Put most simply, the Shepard Tone is a computer-generated tone consisting of every octave of a single pitch superimposed into a single sound.
The Shepard Tone is named after Roger Shepard, the cognitive scientist who first generated Shepard Tones and published his research in a 1964 article published in The Journal of the Acoustical Society of America entitled Circularity in Judgments of Relative Pitch.
While tones played on instruments consist of a fundamental pitch and a series of softer partials, the Shepard Tone essentially has no single fundamental, and any partials are equal in volume.
Due to this, the Shepard Tone allows one to engage with pitch as if all octaves were flattened into a single set of twelve pitch classes that seem to move up or down infinitely, like an auditory barber pole.
In this article, we will explore the Shepard Tone and its uses for both music-related research as well as composition and production.
How Is A Shepard Tone Created?
First, we need to distinguish between a Shepard Tone and a Shepard Scale. If you’ve looked up examples of Shepard Tones, you’ve probably heard a sound that seems to move either up or down but never reaches its destination. In this case, the Shepard Tone has been “animated” to create a Shepard Scale – the illusion you are probably already familiar with. These terms tend to get used interchangeably which can make things confusing.
The most essential building blocks of the Shepard Tone are pure sine waves. These did not exist prior to electronic synthesis, which is why the Shepard Tone only came to be in the 1960s.
While it required some truly innovative computing at the time of its origin, creating a Shepard Tone is fairly simple in the present day.
One simply loads up their DAW of choice and opens a basic synthesizer. In Ableton Live, for example, you can open Operator (which defaults to a sine wave), and proceed to input every iteration of a particular pitch class, covering the entire range of human hearing.
As illustrated below in the case of a Shepard tone constructed on C, the MIDI roll will be composed of every C from C-2 to C8.
Because the Shepard Tone is created using pure sine waves, its spectrograph image indicates a sharp peak at every frequency included from its lowest octave iteration to its highest octave iteration.
Each of these tones is fundamental in the Shepard Tone tone profile and there are no partials along the way. But just by listening to a static Shepard Tone, the familiar illusion is not apparent. Instead, we look to Shepard Scales.
What is the Shepard Scale?
The Shepard Scale is essentially a chromatic scale made up of Shepard Tones. The Shepard “tones” that are lowest in pitch fade in gradually as the scale ascends, and then fade out as they reach the peak frequency.
This creates the illusion of a never-ending ascending scale, much like a barber pole, because one never hears the absolute end.
As one line of the higher pitches fades out, the ear is drawn to one of the lower lines, which continues its ascent until it too fades out. The illusion also works in the reverse if one wishes to create a never-ending descending scale.
The Shepard-Risset Glissando
Jean-Claude Risset, the French composer of computer-based music, first pioneered the use of a Shepard Scale that moves upwards or downwards in continuous pitch as opposed to discrete half-steps.
This is the version of the Shepard Scale that has become most familiar to audiences over time. The steady glissando that seems never to arrive at a conclusion has been known to cause some anxiety in listeners, which makes it a useful tool for composers.
How Has The Shepard Tone Been Used For Research In Music Perception?
Shepard Tones, by including every octave of a pitch class within the audible range, essentially flatten the full breadth of the audible range into a single cycle of pitch classes.
For this reason, Roger Shepard hypothesized that two Shepard Tones of different pitch classes presented sequentially would sound like a bistable figure – neither ascending nor descending.
What Diana Deutsch would discover some years later, in 1986, however, was that there was more to it than first meets the ear…
The Tritone Paradox
The tritone paradox is produced with a pair of Shepard Tones spaced one tritone apart. The tone pair must be played successively, meaning that one Shepard Tone is played first, then the other Shepard Tone follows.
Deutsch found that one person might hear the pattern as ascending in pitch, whereas another person would hear the same pattern as descending.
Over the course of her research, Diana Deutsch discovered that the relationship between Shepard Tones was not bistable, but rather a listener would hear roughly half of the pitch classes as the higher pitch classes and the other half, on the opposite side of the pitch class circle, as the lower pitch classes. This is despite the fact that Shepard Tones are composed of ambiguous height and depths relative to one another.
She found that a listener’s perception varied based on their linguistic background.
In this way, the neutrality of the Shepard Tone brought to the surface an essential and groundbreaking finding in our understanding of how humans perceive music.
What Are Some Examples Of The Shepard Tone In Music And Sound Design?
The Shepard Tone has been used in a wide variety of contexts both for its use as an audio illusion in creating the Shepard Scale, building seemingly endless tension, and directly as a sound effect. A few of the more prominent examples of the Shepard Tone follow below.
Pink Floyd’s Echoes
A particularly strong example of the Shepard-Risset Glissando can be heard at the end of Echoes, beginning just after the 22-minute mark in the Meddle version.
Super Mario 64
A modified Shepard Scale is used to score a moment in Super Mario 64 in which Mario is ascending a staircase meant to appear never-ending.
The audio illusion of an infinite rise accompanies the visual illusion in the video game.
Christopher Nolan’s The Dark Knight And The Dark Knight Rises
The Shepard Tone has made itself invaluable in filmmaking. The sound design for the Batpod, a hyper-futuristic motorcycle, utilizes an ascending Shepard-Risset scale so as to portray a motor that accelerates smoothly with no shifting required.
This is one of many run-ins Christopher Nolan has had with Shepard Tones.
Christopher Nolan’s Dunkirk
Another Nolan film, and another Nolan film scored by Hans Zimmer. The Shepard-Risset scale is used in the sound design of this film not for sound effects or as an overt illusion but as a means of building tension over the course of the film.
The treatment is incredibly effective, making the final release of suspense at the end of the film even more satisfying.
Whether your purpose is to render contour and octave number meaningless or create the feeling of suspense throughout the listening experience (as Hans Zimmer does in the score for Dunkirk), the Shepard Tone and its many uses might just be the perfect tool to accomplish your musical goal.
It is the perfect proof of concept that music and sound are multifaceted entities, capable of moving audiences in many more ways than the standard manipulation of volume and arrangement.
The next time you as a sound designer or composer find yourself in need of a special kind of intensity or an illusion, you can reach for the Shepard Scale and Shepard Tones. For other great ways to create intensity and suspense, make sure you read Suspended Chords (Explained Simply With Audio Examples).