Congettura Collatz

from Musica Razionale by Sebastiano De Gennaro

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Let’s start from any natural number and apply a simple rule: if that number is even, it must then be divided by 2, while if it is odd, we multiply it by 3, and add 1. We then proceed with applying this rule to all the numbers we obtain, and soon discover that the last of the numerical sequences formed will always lead to the number 1, no matter its starting term. This is the so-called Collatz (still unsolved) Conjecture, also known as the ‘3n + 1 problem’. These types of numerical series are called convergent because they ‘converge’ on a known and finite term, in this case 1. The nine sections of this passage represent the numerical strings formed through the Collatz Conjecture, starting from the following numbers: 16, 12, 10, 8, 6, 5, 4, 3 and 2. In this piece the serialization is total, including the stereophonic arrangement of the sounds and the construction of the flute samples. The ten sections are all united by a last single flute breath, which corresponds to the common arrival point of these series: 1.

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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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