The elements : for violin
by Andrián Pertout (2009)
The Elements was commissioned by American violinist Piotr Szewczyk and is a dedication to the late French composer Olivier Messiaen (1908-1992). The title is in reference to Euclid's mathematical and geometric treatise Elements of circa 300 BC, and the work serves as an exploration of Messiaen's 'Modes of Limited Transposition' and 'Nonretrogradable Rhythms' within the structural framework of the first 36 prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, and 151). Every possible mode is subsequently generated from each of the seven 'Modes of Limited Transposition', producing a collection of twenty-two scales, which are combined to produce one-, two-, three-, and four-octave scales. 'Nonretrogradable Rhythms' are then constructed within the scope of each prime, with each numerical value of a prime allocated a duration of a semiquaver note. The structure of The Elements essentially features seven distinct sections individually dedicated to one of the 'Modes of Limited Transposition' and five unique 'Nonretrogradable Rhythms'; an ornamental rhythmic passage following the termination of each section acting as a type of coda. The ratio of 2:1:2 (equal to crotchet+semiquaver+crotchet in the prime number 5) is utilized throughout the rhythmic scheme to delineate a contrasting central region equal to one-fifth of each of the thirty-four quintal palindromes (the primes 2 and 3 unable to yield a palindrome in the context of this scheme).
Duration: 5 min.
Difficulty: Advanced — Professional
Dedication note: Hommage à Olivier Messiaen (1908-1992)
Commission note: Commissioned by American Violinist Piotr Szewczyk
The composer cites the following influences on this work:
Olivier Messiaen (1908-1992) ‘Modes of Limited Transposition’, ‘Nonretrogradable Rhythms’, Euclid’s mathematical and geometric treatise Elements
Winner in the ‘Advanced Level’ Category of the International Music Prizes for Excellence in Composition 2009 (Thessaloniki, Greece)
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