Editing Tritone paradox (section)

{{Short description|Auditory illusion}}
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The '''tritone paradox''' is an [[auditory illusion]] in which a sequentially played pair of [[Shepard tone]]s<ref>R. N. Shepard. "Circularity in judgments of relative pitch". ''Journal of the Acoustical Society of America'', 36(12):2346–2353, 1964.</ref>  separated by an [[interval (music)|interval]] of a [[tritone]], or half octave, is heard as ascending by some people and as descending by others.<ref>Deutsch, D. "A musical paradox". ''Music Perception'', 3:275–280, 1986.</ref> 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]] in 1963 had argued that such tone pairs would be heard ambiguously as either ascending or descending. However, [[music psychology|psychology of music]] researcher [[Diana Deutsch]] 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{{music|sharp}} as ascending and the tone pair G–C{{music|sharp}} as descending. Yet another listener would hear the tone pair C–F{{music|sharp}} as descending and the tone pair G–C{{music|sharp}} 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&nbsp;Hz, accompanied by sinusoid at the higher octaves (880&nbsp;Hz, 1760&nbsp;Hz, etc.) and lower octaves (220&nbsp;Hz, 110&nbsp;Hz, etc.). The other tone might consist of a 311&nbsp;Hz sinusoid, again accompanied by higher and lower octaves (622&nbsp;Hz, 155.5&nbsp;Hz, etc.). The amplitudes of the sinusoids of both complexes are determined by the same fixed-amplitude envelope&mdash;for example, the envelope might be centered at 370&nbsp;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]], 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.<ref>Deutsch, D. "The tritone paradox: An influence of language on music perception". ''Music Perception'', 8:335–347, 1991.</ref> Also, Deutsch, Henthorn and Dolson found that native speakers of [[Vietnamese language|Vietnamese]], a [[Tone (linguistics)|tonal]] language, heard the tritone paradox differently from Californians who were native speakers of English.<ref>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.</ref>