![]() ![]() 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. ![]() (More accurately, 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 thirteenth 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 twelfth 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.C. ![]() (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).Ī sequentially played pair of Shepard tones separated by an interval of a tritone (half an octave) produces the tritone paradox In this auditory illusion, first reported by Diana Deutsch in 1986, the scales may be heard as either descending or ascending. Shepard had predicted that the two tones would constitute a bistable figure, the auditory equivalent of the Necker cube, that could be heard ascending or descending, but never both at the same time. Deutsch later found that perception of which tone was higher depended on the absolute frequencies involved, and that different listeners may perceive the same pattern as being either ascending or descending.The illusion can be constructed by creating a series of overlapping ascending or descending scales. 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). 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). The color of each square indicates the loudness of the note, with purple being the quietest and green the loudest. Each square( in the picture above ) indicates a tone, any set of squares in vertical alignment together making one Shepard tone. ![]()
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