimension that immediately appeals to students.
Conclusion: a superb testing ground
The Shepard Tone shows that our ear, like our eye, can be deceived. With FizziQ, it becomes an excellent tool for understanding how sound works, how it is analyzed, and how our brain interprets—sometimes incorrectly—what it receives.
References:
[1] Roger N. Shepard — “Circularity in Judgments of Relative Pitch.”
Journal of the Acoustical Society of America, vol. 36, no. 12, pp. 2346–2353, 1964.
[2] Jean-Claude Risset — “Pitch Control and Pitch Paradoxes Demonstrated with Computer-Synthesized Sounds.”
Journal of the Acoustical Society of America, vol. 46, p. 88 (Section A), 1969.
[3] E. Vernooij — “Listening to the Shepard–Risset Glissando.”
Frontiers in Psychology, 2016.
[4] I. Braus — “An Overview of Pitch Circularity and Shepard Tones in …”
Music Perception, 1995, vol. 12, pp. 323–351.
[5] E. M. Burns — “Circularity in Relative Pitch Judgments for Inharmonic Complex Tones: The Shepard Demonstration Revisited, Again.”
Perception & Psychophysics, 1981, vol. 30(5), pp. 467–472
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