__NOTOC__ The tritone paradox is an

auditory illusion Auditory illusions are false perceptions of a 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, or sounds that should not be p ...

in which a sequentially played pair of

Shepard tone A Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves. When played with the bass pitch of the tone moving upward or downward, it is referred to as the ''Shepard scale''. This cr ...

s separated by an interval of a

tritone In music theory, the tritone is defined as a musical interval composed of three adjacent 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 decomposed into the three a ...

, 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 The chromatic circle is a clock diagram for displaying relationships among the 12 equal-tempered pitch classes making up the familiar chromatic scale on a circle. Explanation If one starts on any equal-tempered pitch and repeatedly ascends by t ...

as central to the set of "higher" tones.

Roger Shepard Roger Newland Shepard (January 30, 1929 – May 30, 2022) was an American cognitive scientist and author of the " universal law of generalization" (1987). He was considered a father of research on spatial relations. He studied mental rotation, a ...

in 1963 had argued that such tone pairs would be heard ambiguously as either ascending or descending. However,

psychology of music ''Psychology of Music'' is a peer-reviewed academic journal that publishes papers in the field of music psychology. The editor-in-chief is Alexandra Lamont (Keele University). It was established in 1973 and is published by SAGE Publications on beh ...

researcher

Diana Deutsch Diana Deutsch (born 15 February 1938) is a British-American psychologist from London, England. She's 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

. 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 The Necker cube is an optical illusion that was first published as a Rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. It is a simple wire-frame, two dimensional drawing of a cube with no visual cues as to its orientation, so it ...

, 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 a rare ability of a person to identify or re-create a given musical note without the benefit of a reference tone. AP may be demonstrated using linguistic labeling ("naming" a note), associating ...

, which was thought to be extremely 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.

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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 simply 8-bit μ-law-encoded data at an 8000 Hz sample rate. H ...

with 8-bit

G.711 G.711 is a narrowband audio codec originally designed for use in telephony that provides toll-quality audio at 64 kbit/s. G.711 passes audio signals in the range of 300–3400 Hz and samples them at the rate of 8,000 samples per second ...

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

See also

Notes

References

External links