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The tritone paradox is an auditory illusion created by Diana Deutsch (discoverer of a number of auditory illusions) in 1984. The pattern that produces this illusion consists of two successive Shepard tones ^[1] related by a half octave (otherwise known as a tritone). Each tone consists of a set of octave related sinusoids, the amplitudes of which 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 6 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 differently to different tones must involve the ability to hear absolute pitch, 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 heard the tritone paradox differently from Californians who were native speakers of English.

• Audio example (requires Java)
• Diana Deutsch's page on auditory illusions
• Sound example of the tritone paradox

• Deutsch, D. (1986). "An auditory paradox". Journal of the Acoustical Society of America 80: s93.  Abstract
• Deutsch, D. (1986). "A musical paradox". Music Perception 3: 275-280. 
• Deutsch, D. (1987). "The tritone paradox: effects of spectral variables". Percept Psychophys 41 (6): 563-75. PMID 3615152. 
• Deutsch, D., North, T., and Ray, L. (1990). "The tritone paradox: Correlate with the listener's vocal range for speech". Music Perception 7: 371-384. 
• Deutsch, D. (1991). "The tritone paradox: An influence of language on music perception". Music Perception 8: 335-347. 
• Deutsch, D. (1992). "Paradoxes of musical pitch". Scientific American 267: 88-95. PMID 1641627. 
• Deutsch, D. (1992). "Some new sound paradoxes and their implications". Auditory Processing of Complex Sounds; Philosophical Transactions of the Royal Society, Series B 336: 391-397. PMID 1354379. 
• Deutsch, D. (1998). "The tritone paradox: A link between music and speech". Current Directions in Psychological Science 6: 174-180. 
• Deutsch, D., Henthorn, T., and Dolson, M. (2004). "Speech Patterns Heard Early in Life Influence Later Perception of the Tritone Paradox". Music Perception 21: 357-372. 
• Deutsch, D. (2007). "Mothers and their offspring perceive the tritone paradox in closely similar ways.". Archives of Acoustics 32: 3-14. 

1. ^ R.N. Shepard. Circularity in judgments of relative pitch. Journal of the Acoustical Society of America, 36(12):2346–2353, 1964.