Farey Sequence

from Musica Razionale by Sebastiano De Gennaro

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The Farey sequence is a nineteenth-century discovery disputed between English geologist John Farey and French geometer Charles Haros. Regardless of its dubious attribution, this mathematical phenomenon is wonderful, and reminiscent of the famous paradox of Achilles and the Tortoise. The adjectives ‘illusory’ and ‘symmetrical’ are perfect to describe it.

The Farey Sequence is in fact a potentially infinite sequence of fractions that lie between 0 and 1. To be more precise, these fractions—linked by certain singular properties—are precisely ordered in the space that separates 0 and 1/2. What happens is that between 1/2 and 1 the sequence of fractions continues, arranging itself as perfectly mirroring the order of the fractions found between 0 and 1/2. So the apparently finite space that separates 0 and 1 is just an illusion: a sort of ‘cathedral’ with infinite foundations buried within it. A large structure made up of fractions, which thanks to its perfect symmetry recalls a phantasmagoric architecture.

Of the many graphic representations of this peculiar sequence, this piece focuses on the one with denominator 12 (F12), and interprets it as a musical score by performing it from left to right, then proceeding to do so from 0 to 1, after having assigned a specific sound event to each fraction.

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from Musica Razionale, released April 17, 2022

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19'40" London, UK

Music for Adventurous People. Founded in 2016 by Sebastiano De Gennaro, Enrico Gabrielli and Francesco Fusaro.

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