The Shepard Tone Audio Illusion

An example of how humans process information

Much of my research and writing is about how human beings, other animals, and non-animals, such as computers, process information. There should be clear interrelations between my posts about politics and society, art, artificial intelligence, and my posts, such as here, about audio and visual illusions. Illusions demonstrate that there is a difference between physical reality and our perception of physical reality.

The Shepard tone audio illusion is often compared to the neverending staircase where you seem to be continually moving up the staircase (or down, depending which direction you follow the steps), yet end up where you started.

Invented by Stanford University cognitive scientist, psychology professor and U.S. National Medal of Science winner Roger N. Shepard, the Shepard tone is a famous auditory illusion. An auditory illusion is like a visual illusion but involves hearing instead of sight. 

The Shepard tone sounds to the listener as if it's continually going down-- or continually up, depending if the notes are played the opposite way. However, the sound is a repeated scale of notes, much like the repeated loop of steps of the staircase that takes you to where you started. The tones do not continually go down (or up), it only seems that way.  

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How the Shepard tones works

The Shepard tone involves a carefully calculated manipulation of tones, just as the steps in the never-ending staircase were carefully crafted to trick the eye. The audio illusion manipulation involves not only which tones are played but the volume of the individual notes in the tones. 

Each tone is comprised of several notes played simultaneously, and at each moment, different notes are played at different volumes. Some notes are played loudly, while others are nearly inaudible. The volume changes have the listener focusing on certain notes and not others. As with the steps in the staircase, the key to the trickery is each tone seems to sound lower than the preceding (higher if the notes are played the other way) even if it isn't. 

The listener judges subtle gradations in tone by comparing it to the preceding notes, not to tones from twenty or thirty seconds ago and certainly not to future notes. If each tone appears lower than the previous, the listener will think the sound continually going down.

So how the heck can you make a lower tone sound higher?

At first, this may seem impossible, but it's simple when you manipulate the volumes of the notes within the tone. Just look at the below tones.

The above a and b are the same tone, each with the same three notes. How would you lower the notes in tone b, while making it sound higher than a? The answer is by changing the volumes of the notes.

If you alter the volumes of the notes, you can make lowered b sound higher. The black notes are played loudly, while the whites are played very softly. As you can see, the loud notes of b are higher than the two loud notes of a.

The changing volume works as an audial mask, with masking or hiding of information being a common element of both audial and visual illusions. If you put your fingers or pieces of white paper over the white notes in the bottom picture, tone b will also look like a higher tone. This shows you that the Shepard tone is much like a visual illusion.

The repeated Shepard tone involves a much more complex and larger variety of tones, notes and volume manipulations.

The Shepard tone has been used in music. Music soundtrack composer Hans Zimmer has used it several times in movies, including in the below piece used in Blade Runner 2049.

A life’s work in illusions

The son of an engineering professor, Shepard had an interest in illusions since he was a child. His life’s work studied how humans and animals imperfectly process sensory information. This included studying and producing visual illusions.

His most famous visual illusion is called the Shepard Tables. Though the table tops appear of different sizes and dimensions, they are the same.

The below short video demonstrates that the table tops are the same size and dimensions