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A Shepard tone, named after Roger Shepard, is a sound 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.

The acoustical 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 lithograph Ascending and Descending, or a barber’s pole.

As an example, consider a brass trio consisting of a trumpet, a horn, and a tuba. They all start to play a repeating C scale in their respective ranges, i.e. they all start playing Cs, but their notes are all in different octaves. When they reach the G of the scale, the trumpet drops down an octave, but the horn and tuba continue climbing. They’re all still playing the same pitch class, but at different octaves. When they reach the B, the horn similarly drops down an octave, but the trumpet and tuba continue to climb, and when they get to what would be the second D of the scale, the tuba drops down to repeat the last seven notes of the scale. So no instrument ever exceeds an octave range, and essentially keeps playing the exact same seven notes over and over again. But because two of the instruments are always “covering” the one that drops down an octave, it seems that the scale never stops rising.

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. When done correctly, the tone appears to rise continuously in pitch, yet return to its starting note. Risset has also created a similar effect with rhythm in which tempo seems to increase or decrease endlessly.

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, created a piece utilizing this effect, For Ann. 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 ratio, 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. Echoes, a 23-minute song by Pink Floyd, concludes with a rising Shepard tone. The Shepard tone is also featured in the fading piano outro to A Last Straw, from Robert Wyatt’s 1974 opus Rock Bottom.

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