![]() ![]() ![]() 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. Shepard scales in music Īlthough 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). Risset has also created a similar effect with rhythm in which tempo seems to increase or decrease endlessly. When done correctly, the tone appears to rise (or descend) continuously in pitch, yet return to its starting note. 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. But because two of the instruments are always "covering" the one that drops down an octave, it seems that the scale never stops rising. So no instrument ever exceeds an octave range, and essentially keeps playing the exact same seven notes over and over again. 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. They're all still playing the same pitch class, but at different octaves. When they reach the G of the scale, the trumpet drops down an octave, but the horn and tuba continue climbing. they all start playing Cs, but their notes are all in different octaves. They all start to play a repeating C scale (C–D–E–F–G–A–B–C) in their respective ranges, i.e. The illusion is more convincing if there is a short time between successive notes ( staccato or marcato instead of legato or portamento).Īs a more concrete example, consider a brass trio consisting of a trumpet, a horn, and a tuba. The scale as described, with discrete steps between each tone, is known as the discrete Shepard scale. (In other words, each tone consists of ten sine waves with frequencies separated by octaves the intensity of each is a gaussian function of its separation in semitones from a peak frequency, which in the above example would be B(4).) The twelfth tone would then be the same as the first, and the cycle could continue indefinitely. ![]() The two frequencies would be equally loud at the middle of the octave (F#), and the eleventh tone would be a loud B(4) and an almost inaudible B(5) with the addition of an almost inaudible B(3). The next would be a slightly louder C#(4) and a slightly quieter C#(5) the next would be a still louder D(4) and a still quieter D(5). As a conceptual example of an ascending Shepard scale, the first tone could be an almost inaudible C(4) ( middle C) and a loud C(5) (an octave higher). Overlapping notes that play at the same time are exactly one octave apart, and each scale fades in and fades out so that hearing the beginning or end of any given scale is impossible. The color of each square indicates the loudness of the note, with purple being the quietest and green the loudest. Escher's lithograph Ascending and Descending) or a barber's pole, the basic concept is shown in Figure 1.Įach square in the figure indicates a tone, any set of squares in vertical alignment together making one Shepard tone. Similar to the Penrose stairs optical illusion (as in M. The acoustical illusion can be constructed by creating a series of overlapping ascending or descending scales. ![]()
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