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A Shepard tone is a sound, named after Roger Shepard, consisting of a superposition of sine waves separated by octaves. When played with the base pitch of the tone moving upwards or downwards, it is referred to as the Shepard scale. This creates the auditory illusion of a tone that continually ascends or descends in pitch, yet which ultimately seems to get no higher or lower.
Construction of a Shepard scale
The illusion can be constructed by creating a series of overlapping ascending or descending scales. Similar to the Penrose stairs optical illusion (as in M.C. Escher's lithography Ascending and Descending) or a barber's pole, the basic concept is shown in Figure 1.
Each square in the figure indicates a tone, any set of squares in vertical alignment together making one Shepard tone. The color of each square indicates the loudness of the note, with purple being the quietest and green the loudest. Overlapping notes that play at the same time should be exactly one octave apart, and each scale should fade in and fade out, such that it is impossible to hear the beginning or end of any given scale. The scale as described, with discrete steps between each tone, is known as the discrete Shepard scale. Jean-Claude Risset subsequently created a version of the scale where the steps between each tone are continuous, and it is appropriately called the continuous Risset scale or Shepard-Risset glissando. Risset has also created a similar effect with rhythm in which tempo seems to increase or decrease endlessly.
To make the illusion more convincing, it helps to have some amount of space between each note (staccato or marcato instead of legato or portamento). When done correctly, the tone appears to rise (or descend) continuously in pitch, yet return to its starting note.
Shepard scales in music
Although it is difficult to recreate the illusion with acoustic instruments, James Tenney, who worked with Roger Shepard at Bell Labs in the early 1960s, has created a piece utilizing this effect, For Ann (rising). The piece, in which up to twelve closely- but not quite consistently-spaced computer-generated sine waves rise steadily from an A pitched below audibility to an A above, fading in, and back out, of audible volume, was then scored for twelve string players. The effect of the electronic work consists both of the Shepard scale, seamless endlessly (rising) glissandos, and of a shimmering caused by the highest perceivable frequency and the inability to focus on the multitude of rising tones. Tenney has also proposed that the piece be revised and realized so that all entrances are timed in such a way that the ratio between successive pitches is the golden mean, which would make each lower first order combination tone of each successive pair coincide with subsequently spaced, lower, tones.
An independently discovered version of the Shepard tone appears at the beginning and end of the 1976 album A Day At The Races by the band Queen. The piece consists of a number of electric guitar parts following each other up a scale in harmony with the notes at the top of the scale fading out as new ones fade in at the bottom. Lose Control by Missy Elliott also seems to feature an ascending Shepard tone as a recurring theme. Echoes, a 23-minute song by Pink Floyd, concludes with a rising Shepard tone.
Another independent discovery, in classical music, occurs in the Fantasy and Fugue in G minor for organ, BWV 542, by Bach. Midway through the Fantasy there is a descending pedal bass line under a chord sequence which traverses the circle of fifths. By gradually adding stops up to full organ sound, something akin to a barber pole pattern occurs, and an illusion of ever-deeper descent is created, even though the bass line actually skips octaves.
Example
References
External links
"Shepard tone"