Die kunst der zahlen : (The art of numbers), étude for chamber orchestra
by Andrián Pertout (2012)
Also known as: Art of numbers
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'Die Kunst der Zahlen' or 'The Art of Numbers' was commissioned by Cristóbal Urrutia and the Orquesta de Cámara de Valdivia (Valdivia, Chile) with funds provided by the Consejo Nacional de la Cultura y las Artes (Santiago, Chile). The work represents a Homenaje a Johann Sebastian Bach (1685-1750), and was additionally composed in Celebration of the 100th Anniversary of John Cage's Birth (1912-1992). The étude for chamber orchestra integrates musical materials from a book by Gina Allende Martínez published in 2011 entitled Puro Ritmo: Manual para la práctica integrada del ritmo en la clase de solfeo, or Pure Rhythm: Manual for the Integrated Practice of Rhythm in the Rudiments of Music Class, and explores not only John Cage's 'micro-macrocosmic' rhythmic structures, polymodality/polytonality, the Baroque fugue, De Bruijn cycles and probability theory, but also True Random Number Generators (TRNGs are nondeterministic and aperiodic, and based on atmospheric noise, as opposed to Pseudo-Random Number Generators, or PRNGs, which are deterministic and periodic, and based on algorithms that use mathematical formulae) to make decisions on rhythmic colour orderings on the basis of random integer generation.
The 'micro-macrocosmic' rhythmic structure (the "symmetrical arrangement of phrase lengths," and the "grouping of phrases into larger units") of John Cage's First Construction in Metal (1939) is systematically incorporated into the structural framework of 'Die Kunst der Zahlen'. In The Music of John Cage (1993) James Pritchett explains the essence of this rhythmic structure: "The piece (First Construction) consists of 16 units, each with a duration of 16 measures, for a total of 256 measures. The 16 measures of each and every unit of the piece are divided into five phrases with lengths of 4, 3, 2, 3, and 4 measures respectively. Because there are also 16 units in the piece, the same numbers are used to group the 16 units, resulting in five large sections of 64, 48, 32, and 64 measures. Thus the structure of First Construction is based on a single number series that controls both the lengths of phrases in terms of measures and the lengths of sections in terms of these phrase-group units." In 'Die Kunst der Zahlen', Cage's 4, 3, 2, 3, and 4 measure units are transformed into the durations 24, 18, 12, 18, and 24 crotchet-pulse units respectively, and similarly to Cage's First Construction the inclusion of a coda section at the end of the work provides a conclusive ending for the form.
Instrumentation: Flute, 2 oboes, bassoon, 2 horns, strings.
Duration: 12 min.
Difficulty: Advanced — Professional
Dedication note: Homenaje a Johann Sebastian Bach (1685-1750). Composed in Celebration of the 100th Anniversary of John Cage’s birth (1912-1992)
Commission note: Commissioned by the Orquesta de Cámara de Valdivia (Valdivia, Chile) with funds provided by the Consejo Nacional de la Cultura y las Artes (Santiago, Chile)
The composer notes the following styles, genres, influences, etc on this work:
Johann Sebastian Bach (1685-1750), John Cage (1912-1992), Gina Allende Martínez’s Puro Ritmo: Manual para la práctica integrada del ritmo en la clase de solfeo, ‘micro-macrocosmic’ rhythmic structures, polymodality/polytonality, Baroque fugue, De Bruijn cycles and probability theory, True Random Number Generators
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