The following graph of Shepard’s paradox shows frequency versus time. You can plainly see that the single pitch section appears to be increasing. Note that if the same graph is looped you can see that the finishing pitch is the same as the starting pitch.
It may be obvious to the eye, but the ear cannot perceive where the sample starts and finishes. If you listen to this sample the tones will appear to increase in pitch even if the sample loops back to the beginning and starts over. Here are the Audio Samples. This effect works best if you put on your head-phones. If the players below don’t work for you, download the mp3s, and loop them in your player.
Shepard’s ascending tones (MP3) – This is a recording of Shepard’s paradox synthesized by Jean-Claude Risset. Pairs of chords sound as if they are advancing up the scale, but in fact the starting pair of chords is the same as the finishing pair. If you loop this sample seamlessly then it should be impossible to tell where the sample begins and ends.
Falling bells (MP3) – This is a recording of a paradox where bells sound as if they are falling through space. As they fall their pitch seems to be getting lower, but in fact the pitch gets higher. If you loop this sample you will clearly see the pitch jump back down when the sample repeats. This reveals that the start pitch is obviously much lower than the finishing pitch.
Quickening Beat (MP3) – This recording is subtle. A drum beat sounds as if it is quickening in tempo, but the starting tempo is the same as this finishing tempo.