What to observe

Listen to the sequence of tones. Maybe adjust volume (it's preset at 5% to reduce possible annoyance when opening this page). The tone rises in pitch from step to step –  and continues to do so, endlessly. Really? That's impossible…

What to do

The tone is composed of a mixture of various octaves. You can change the number of voices (default 10), and the base pitch (octave). The latter needs to be incremented if you markedly reduce the number of voices.


Roger Shepard invented this acoustic illusion in 1964. His basic idea was as follows: When the pitch rises one step, the harmonic composition is altered (a little less high, a little more low harmonics). This is done in such a way that after 11 steps the harmonic content corresponds nearly to a tone one octave lower. With the next step the sequence resorts to the first one (the note ‘A’. In Hofstaedter's Gödel, Escher, Bach there's also a nice explanation.

In his 1964-article Shepard himself likened this to Escher' ever-rising staircase. In fact, the icon on top right is lifted from Shepard's paper.

This happens to be the first illusion demo I published, ever: In 1991, in the German computer journal “c't” I described the effect and printed a full Mac program (560 lines of Pascal code) that demonstrated the Shepard tone with the 4-voice synthesizer of the original Macintosh. Nowadays it's little easier: there's Web Audio, wrapped in P5, 125 lines.


Roger Shepard (1964) Circularity in Judgements of Relative Pitch. Journal of the Acoustical Society of America 36 (12): 2346–2353. doi: 10.1121/1.1919362 (paywall).

Bach M (1991) Mac mogelt · Demonstration einer akustischen Täuschung auf dem Macintosh. Computertechnik (c't) 5:274–282

Wikipedia “Shepard tone”


Created: 2016-07-25

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Last update 2016-07-27 by Michael Bach (G+)