The Shepard Tempo Illusion

by Graham Waldon

Sound File | Code

This project is based on the Shepard Tone illusion, but instead of a continuously rising tone, I have tried to create a continuously accelerating beat. As with the Shepard Tone, there are actually multiple voices, but as they accelerate, the faster voices fade out and the slower ones become louder, so it can loop indefinitely. It should sound as though it is continuously accelerating, while actually returning to the original tempo every few seconds. This first image shows the example sound file, in which you can clearly see three repeated periods.

This is what the quarter note voice looks like by itself. It maintains a constant amplitude over the course of one period and it doubles in speed to be equivalent to eighth notes.

This is what a complete single period looks like, with the eighth note voice added. The eighth notes decrease in amplitude so that they go to zero by the end when they are the speed of sixteenth notes. When the period starts over, every other quarter note (at the new tempo) gets reinterpreted as an eighth and the cycle starts over.

Here is one of the previous versions I tried with three voices - quarters, eighths and sixteenths. The eighths vary in amplitude twice in a period while the sixteenths fade out like the eighths in the final version. Again, the problem was to mask the disappearance of that voice, which is why the eighths do not go all the way to zero. I found, however, that it was more effective with the eighths not varying at all, which made it equivalent to only two voices.