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The tritone paradox is an
auditory illusion
Auditory illusions are Illusion, illusions of real sound or outside stimulus. These false perceptions are the equivalent of an optical illusion: the listener hears either sounds which are not present in the Stimulus (physiology), stimulus, or sound ...
in which a sequentially played pair of
Shepard tones separated by an
interval of a
tritone
In music theory, the tritone is defined as a interval (music), musical interval spanning three adjacent Major second, whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be ...
, or half octave, is heard as ascending by some people and as descending by others. Different populations tend to favor one of a limited set of different spots around the
chromatic circle as central to the set of "higher" tones.
Roger Shepard
Roger Newland Shepard (January 30, 1929 – May 30, 2022) was an American cognitive science, cognitive scientist and author of the "universal law of generalization" (1987). He was considered a father of research on spatial relations. He studied m ...
in 1963 had argued that such tone pairs would be heard ambiguously as either ascending or descending. However,
psychology of music researcher
Diana Deutsch
Diana Deutsch (born 15 February 1938) is a British-American psychologist from London, England. She is a professor of psychology at the University of California, San Diego, and is a prominent researcher on the psychology of music. Deutsch is ...
in 1986 discovered that when the judgments of individual listeners were considered separately, their judgments depended on the positions of the tones along the
chromatic circle. For example, one listener would hear the tone pair C–F as ascending and the tone pair G–C as descending. Yet another listener would hear the tone pair C–F as descending and the tone pair G–C as ascending. Furthermore, the way these tone pairs were perceived varied depending on the listener's language or dialect.
Each Shepard tone consists of a set of octave-related sinusoids, whose amplitudes are scaled by a fixed bell-shaped spectral envelope based on a log frequency scale. For example, one tone might consist of a sinusoid at 440 Hz, accompanied by sinusoid at the higher octaves (880 Hz, 1760 Hz, etc.) and lower octaves (220 Hz, 110 Hz, etc.). The other tone might consist of a 311 Hz sinusoid, again accompanied by higher and lower octaves (622 Hz, 155.5 Hz, etc.). The amplitudes of the sinusoids of both complexes are determined by the same fixed-amplitude envelope—for example, the envelope might be centered at 370 Hz and span a six-octave range.
Shepard 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. Diana Deutsch later found that perception of which tone was higher depended on the absolute frequencies involved: an individual will usually find the same tone to be higher, and this is determined by the tones' absolute pitches. This is consistently done by a large portion of the population, despite the fact that responding to different tones in different ways must involve the ability to hear
absolute pitch
Absolute pitch (AP), often called perfect pitch, is the ability to identify or re-create a given musical note without the benefit of a reference tone. AP may be demonstrated using linguistic labelling ("naming" a note), associating mental image ...
, which was thought to be rare. This finding has been used to argue that latent absolute-pitch ability is present in a large proportion of the population. In addition, Deutsch found that subjects from the south of England and from California resolved the ambiguity the opposite way. Also, Deutsch, Henthorn and Dolson found that native speakers of
Vietnamese, a
tonal language, heard the tritone paradox differently from Californians who were native speakers of English.
[Deutsch, D., Henthorn T. and Dolson, M. "Speech patterns heard early in life influence later perception of the tritone paradox". ''Music Perception'', 21:357–372, 2004.]
See also
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Barberpole illusion
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Flanging
Flanging is an audio signal processing, audio effect produced by mixing two identical audio signal, signals together, one signal delayed by a small and (usually) gradually changing period, usually smaller than 20 milliseconds. This produces a ...
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Missing fundamental
The pitch being perceived with the first harmonic being absent in the waveform is called the missing fundamental phenomenon.
It is established in psychoacoustics that the auditory system, with its natural tendency to distinguish a tone from anoth ...
Notes
References
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External links
** Audio links in Au file format
The Au file format is a simple audio file format introduced by Sun Microsystems. The format was common on NeXT systems and on early Web pages. Originally it was headerless, being 8-bit μ-law algorithm, μ-law-encoded data at an 8000 Hz sample rat ...
with 8-bit G.711 μ-law data encoding at 8000 samples per second with 1 channel
tt/a110.au tt/b110.au tt/a160.au tt/b160.au
Diana Deutsch's page on auditory illusions
Sound example of the tritone paradox
{{Music psychology
Auditory illusions
Paradoxes
Tritones
de:Akustische Täuschung#Tritonus-Paradoxon