Saturday, 31 January 2009


The tritone paradox is an auditory hallucination – a kind of aural version of the Necker Cube. A pair of Shepherd tones (sets of octave-related sinusoids, with amplitudes scaled by a fixed bell-shaped spectral envelope based on a log frequency scale) are played sequentially with an interval of a tritone. This interval is interpreted as ascending by some people, and descending by others.

Interestingly, different populations and cultural groups were shown to favour different interpretations. Native speakers of Vietnamese heard the paradox differently from native English-speaking Californians. This is explained by different populations tending to favour different points around the chromatic circle as central to the set of ‘higher’ tones.

As this hallucination is powered by a tritone, it has a relationship to the diabolos in musica (literally, ‘the devil in music’), the dissonant tritone interval which was interpreted as ‘evil’ by the Vatican, and was allegedly banned from church music following Guido of Arezzo’s foundation of the hexachordal system. Church musicians found to be exploiting the dark energy of the interval were officially excommunicated.


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