31 August 2025

The Infinite Climb: Shepard Tones, Rock Music, and the Fractal Mind

What Is a Shepard Tone?

A Shepard tone is an auditory illusion that creates the impression of a continuously ascending or descending pitch, without ever reaching a peak or a bottom. The effect is achieved by layering sine waves separated by octaves, with their amplitudes carefully faded in and out. As one tone fades out, another fades in, creating a seamless loop that tricks the brain into perceiving an endless rise or fall (Deutsch).

Shepard Tones in Rock Music

While Shepard tones are often associated with film scores (Zimmer famously used them in Dunkirk), they have also found a place in rock music, where their hypnotic and disorienting qualities can heighten the listener’s experience.

Pink Floyd – “Echoes”

In the final section of Pink Floyd’s “Echoes” (1971), the band employed tape loops that create Shepard-like effects. Two tape recorders were placed at opposite ends of a room: one playing the main chords, the other re-recording and delaying them. The result warped harmonic structures and produced the illusion of a tone climbing endlessly (Wikipedia, Echoes).

Muse – “The Handler”

Muse used a Shepard tone in “The Handler” (2015). During the bridge, the illusion of continuous ascent heightens the song’s tension, reinforcing its themes of manipulation and resistance (Splice).

King Crimson – “VROOOM”

King Crimson’s “VROOOM” (1994) employs a Shepard-like ascending riff. The layering of guitars and synths produces the sensation of perpetual motion, consistent with the band’s broader use of recursive, fractal-like rhythmic patterns (Tamm 214).

The Fractal Connection

Fractals are geometric figures that show self-similarity across scales. Shepard tones embody this principle in sound: each octave is a miniature version of the whole, fading in and out as part of the larger pattern (Hofstadter 10).

In rock music, this creates the perception of infinity. Recursive riffs, looping structures, and polyrhythms echo fractal mathematics. A Shepard tone translates this principle into an auditory paradox: motion without resolution, infinity folded into sound.

Conclusion

The Shepard tone is both a scientific illusion and a musical metaphor for infinity. In rock, it bridges physics, mathematics, and artistry, creating music that feels perpetually alive. Its connection to fractals highlights how rock musicians have tapped into deep structures of perception—patterns that are both mathematical and emotional, endlessly recursive yet profoundly human.

Works Cited

Deutsch, Diana. The Psychology of Music. Academic Press, 2013.
Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid. Basic Books, 1979.
Splice. “Shepard Tone: The Sonic Illusion Behind Dunkirk and Muse.” Splice Blog, 2019, https://splice.com/blog/shepard-tone-illusion.
Tamm, Eric. Robert Fripp: From King Crimson to Guitar Craft. Faber & Faber, 1990.
Wikipedia contributors. “Echoes (Pink Floyd song).” Wikipedia, Wikimedia Foundation, https://en.wikipedia.org/wiki/Echoes_(Pink_Floyd_song).
Wikipedia contributors. “Shepard tone.” Wikipedia, Wikimedia Foundation, https://en.wikipedia.org/wiki/Shepard_tone.