Zero all'infinita : for guitar
by Andrián Pertout (2009)
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'Zero all'infinita' or 'Zero to Infinity' was especially composed for Australian guitarist Gareth Koch and serves as an exploration of the musical properties of Pascal's Triangle - a "geometric arrangement of the binomial coefficients in a triangle" named after French mathematician, physicist, and philosopher Blaise Pascal (1623-1662). The work includes pitch material derived from the Hungarian Major Scale (C, D#, E, F#, G, A, Bb and C) harmonically juxtaposed against a series of voicings (or movable forms in relation to the guitar) of the '7 sharp 9' chord (C, E, G, Bb and D#). The first eleven rows of Pascal's Triangle (an arrangement of numbers where "every number is the sum of the two above it") are adopted in the structural plan, but reduced to the 'secret number' via the application of the sigma code - a "digital code with only nine values" generated via the summing up of the integers in order to generate single digits. "The sigma value of a number is the ultimate essence of a number," explains Balmond. "It is the hidden mark which lurks within the greater construction; in this sense it is the primary code, the imprint." Each row of the triangle (with sigma values) is utilized systematically - the first '1' of row 1 represented with a crotchet rest, followed by an inverted triangular pattern (right horizontal to left diagonal) delivering 1, 1, 2 of rows 2 and 3 followed by 1, 2, 3 and 2, 1, 3 of rows 3 and 4, and so on. The compositional strategy involves associating the first and second numbers of each 3-tuple with their respective subdivisions of the pulse (1 equal to 1 crotchet, 2 equal to 2 quavers, 3 equal to 3 quaver triplets, 4 equal to 4 semiquavers, 5 equal to 5 semiquaver quintuplets, 6 equal to 6 semiquaver sextuplets, 7 equal to 7 semiquaver septuplets, 8 equal to 8 demisemiquavers, and 9 equal to 9 semiquaver nuntuplets), while the concluding left diagonal action representing a metric modulation. In other words, the second 3-tuple set of the work (1, 2, 3) represented with the rhythmic values of 1 crotchet followed by 2 crotchets and 3 crotchets, while the third 3-tuple set of the work (2, 1, 3) with 2 quavers followed by 1 crotchet and 3 crotchets.
Instrumentation: Acoustic guitar.
Duration: 2 min.
Difficulty: Advanced — Professional.
Written for: Gareth Koch
The composer cites the following influences on this work:
Pascal’s Triangle, Hungarian Major Scale ‘7 sharp 9’ chord
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