How to Orchestrate an Endless Rising Tone Effect

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The “Shepard Tone,” also known as the “Shepard Scale” or “Shepard Illusion,” is an auditory illusion discovered by American cognitive scientist Roger Shepard in 1964. Shepard presented his findings in an article titled “Circularity in Judgments of Relative Pitch” published by The Journal of the Acoustical Society of America¹. When this illusory effect is achieved, the listener perceives a tone that ascends or descends in perpetuity, an auditory version of M.C. Escher’s never-ending staircase, or I’ve also heard it called a “sonic barber pole.”

In other words, it sounds like the tones keep rising or falling forever fluidly, and it sounds pretty scary. Just listen:

The effect can be achieved easily via synthesis, either with a stepwise scale, as computer scientist Michael Bach demonstrates here, or through the use of glissandi (below). But it’s definitely possible to create the illusion using orchestral instruments too, as we’ll see  below. In either case, multiple voices moving in tandem upwards or downwards need to be utilized.

Synthesized Instruments

In Michael Bach’s example, a computer program is designed to play a chromatic scale repeating in octave mixtures. With each step in the scale, the harmonic content changes; a little more of the low frequencies and a little less of the high until by the 11th step, it corresponds nearly to a tone one octave lower and the sequence starts over, without us ever knowing.

With the higher partials slowly fading out and lower partials slowly fading in, the ear’s memory is checked and the higher octave is perpetually picking up where the lower voice left off. This can also be done in the opposite direction by the higher partials increasing in amplitude as the pitches descend and the lower partials decreasing.

In the second example, developed by composer/computer musician Jean-Claude Risset and often referred to as the “Shepard-Risset Glissando,” there is even less for the listener to grasp onto as the glissando allows for the full range of microtonal frequencies within the octave to be covered.

Risset was at Bell Labs in the 1960s where he worked with early computer software, experimented with FM synthesis, and used spectral analysis of acoustic instruments to develop digital approximations. He also developed a similar “Shepard effect” with rhythm in which the listener perceives a tempo that perpetually increases or decreases.

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Acoustic Instruments

Acoustic instruments don’t allow for the same measured precision as a computer program might in achieving the exact effect that Shepard posited, but it certainly is possible to utilize string instruments to create this illusion, and there is definitely ample room for creative exploration.

Here is a clear, fun, and engaging example of the effect being explored by composer Alba S. Torremocha in a piece for string quartet titled “Shepard Roots.”

The consistency of timbre in the string quartet and the instruments’ ability to glissando between notes makes the string section particularly well-suited for exploring the concept.

Here’s a funny version done with slide whistles.

Try to emulate Michael Bach’s stepwise program with two acoustic instruments playing a chromatic scale in octaves. The upper voice should start forte and decrescendo as it ascends, and the lower voice should start pianissimo or even niente and crescendo as it ascends. As they pass each other in amplitude, they’ll pass off the listener’s attention to one another to keep the illusion alive in the ear.

It’s harder to emulate the glissando version acoustically, since you’ll have to account for dissonance if the octaves aren’t totally lined up, but try it nonetheless! Some things to keep in mind as you listen back:

  • Is the jump back down an octave noticeable?
  • What can be done to obscure it? Perhaps adding more voices and octaves will help to smooth it over?
  • What’s the difference between a string quartet playing this vs. a string section in a larger orchestra?

Again one of the reasons the loop beginning again is not noticeable in Bach’s program is on account of the computer’s ability to execute precisely measured frequency and amplitude. In the program’s case, each pitch can almost be thought of as one tone with the first partial of the overtone series increasing and decreasing as desired.

If you don’t have access to acoustic instruments, you might begin exploring the concept in MIDI with a digital string library. Here are some instructions for how make a Shepard Tone in a DAW.

Beyond attempting to simulate the effect with acoustic means, this can be a great jumping off point to explore composing with glissandi, dynamic balance, and shifting volume within an ensemble.

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¹ Abstract of Shepard’s “Circularity in Judgments of Relative Pitch” in The Journal of the Acoustical Society of America.

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