Shepard scale
The Shepard scale or Shepard scale , introduced in 1964 by the psychologist Roger Shepard , is the illusion of an infinitely rising or falling scale that never exceeds the limit of one's own hearing.
This effect is achieved by a number of different sine tones (usually more than eight), which slowly increase or decrease in frequency and are cyclically exchanged with each other by slowly increasing and decreasing the volume. The frequencies of the individual sine tones are each one octave apart and are slowly shifted in parallel over a limited frequency range. Tones that approach the limit of the frequency range are faded out; for every tone that falls outside the frequency range at one end, a new one is faded in at the other end. The spectrum of the resulting sound is practically given an unchangeable bell-shaped envelope , which is traversed by the sequence of partials .
Depending on the direction of the frequency shift, the listener is given the impression of a tone sequence that is continuously rising or falling in pitch.
If the frequency change takes place in discrete tone steps in the form of short sounds that follow one another with a time interval, one speaks of the Shepard scale . If the partials are held permanently and their frequencies are continuously changed, the resulting effect is called Shepard-Risset-Glissando after the composer Jean-Claude Risset .
The human hearing sensation cannot distinguish which tone is the fundamental frequency and which is an overtone due to the continuous, time-shifted swelling of the individual sinusoidal tones: the auditory impression changes imperceptibly between the fundamental and harmonic. This acoustic illusion is comparable to the optical illusion of a barber-pole illusion , which, depending on the direction of rotation, seems to move forever down or up.
The perception of the Shepard scale is based on the gestalt psychological law of proximity. If you look at the whole thing in terms of the scale , a jump from C to C sharp, for example, is perceived as a rising semitone step, while a jump from C to B as a falling semitone step. As the size of the intervals that law loses close in intensity, culminating in the tritone in the tritone paradox .
The Hungarian composer György Ligeti mimicked the effect of the Shepard scale in his piano etude L'escalier du diable [The Devil's Ladder] (No. 13 from the 2nd book of the Études pour piano [1988/94]).
An effect similar to the Shepard scale is achieved with repeating sound crowns in the pipe organ.
Audio sample
Web links
- Explanation of the Shepard scale in English ( Memento of March 13, 2007 in the Internet Archive )