Muse – “The Handler”

Muse incorporated a Shepard tone in The Handler (2015), during a bridge where the illusion of continuous ascent amplifies the song’s narrative tension. The endless rise mirrors the psychological manipulation described in the lyrics, reinforcing the theme of inescapable control (Splice 2019).

King Crimson – “VROOOM”

King Crimson’s VROOOM (1994) demonstrates a Shepard-like ascending riff layered across guitars and synths, producing the sensation of perpetual motion. This approach reflects the band’s fascination with recursive and fractal-like rhythms, in which musical motifs echo across scales, creating an impression of infinite development within a finite passage (Tamm 1990).

Radiohead – “Everything in Its Right Place”

In Radiohead’s Kid A (2000), Shepard tones subtly underscore transitions, adding unease and forward momentum. The continuous tension aligns with the album’s exploration of alienation and technological dislocation, showing how minimalistic electronic elements can evoke complex psychological responses.

The Physics and Psychology of Perpetual Motion

Shepard tones are not just tricks—they reveal how humans perceive pitch, tension, and musical expectation. By overlapping octaves and fading amplitudes, these tones prevent auditory closure. Listeners perceive motion without destination, a paradox that challenges linear time in music. In rock, this can heighten emotional impact, creating anxiety, excitement, or awe (Deutsch 2013).

Musicians can leverage this effect to mimic narrative or emotional arcs: the rise may feel like escalation, struggle, or aspiration; the fall can evoke despair or suspense. The listener experiences a loop that never resolves, an “infinite climb” that mirrors cognitive and emotional cycles.

The Fractal Connection

Fractals are geometric figures that exhibit self-similarity at different scales. Shepard tones embody a sonic fractal: each octave is a miniature version of the whole, fading in and out as part of a larger auditory pattern (Hofstadter 1979). In rock music, this translates to recursive riffs, looping structures, and polyrhythms that echo fractal mathematics.

This connection to fractals aligns with the cognitive effect of infinity: listeners perceive patterns that repeat endlessly, producing both fascination and slight disorientation. Bands like Tool, King Crimson, and Yes use these recursive principles, often layering Shepard-like effects with polyrhythms and modal harmonies to extend the sense of timelessness.

Shepard Tones as Emotional and Narrative Tools

• Tension and Release: Continuous rise without resolution amplifies musical tension, making subsequent climaxes feel more dramatic.
• Psychological Disorientation: The endless rise or fall can create unease, uncertainty, or anticipation, enhancing lyrical or thematic content.
• Symbolism of Infinity: By implying endless motion, Shepard tones suggest concepts like ambition, struggle, or cosmic scale, aligning with lyrical themes of transcendence or existential inquiry.
• Structural Unity: They can tie together disparate sections of a song, providing a continuous auditory thread across different tempos, keys, or textures.

Conclusion

The Shepard tone is both a scientific illusion and a metaphor for infinity. In rock music, it bridges mathematics, psychology, and artistry, creating sounds that feel perpetually alive. Its connection to fractals highlights the capacity of musicians to manipulate perception, turning auditory experience into a recursive, self-similar journey. From Pink Floyd to Muse, from King Crimson to Radiohead, Shepard tones transform music into a loop without end—an infinite climb that reflects the human fascination with boundless motion, tension, and emotional depth.

Image Credit: Freepik.com