Shepard's tones present a musical illusion of either infinitely rising (or infinitely falling) set of pitches from repetition of just a finite set. Click on the first link below to listen to an audio file of a set of rising Shepard tones. The next link provides a musical example using the illusion.
Shepard's tones (audio)
Sierpinski round (audio). An example of ambient music using the Shepard tone illusion.
Musical Precursors: Bach and Tchaikovsky
It would be surprising if, in the long history of music, there were no precursors to Shepard's illusion. We consider two examples here. One, from a passage of Bach's, partially exhibits the illusion - if one listens in the right way . The second example, from a passage of Tchaikovsky, is a more definitive exhibition of the illusion.
Here we have two clips from different recordings of Bach's Jesu, Joy of Man's Desiring which show that perhaps Bach was there first. In each one, if you focus attention on the base line you should perceive (to a degree) the infinitely rising pitch: which is illustrative of the religious theme of the piece. Bach interleaves both ascending and descending notes so the illusion is only partly discernable (whether that was Bach's intention, of course, is unknown).
Jesu, Joy of Man's Desiring (piano arrangement)
Jesu, Joy of Man's Desiring (instrumental version following the cantata score, BWV 147)
A more convincing example perhaps is the following passage from Tchaikovsky's Symphony No. 6 in B Minor (Pathetique). You should hear a continuously rising string sound. The spectrogram below will make it clear that this continuously rising tone is a Shepard illusion - realized in music, more than half a decade before Shepard's example!
Tchaikovsky Pathetique passage
The spectrograms for these passages, especially the Shepard's tones, the Sierpinski round, and the Tchaikovsky passage, illustrate how the illusions are created. Click on each link to see the spectrogram and to play a video of the spectrogram tracing along with the sound. We also have provided some musical scores for the Bach and Tchaikovsky passages.
Shepard's tones (spectrogram and video)
Sierpinski round (spectrogram and video)
Jesu, Joy of Man's Desiring (piano arrangement) (spectrogram, video, and musical score)
Jesu, Joy of Man's Desiring (instrumental version, BWV 147) (spectrogram, video, and musical score)
Tchaikovsky Pathetique passage (spectrogram, video, and musical score)
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